Finite Group Databasebeta

← C107×#17597 #41043561

Subgroups — C107×#17597 #41043561

Order 27392.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3519C211yesmaximal, characteristic
2C107×#2974C211yesmaximal, characteristic, complemented
3C107×#2318C211yesmaximal, characteristic, complemented
4C107×#1521C211yesmaximal, characteristic, complemented
5C107×#1519C211yesmaximal, characteristic, complemented
6C107×#1517C211yesmaximal, characteristic, complemented
7C107×#1516C211yesmaximal, characteristic, complemented
8C107×#1514C211yesmaximal, characteristic, complemented
9C107×#1513C211yesmaximal, characteristic, complemented
10C107×#1512C211yesmaximal, characteristic, complemented
11C107×#1510C211yesmaximal, characteristic, complemented
12C107×#1507C211yesmaximal, characteristic, complemented
13C107×#1504C211yesmaximal, characteristic, complemented
14C107×#1501C211yesmaximal, characteristic, complemented
15C2×#327×C107C211yesmaximal, characteristic, complemented
16#555×C107C411yescharacteristic, complemented
17#554×C107C411yescharacteristic, complemented
18#553×C107—21no—
19#553×C107C411yescharacteristic, complemented
20#553×C107C411yescharacteristic, complemented
21#550×C107C411yescharacteristic, complemented
22#546×C107—21no—
23#546×C107—21no—
24#546×C107C411yescharacteristic, complemented
25#546×C107C411yescharacteristic, complemented
26D42×C107—21no—
27D42×C107C411yescharacteristic, complemented
28#540×C107—21no—
29#538×C107—21no—
30#538×C107—21no—
31#532×C107C2211yescharacteristic
32#529×C107C2211yescharacteristic
33#525×C107C2211yescharacteristic
34#525×C107C2211yescharacteristic
35C2×#121×C107C2211yescharacteristic
36C2×#121×C107C2211yescharacteristic
37#518×C107—21no—
38C2×C4×D4×C107C2211yescharacteristic
39#436×C107—21no—
40#435×C107—21no—
41#435×C107—21no—
42C8×D4×C107—21no—
43#432×C107C2211yescharacteristic, complemented
44#431×C107C2211yescharacteristic, complemented
45#407×C107C2211yescharacteristic, complemented
46#407×C107C2211yescharacteristic, complemented
47C2×C22⋊C8×C107C2211yescharacteristic, complemented
48C2×C22⋊C8×C107C2211yescharacteristic, complemented
49#388×C107—21no—
50#387×C107—21no—
51#386×C107—21no—
52#385×C107—21no—
53#383×C107C2211yescharacteristic, complemented
54#382×C107C2211yescharacteristic, complemented
55#381×C107C2211yescharacteristic, complemented
56#380×C107C2211yescharacteristic, complemented
57C4×C22⋊C4×C107C2211yescharacteristic, complemented
58C2×#95×C107C2211yescharacteristic, complemented
59#328×C107C2211yescharacteristic, complemented
60#328×C107C2211yescharacteristic, complemented
61#328×C107C2211yescharacteristic, complemented
62#328×C107C2211yescharacteristic, complemented
63#327×C107C2211yescharacteristic
64#327×C107C2211yescharacteristic
65#327×C107C2211yescharacteristic
66#327×C107C2211yescharacteristic
67#327×C107C2211yescharacteristic, complemented
68#327×C107C2211yescharacteristic, complemented
69#327×C107C2211yescharacteristic, complemented
70#327×C107C2211yescharacteristic, complemented
71#327×C107C2211yescharacteristic, complemented
72#327×C107C2211yescharacteristic, complemented
