Finite Group Databasebeta

← C103×#17597 #39922872

Subgroups — C103×#17597 #39922872

Order 26368.

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
1C103×#3519C211yesmaximal, characteristic
2C103×#2974C211yesmaximal, characteristic, complemented
3C103×#2318C211yesmaximal, characteristic, complemented
4C103×#1521C211yesmaximal, characteristic, complemented
5C103×#1519C211yesmaximal, characteristic, complemented
6C103×#1517C211yesmaximal, characteristic, complemented
7C103×#1516C211yesmaximal, characteristic, complemented
8C103×#1514C211yesmaximal, characteristic, complemented
9C103×#1513C211yesmaximal, characteristic, complemented
10C103×#1512C211yesmaximal, characteristic, complemented
11C103×#1510C211yesmaximal, characteristic, complemented
12C103×#1507C211yesmaximal, characteristic, complemented
13C103×#1504C211yesmaximal, characteristic, complemented
14C103×#1501C211yesmaximal, characteristic, complemented
15C2×#327×C103C211yesmaximal, characteristic, complemented
16#555×C103C411yescharacteristic, complemented
17#554×C103C411yescharacteristic, complemented
18#553×C103—21no—
19#553×C103C411yescharacteristic, complemented
20#553×C103C411yescharacteristic, complemented
21#550×C103C411yescharacteristic, complemented
22#546×C103—21no—
23#546×C103—21no—
24#546×C103C411yescharacteristic, complemented
25#546×C103C411yescharacteristic, complemented
26D42×C103—21no—
27D42×C103C411yescharacteristic, complemented
28#540×C103—21no—
29#538×C103—21no—
30#538×C103—21no—
31#532×C103C2211yescharacteristic
32#529×C103C2211yescharacteristic
33#525×C103C2211yescharacteristic
34#525×C103C2211yescharacteristic
35C2×#121×C103C2211yescharacteristic
36C2×#121×C103C2211yescharacteristic
37#518×C103—21no—
38C2×C4×D4×C103C2211yescharacteristic
39#436×C103—21no—
40#435×C103—21no—
41#435×C103—21no—
42C8×D4×C103—21no—
43#432×C103C2211yescharacteristic, complemented
44#431×C103C2211yescharacteristic, complemented
45#407×C103C2211yescharacteristic, complemented
46#407×C103C2211yescharacteristic, complemented
47C2×C22⋊C8×C103C2211yescharacteristic, complemented
48C2×C22⋊C8×C103C2211yescharacteristic, complemented
49#388×C103—21no—
50#387×C103—21no—
51#386×C103—21no—
52#385×C103—21no—
53#383×C103C2211yescharacteristic, complemented
54#382×C103C2211yescharacteristic, complemented
55#381×C103C2211yescharacteristic, complemented
56#380×C103C2211yescharacteristic, complemented
57C4×C22⋊C4×C103C2211yescharacteristic, complemented
58C2×#95×C103C2211yescharacteristic, complemented
59#328×C103C2211yescharacteristic, complemented
60#328×C103C2211yescharacteristic, complemented
61#328×C103C2211yescharacteristic, complemented
62#328×C103C2211yescharacteristic, complemented
63#327×C103C2211yescharacteristic
64#327×C103C2211yescharacteristic
65#327×C103C2211yescharacteristic
66#327×C103C2211yescharacteristic
67#327×C103C2211yescharacteristic, complemented
68#327×C103C2211yescharacteristic, complemented
69#327×C103C2211yescharacteristic, complemented
70#327×C103C2211yescharacteristic, complemented
71#327×C103C2211yescharacteristic, complemented
72#327×C103C2211yescharacteristic, complemented
73#327×C103C2211yescharacteristic, complemented