73#327×C107C2211yescharacteristic, complemented
74#327×C107C2211yescharacteristic, complemented
75C2×#41×C107—21no—
76C2×#41×C107C2×C411yescharacteristic
77C2×#41×C107C2×C411yescharacteristic, complemented
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107—21no—
81C22×D4×C107C2×C411yescharacteristic
82C22×D4×C107C2×C411yescharacteristic, complemented
83C22×D4×C107D411yescharacteristic
84C23×C4×C107—21no—
85C23×C4×C107C2311yescharacteristic
86C23×C4×C107C2311yescharacteristic
87C2×M16×C107—21no—
88C2×M16×C107—21no—
89C22×C8×C107—21no—
90C22×C8×C107—21no—
91C4⋊Q8×C107C2×C411yescharacteristic, complemented
92#127×C107—21no—
93#127×C107C2×C411yescharacteristic, complemented
94#126×C107—21no—
95#126×C107—21no—
96#126×C107—21no—
97#125×C107—21no—
98#125×C107C2×C411yescharacteristic, complemented
99#124×C107—21no—
100#124×C107—21no—
101#124×C107—21no—
102#124×C107C2×C411yescharacteristic, complemented
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108#123×C107—21no—
109#123×C107—21no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—21no—
112C22⋊Q8×C107C2×C411yescharacteristic
113C22⋊Q8×C107C2×C411yescharacteristic, complemented
114C22⋊Q8×C107C2311yescharacteristic
115#121×C107—21no—
116#121×C107—21no—
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107C2×C411yescharacteristic
129#121×C107C2×C411yescharacteristic
130#121×C107C2×C411yescharacteristic
131#121×C107C2×C411yescharacteristic, complemented
132#121×C107C2×C411yescharacteristic, complemented
133#121×C107C2×C411yescharacteristic, complemented
134#121×C107C2311yescharacteristic
135#121×C107C2311yescharacteristic
136#121×C107C2311yescharacteristic
137#120×C107—21no—
138#120×C107—21no—
139#120×C107—21no—
140#120×C107—21no—
141#120×C107—21no—
142#120×C107—21no—
143C4×Q8×C107C2×C411yescharacteristic, complemented
144C4×D4×C107—21no—
145C4×D4×C107—21no—
146C4×D4×C107—21no—
147C4×D4×C107—21no—
148C4×D4×C107—21no—
149C4×D4×C107—21no—
150C4×D4×C107—21no—
151C4×D4×C107—21no—
152C4×D4×C107—21no—
153C4×D4×C107—21no—
154C4×D4×C107C2×C411yescharacteristic
155C4×D4×C107C2×C411yescharacteristic
156C4×D4×C107C2×C411yescharacteristic
157C4×D4×C107C2×C411yescharacteristic
158C4×D4×C107C2×C411yescharacteristic, complemented
159C4×D4×C107C2×C411yescharacteristic, complemented
160C4×D4×C107C2×C411yescharacteristic, complemented
161C4×D4×C107D411yescharacteristic
162C4×D4×C107D411yescharacteristic
163C4×D4×C107D411yescharacteristic
164C4×D4×C107D411yescharacteristic
165#117×C107—21no—
166#117×C107—21no—
167#117×C107C2×C411yescharacteristic
168#117×C107C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C107—21no—
170C2×C4⋊C4×C107—21no—
171C2×C4⋊C4×C107C2×C411yescharacteristic
172C2×C4⋊C4×C107C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C107D411yescharacteristic
174C2×C22⋊C4×C107—21no—
175C2×C22⋊C4×C107—21no—
176C2×C22⋊C4×C107—21no—
177C2×C22⋊C4×C107—21no—
178C2×C22⋊C4×C107—21no—
179C2×C22⋊C4×C107—21no—
180C2×C22⋊C4×C107—21no—
181C2×C22⋊C4×C107D411yescharacteristic
182C2×C22⋊C4×C107D411yescharacteristic
183C2×C42×C107—21no—
184C2×C42×C107C2311yescharacteristic
185C4⋊C8×C107—21no—
186C4⋊C8×C107—21no—
187C22⋊C8×C107—21no—
188C22⋊C8×C107—21no—
189C22⋊C8×C107—21no—
190C22⋊C8×C107—21no—
191C22⋊C8×C107C2311yescharacteristic
192C22⋊C8×C107C2311yescharacteristic
193C22⋊C8×C107C2311yescharacteristic
194C22⋊C8×C107C2311yescharacteristic
195#97×C107—21no—
196C4×C8×C107—21no—
197#95×C107—21no—
198#95×C107—21no—
199#95×C107—21no—
200#95×C107—21no—
201#95×C107—21no—
202#95×C107C2311yescharacteristic
203#95×C107C2311yescharacteristic
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209C24×C107C2×D411yescharacteristic
210#41×C107—81no—
211#41×C107—81no—
212#41×C107—81no—
213#41×C107—81no—
214C2×Q8×C107—21no—
215C2×Q8×C107C22×C411yescharacteristic
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—21no—
224C2×D4×C107—21no—
225C2×D4×C107—21no—
226C2×D4×C107—21no—
227C2×D4×C107—21no—
228C2×D4×C107—21no—
229C2×D4×C107—21no—
230C2×D4×C107—21no—
231C2×D4×C107—42no—
232C2×D4×C107—44no—
233C2×D4×C107—81no—
234C2×D4×C107—81no—
235C2×D4×C107—81no—
236C2×D4×C107—81no—
237C2×D4×C107—81no—
238C2×D4×C107—81no—
239C2×D4×C107C22⋊C411yescharacteristic
240C2×D4×C107C22⋊C411yescharacteristic
241C2×D4×C107C22⋊C411yescharacteristic
242C2×D4×C107C22⋊C411yescharacteristic
243C2×D4×C107C22×C411yescharacteristic
244C2×D4×C107C22×C411yescharacteristic
245C2×D4×C107C22×C411yescharacteristic
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—21no—
256C22×C4×C107—21no—
257C22×C4×C107—42no—
258C22×C4×C107—81no—
259C22×C4×C107—81no—
260C22×C4×C107—81no—
261C22×C4×C107—81no—
262C22×C4×C107C22×C411yescharacteristic
263C22×C4×C107C22×C411yescharacteristic
264C22×C4×C107C22×C411yescharacteristic
265C22×C4×C107C22×C411yescharacteristic
266C22×C4×C107C2×D411yescharacteristic
267C22×C4×C107C2×D411yescharacteristic
268C22×C4×C107C2×D411yescharacteristic
269C22×C4×C107C2×D411yescharacteristic
270C22×C4×C107C2×D411yescharacteristic
271C22×C4×C107C2×D411yescharacteristic
272C22×C4×C107C2×D411yescharacteristic
273C22×C4×C107C2×D411yescharacteristic
274C22×C4×C107C2411yescharacteristic
275M16×C107—81no—
276M16×C107—81no—
277C2×C8×C107—21no—
278C2×C8×C107—21no—
279C2×C8×C107—21no—
280C2×C8×C107—21no—
281C2×C8×C107—81no—
282C2×C8×C107—81no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—21no—
292C4⋊C4×C107—81no—
293C4⋊C4×C107—81no—
294C4⋊C4×C107C22⋊C411yescharacteristic
295C4⋊C4×C107C22⋊C411yescharacteristic
296C4⋊C4×C107C22⋊C411yescharacteristic
297C4⋊C4×C107C22⋊C411yescharacteristic
298C4⋊C4×C107C22×C411yescharacteristic
299C4⋊C4×C107C22×C411yescharacteristic
300C4⋊C4×C107C22×C411yescharacteristic
301C4⋊C4×C107C22×C411yescharacteristic
302C22⋊C4×C107—21no—
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—21no—
317C22⋊C4×C107—21no—
318C22⋊C4×C107—21no—
319C22⋊C4×C107—21no—
320C22⋊C4×C107—21no—
321C22⋊C4×C107—42no—
322C22⋊C4×C107—81no—
323C22⋊C4×C107—81no—
324C22⋊C4×C107C22⋊C411yescharacteristic
325C22⋊C4×C107C22⋊C411yescharacteristic
326C22⋊C4×C107C22⋊C411yescharacteristic
327C22⋊C4×C107C22⋊C411yescharacteristic
328C22⋊C4×C107C22⋊C411yescharacteristic
329C22⋊C4×C107C22⋊C411yescharacteristic
330C22⋊C4×C107C22⋊C411yescharacteristic
331C22⋊C4×C107C22⋊C411yescharacteristic
332C42×C107—21no—
333C42×C107—21no—
334C42×C107—21no—
335C42×C107—81no—
336C42×C107C22×C411yescharacteristic
337C42×C107C22×C411yescharacteristic
338C42×C107C2×D411yescharacteristic
339C42×C107C2×D411yescharacteristic
340C23×C107—21no—
341C23×C107—21no—
342C23×C107—22no—
343C23×C107—21no—
344C23×C107—21no—
345C23×C107—21no—
346C23×C107—21no—
347C23×C107—21no—
348C23×C107—41no—
349C23×C107—41no—
350C23×C107—41no—
351C23×C107—42no—
352C23×C107—42no—
353C23×C107—81no—
354C23×C107—81no—
355C23×C107—81no—
356C23×C107—81no—
357C23×C107C2×C22⋊C411yescharacteristic
358C23×C107C2×C22⋊C411yescharacteristic
359C23×C107C2×C22⋊C411yescharacteristic
360C23×C107C2×C22⋊C411yescharacteristic
361C23×C107C22×D411yescharacteristic
362Q8×C107—41no—
363Q8×C107—81no—
364D4×C107—22no—
365D4×C107—22no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—42no—
372D4×C107—42no—
373D4×C107—41no—
374D4×C107—41no—
375D4×C107—41no—
376D4×C107—41no—
377D4×C107—41no—
378D4×C107—41no—
379D4×C107—42no—
380D4×C107—81no—
381D4×C107—81no—
382D4×C107—81no—
383D4×C107—81no—
384D4×C107—81no—
385D4×C107—81no—
386D4×C107—81no—
387D4×C107—81no—
388D4×C107—81no—
389C2×C4×C107—21no—
390C2×C4×C107—21no—
391C2×C4×C107—21no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—21no—
395C2×C4×C107—21no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—42no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—41no—
416C2×C4×C107—41no—
417C2×C4×C107—41no—
418C2×C4×C107—41no—
419C2×C4×C107—41no—
420C2×C4×C107—41no—
421C2×C4×C107—81no—
422C2×C4×C107—81no—
423C2×C4×C107—81no—
424C2×C4×C107—81no—
425C2×C4×C107—81no—
426C2×C4×C107—81no—
427C2×C4×C107—84no—
428C2×C4×C107C2×C22⋊C411yescharacteristic
429C2×C4×C107C2×C22⋊C411yescharacteristic
430C2×C4×C107C2×C22⋊C411yescharacteristic
431C2×C4×C107C2×C22⋊C411yescharacteristic
432C2×C4×C107C2×C22⋊C411yescharacteristic
433C2×C4×C107C2×C22⋊C411yescharacteristic
434C2×C4×C107C2×C22⋊C411yescharacteristic
435C2×C4×C107C2×C22⋊C411yescharacteristic
436C2×C4×C107C23×C411yescharacteristic
437C2×C4×C107C22×D411yescharacteristic
438C8×C107—41no—
439C8×C107—41no—
440C8×C107—41no—
441C8×C107—41no—
442C22×C107—21no—
443C22×C107—21no—
444C22×C107—21no—
445C22×C107—21no—
446C22×C107—21no—
447C22×C107—21no—
448C22×C107—21no—
449C22×C107—21no—
450C22×C107—21no—
451C22×C107—21no—
452C22×C107—21no—
453C22×C107—21no—
454C22×C107—21no—
455C22×C107—42no—
456C22×C107—42no—
457C22×C107—41no—
458C22×C107—41no—
459C22×C107—41no—
460C22×C107—41no—
461C22×C107—41no—
462C22×C107—41no—
463C22×C107—41no—
464C22×C107—41no—
465C22×C107—41no—
466C22×C107—81no—
467C22×C107—81no—
468C22×C107—162no—
469C22×C107—162no—
470C22×C107#42112yes—
471C22×C107C22×C22⋊C411yescharacteristic
472C22×C107#57611yescharacteristic
473C22×C107#57711yescharacteristic
474C4×C107—21no—
475C4×C107—21no—
476C4×C107—21no—
477C4×C107—21no—
478C4×C107—21no—
479C4×C107—21no—
480C4×C107—21no—
481C4×C107—21no—
482C4×C107—21no—
483C4×C107—21no—
484C4×C107—41no—
485C4×C107—41no—
486C4×C107—41no—
487C4×C107—41no—
488C4×C107—41no—
489C4×C107—81no—
490C4×C107—81no—
491C4×C107—81no—
492C4×C107—81no—
493#17597C10711yesmaximal, characteristic, direct product factor, Sylow
494C2×C107—21no—
495C2×C107—21no—
496C2×C107—22no—
497C2×C107—41no—
498C2×C107—41no—
499C2×C107—41no—
500C2×C107—81no—
501C2×C107—81no—
502C2×C107—81no—
503C2×C107#288311yescharacteristic
504C2×C107#289711yescharacteristic
505C2×C107C2×#42111yescharacteristic
506#3519C2×C10711yescharacteristic
507#2974C2×C10711yescharacteristic, complemented
508#2318C2×C10711yescharacteristic, complemented
509#1521C2×C10711yescharacteristic, complemented
510#1519C2×C10711yescharacteristic, complemented
511#1517C2×C10711yescharacteristic, complemented
512#1516C2×C10711yescharacteristic, complemented
513#1514C2×C10711yescharacteristic, complemented
514#1513C2×C10711yescharacteristic, complemented
515#1512C2×C10711yescharacteristic, complemented
516#1510C2×C10711yescharacteristic, complemented
517#1507C2×C10711yescharacteristic, complemented
518#1504C2×C10711yescharacteristic, complemented
519#1501C2×C10711yescharacteristic, complemented
520C2×#327C2×C10711yescharacteristic, complemented
521C107#1759711yescharacteristic, direct product factor, Sylow
522#555C4×C10711yescharacteristic, complemented
523#554C4×C10711yescharacteristic, complemented
524#553—21no—
525#553C4×C10711yescharacteristic, complemented
526#553C4×C10711yescharacteristic, complemented
527#550C4×C10711yescharacteristic, complemented
528#546—21no—
529#546—21no—
530#546C4×C10711yescharacteristic, complemented
531#546C4×C10711yescharacteristic, complemented
532D42—21no—
533D42C4×C10711yescharacteristic, complemented
534#540—21no—
535#538—21no—
536#538—21no—
537#532C22×C10711yescharacteristic
538#529C22×C10711yescharacteristic
539#525C22×C10711yescharacteristic
540#525C22×C10711yescharacteristic
541C2×#121C22×C10711yescharacteristic
542C2×#121C22×C10711yescharacteristic
543#518—21no—
544C2×C4×D4C22×C10711yescharacteristic
545#436—21no—
546#435—21no—
547#435—21no—
548C8×D4—21no—
549#432C22×C10711yescharacteristic, complemented
550#431C22×C10711yescharacteristic, complemented
551#407C22×C10711yescharacteristic, complemented
552#407C22×C10711yescharacteristic, complemented
553C2×C22⋊C8C22×C10711yescharacteristic, complemented
554C2×C22⋊C8C22×C10711yescharacteristic, complemented
555#388—21no—
556#387—21no—
557#386—21no—
558#385—21no—
559#383C22×C10711yescharacteristic, complemented
560#382C22×C10711yescharacteristic, complemented
561#381C22×C10711yescharacteristic, complemented
562#380C22×C10711yescharacteristic, complemented
563C4×C22⋊C4C22×C10711yescharacteristic, complemented
564C2×#95C22×C10711yescharacteristic, complemented
565#328C22×C10711yescharacteristic, complemented
566#328C22×C10711yescharacteristic, complemented
567#328C22×C10711yescharacteristic, complemented
568#328C22×C10711yescharacteristic, complemented
569#327C22×C10711yescharacteristic
570#327C22×C10711yescharacteristic
571#327C22×C10711yescharacteristic
572#327C22×C10711yescharacteristic
573#327C22×C10711yescharacteristic, complemented
574#327C22×C10711yescharacteristic, complemented
575#327C22×C10711yescharacteristic, complemented
576#327C22×C10711yescharacteristic, complemented
577#327C22×C10711yescharacteristic, complemented
578#327C22×C10711yescharacteristic, complemented
579#327C22×C10711yescharacteristic, complemented
580#327C22×C10711yescharacteristic, complemented
581C2×#41—21no—
582C2×#41C2×C4×C10711yescharacteristic
583C2×#41C2×C4×C10711yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C10711yescharacteristic
588C22×D4C2×C4×C10711yescharacteristic, complemented
589C22×D4D4×C10711yescharacteristic
590C23×C4—21no—
591C23×C4C23×C10711yescharacteristic
592C23×C4C23×C10711yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C10711yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C10711yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C10711yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C10711yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×C4×C10711yescharacteristic
619C22⋊Q8C2×C4×C10711yescharacteristic, complemented
620C22⋊Q8C23×C10711yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×C4×C10711yescharacteristic
635#121C2×C4×C10711yescharacteristic
636#121C2×C4×C10711yescharacteristic
637#121C2×C4×C10711yescharacteristic, complemented
638#121C2×C4×C10711yescharacteristic, complemented
639#121C2×C4×C10711yescharacteristic, complemented
640#121C23×C10711yescharacteristic
641#121C23×C10711yescharacteristic
642#121C23×C10711yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C10711yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×C4×C10711yescharacteristic
661C4×D4C2×C4×C10711yescharacteristic
662C4×D4C2×C4×C10711yescharacteristic
663C4×D4C2×C4×C10711yescharacteristic
664C4×D4C2×C4×C10711yescharacteristic, complemented
665C4×D4C2×C4×C10711yescharacteristic, complemented
666C4×D4C2×C4×C10711yescharacteristic, complemented
667C4×D4D4×C10711yescharacteristic
668C4×D4D4×C10711yescharacteristic
669C4×D4D4×C10711yescharacteristic
670C4×D4D4×C10711yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C10711yescharacteristic
674#117C2×C4×C10711yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C10711yescharacteristic
678C2×C4⋊C4C2×C4×C10711yescharacteristic, complemented
679C2×C4⋊C4D4×C10711yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4D4×C10711yescharacteristic
688C2×C22⋊C4D4×C10711yescharacteristic
689C2×C42—21no—
690C2×C42C23×C10711yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C10711yescharacteristic
698C22⋊C8C23×C10711yescharacteristic
699C22⋊C8C23×C10711yescharacteristic
700C22⋊C8C23×C10711yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C10711yescharacteristic
709#95C23×C10711yescharacteristic
710#95C23×C10711yescharacteristic
711#95C23×C10711yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C10711yescharacteristic
715C24C2×D4×C10711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C10711yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C10711yescharacteristic
746C2×D4C22⋊C4×C10711yescharacteristic
747C2×D4C22⋊C4×C10711yescharacteristic
748C2×D4C22⋊C4×C10711yescharacteristic
749C2×D4C22×C4×C10711yescharacteristic
750C2×D4C22×C4×C10711yescharacteristic
751C2×D4C22×C4×C10711yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C10711yescharacteristic
769C22×C4C22×C4×C10711yescharacteristic
770C22×C4C22×C4×C10711yescharacteristic
771C22×C4C22×C4×C10711yescharacteristic
772C22×C4C2×D4×C10711yescharacteristic
773C22×C4C2×D4×C10711yescharacteristic
774C22×C4C2×D4×C10711yescharacteristic
775C22×C4C2×D4×C10711yescharacteristic
776C22×C4C2×D4×C10711yescharacteristic
777C22×C4C2×D4×C10711yescharacteristic
778C22×C4C2×D4×C10711yescharacteristic
779C22×C4C2×D4×C10711yescharacteristic
780C22×C4C24×C10711yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C10711yescharacteristic
801C4⋊C4C22⋊C4×C10711yescharacteristic
802C4⋊C4C22⋊C4×C10711yescharacteristic
803C4⋊C4C22⋊C4×C10711yescharacteristic
804C4⋊C4C22×C4×C10711yescharacteristic
805C4⋊C4C22×C4×C10711yescharacteristic
806C4⋊C4C22×C4×C10711yescharacteristic
807C4⋊C4C22×C4×C10711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C10711yescharacteristic
831C22⋊C4C22⋊C4×C10711yescharacteristic
832C22⋊C4C22⋊C4×C10711yescharacteristic
833C22⋊C4C22⋊C4×C10711yescharacteristic
834C22⋊C4C22⋊C4×C10711yescharacteristic
835C22⋊C4C22⋊C4×C10711yescharacteristic
836C22⋊C4C22⋊C4×C10711yescharacteristic
837C22⋊C4C22⋊C4×C10711yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C10711yescharacteristic
843C42C22×C4×C10711yescharacteristic
844C42C2×D4×C10711yescharacteristic
845C42C2×D4×C10711yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C10711yescharacteristic
864C23C2×C22⋊C4×C10711yescharacteristic
865C23C2×C22⋊C4×C10711yescharacteristic
866C23C2×C22⋊C4×C10711yescharacteristic
867C23C22×D4×C10711yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C10711yescharacteristic
935C2×C4C2×C22⋊C4×C10711yescharacteristic
936C2×C4C2×C22⋊C4×C10711yescharacteristic
937C2×C4C2×C22⋊C4×C10711yescharacteristic
938C2×C4C2×C22⋊C4×C10711yescharacteristic
939C2×C4C2×C22⋊C4×C10711yescharacteristic
940C2×C4C2×C22⋊C4×C10711yescharacteristic
941C2×C4C2×C22⋊C4×C10711yescharacteristic
942C2×C4C23×C4×C10711yescharacteristic
943C2×C4C22×D4×C10711yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22#421×C10712yes—
977C22C22×C22⋊C4×C10711yescharacteristic
978C22#576×C10711yescharacteristic
979C22#577×C10711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C107×#288311yescharacteristic
1009C2C107×#289711yescharacteristic
1010C2C2×#421×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C22×C22⋊C4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC107×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C107×#2974C2semidirect
3. C107×#2318C2semidirect
4. C107×#1521C2semidirect
5. C107×#1519C2semidirect
6. C107×#1517C2semidirect
7. C107×#1516C2semidirect
8. C107×#1514C2semidirect
9. C107×#1513C2semidirect
10. C107×#1512C2semidirect
11. C107×#1510C2semidirect
12. C107×#1507C2semidirect
13. C107×#1504C2semidirect
14. C107×#1501C2semidirect
15. C2×#327×C107C2semidirect
16. #555×C107C4semidirect
17. #554×C107C4semidirect
19. #553×C107C4semidirect
20. #553×C107C4semidirect
21. #550×C107C4semidirect
24. #546×C107C4semidirect
25. #546×C107C4semidirect
27. D42×C107C4semidirect
43. #432×C107C22semidirect
44. #431×C107C22semidirect
45. #407×C107C22semidirect
46. #407×C107C22semidirect
47. C2×C22⋊C8×C107C22semidirect
48. C2×C22⋊C8×C107C22semidirect
53. #383×C107C22semidirect
54. #382×C107C22semidirect
55. #381×C107C22semidirect
56. #380×C107C22semidirect
57. C4×C22⋊C4×C107C22semidirect
58. C2×#95×C107C22semidirect
59. #328×C107C22semidirect
60. #328×C107C22semidirect
61. #328×C107C22semidirect
62. #328×C107C22semidirect
67. #327×C107C22semidirect
68. #327×C107C22semidirect
69. #327×C107C22semidirect
70. #327×C107C22semidirect
71. #327×C107C22semidirect
72. #327×C107C22semidirect
73. #327×C107C22semidirect
74. #327×C107C22semidirect
77. C2×#41×C107C2×C4semidirect
82. C22×D4×C107C2×C4semidirect
91. C4⋊Q8×C107C2×C4semidirect
93. #127×C107C2×C4semidirect
98. #125×C107C2×C4semidirect
102. #124×C107C2×C4semidirect
113. C22⋊Q8×C107C2×C4semidirect
131. #121×C107C2×C4semidirect
132. #121×C107C2×C4semidirect
133. #121×C107C2×C4semidirect
143. C4×Q8×C107C2×C4semidirect
158. C4×D4×C107C2×C4semidirect
159. C4×D4×C107C2×C4semidirect
160. C4×D4×C107C2×C4semidirect
168. #117×C107C2×C4semidirect
172. C2×C4⋊C4×C107C2×C4semidirect
493. #17597C107direct (N × H)
507. #2974C2×C107semidirect
508. #2318C2×C107semidirect
509. #1521C2×C107semidirect
510. #1519C2×C107semidirect
511. #1517C2×C107semidirect
512. #1516C2×C107semidirect
513. #1514C2×C107semidirect
514. #1513C2×C107semidirect
515. #1512C2×C107semidirect
516. #1510C2×C107semidirect
517. #1507C2×C107semidirect
518. #1504C2×C107semidirect
519. #1501C2×C107semidirect
520. C2×#327C2×C107semidirect
521. C107#17597direct (N × H)
522. #555C4×C107semidirect
523. #554C4×C107semidirect
525. #553C4×C107semidirect
526. #553C4×C107semidirect
527. #550C4×C107semidirect
530. #546C4×C107semidirect
531. #546C4×C107semidirect
533. D42C4×C107semidirect
549. #432C22×C107semidirect
550. #431C22×C107semidirect
551. #407C22×C107semidirect
552. #407C22×C107semidirect
553. C2×C22⋊C8C22×C107semidirect
554. C2×C22⋊C8C22×C107semidirect
559. #383C22×C107semidirect
560. #382C22×C107semidirect
561. #381C22×C107semidirect
562. #380C22×C107semidirect
563. C4×C22⋊C4C22×C107semidirect
564. C2×#95C22×C107semidirect
565. #328C22×C107semidirect
566. #328C22×C107semidirect
567. #328C22×C107semidirect
568. #328C22×C107semidirect
573. #327C22×C107semidirect
574. #327C22×C107semidirect
575. #327C22×C107semidirect
576. #327C22×C107semidirect
577. #327C22×C107semidirect
578. #327C22×C107semidirect
579. #327C22×C107semidirect
580. #327C22×C107semidirect
583. C2×#41C2×C4×C107semidirect
588. C22×D4C2×C4×C107semidirect
597. C4⋊Q8C2×C4×C107semidirect
599. #127C2×C4×C107semidirect
604. #125C2×C4×C107semidirect
608. #124C2×C4×C107semidirect
619. C22⋊Q8C2×C4×C107semidirect
637. #121C2×C4×C107semidirect
638. #121C2×C4×C107semidirect
639. #121C2×C4×C107semidirect
649. C4×Q8C2×C4×C107semidirect
664. C4×D4C2×C4×C107semidirect
665. C4×D4C2×C4×C107semidirect
666. C4×D4C2×C4×C107semidirect
674. #117C2×C4×C107semidirect
678. C2×C4⋊C4C2×C4×C107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C107×#35192
C107×#29742
C107×#23182
C107×#15212
C107×#15192
C107×#15172
C107×#15162
C107×#15142
C107×#15132
C107×#15122
C107×#15102
C107×#15072
C107×#15042
C107×#15012
C2×#327×C1072
#17597107