74#327×C103C2211yescharacteristic, complemented
75C2×#41×C103—21no—
76C2×#41×C103C2×C411yescharacteristic
77C2×#41×C103C2×C411yescharacteristic, complemented
78C22×D4×C103—21no—
79C22×D4×C103—21no—
80C22×D4×C103—21no—
81C22×D4×C103C2×C411yescharacteristic
82C22×D4×C103C2×C411yescharacteristic, complemented
83C22×D4×C103D411yescharacteristic
84C23×C4×C103—21no—
85C23×C4×C103C2311yescharacteristic
86C23×C4×C103C2311yescharacteristic
87C2×M16×C103—21no—
88C2×M16×C103—21no—
89C22×C8×C103—21no—
90C22×C8×C103—21no—
91C4⋊Q8×C103C2×C411yescharacteristic, complemented
92#127×C103—21no—
93#127×C103C2×C411yescharacteristic, complemented
94#126×C103—21no—
95#126×C103—21no—
96#126×C103—21no—
97#125×C103—21no—
98#125×C103C2×C411yescharacteristic, complemented
99#124×C103—21no—
100#124×C103—21no—
101#124×C103—21no—
102#124×C103C2×C411yescharacteristic, complemented
103#123×C103—21no—
104#123×C103—21no—
105#123×C103—21no—
106#123×C103—21no—
107#123×C103—21no—
108#123×C103—21no—
109#123×C103—21no—
110C22⋊Q8×C103—21no—
111C22⋊Q8×C103—21no—
112C22⋊Q8×C103C2×C411yescharacteristic
113C22⋊Q8×C103C2×C411yescharacteristic, complemented
114C22⋊Q8×C103C2311yescharacteristic
115#121×C103—21no—
116#121×C103—21no—
117#121×C103—21no—
118#121×C103—21no—
119#121×C103—21no—
120#121×C103—21no—
121#121×C103—21no—
122#121×C103—21no—
123#121×C103—21no—
124#121×C103—21no—
125#121×C103—21no—
126#121×C103—21no—
127#121×C103—21no—
128#121×C103C2×C411yescharacteristic
129#121×C103C2×C411yescharacteristic
130#121×C103C2×C411yescharacteristic
131#121×C103C2×C411yescharacteristic, complemented
132#121×C103C2×C411yescharacteristic, complemented
133#121×C103C2×C411yescharacteristic, complemented
134#121×C103C2311yescharacteristic
135#121×C103C2311yescharacteristic
136#121×C103C2311yescharacteristic
137#120×C103—21no—
138#120×C103—21no—
139#120×C103—21no—
140#120×C103—21no—
141#120×C103—21no—
142#120×C103—21no—
143C4×Q8×C103C2×C411yescharacteristic, complemented
144C4×D4×C103—21no—
145C4×D4×C103—21no—
146C4×D4×C103—21no—
147C4×D4×C103—21no—
148C4×D4×C103—21no—
149C4×D4×C103—21no—
150C4×D4×C103—21no—
151C4×D4×C103—21no—
152C4×D4×C103—21no—
153C4×D4×C103—21no—
154C4×D4×C103C2×C411yescharacteristic
155C4×D4×C103C2×C411yescharacteristic
156C4×D4×C103C2×C411yescharacteristic
157C4×D4×C103C2×C411yescharacteristic
158C4×D4×C103C2×C411yescharacteristic, complemented
159C4×D4×C103C2×C411yescharacteristic, complemented
160C4×D4×C103C2×C411yescharacteristic, complemented
161C4×D4×C103D411yescharacteristic
162C4×D4×C103D411yescharacteristic
163C4×D4×C103D411yescharacteristic
164C4×D4×C103D411yescharacteristic
165#117×C103—21no—
166#117×C103—21no—
167#117×C103C2×C411yescharacteristic
168#117×C103C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C103—21no—
170C2×C4⋊C4×C103—21no—
171C2×C4⋊C4×C103C2×C411yescharacteristic
172C2×C4⋊C4×C103C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C103D411yescharacteristic
174C2×C22⋊C4×C103—21no—
175C2×C22⋊C4×C103—21no—
176C2×C22⋊C4×C103—21no—
177C2×C22⋊C4×C103—21no—
178C2×C22⋊C4×C103—21no—
179C2×C22⋊C4×C103—21no—
180C2×C22⋊C4×C103—21no—
181C2×C22⋊C4×C103D411yescharacteristic
182C2×C22⋊C4×C103D411yescharacteristic
183C2×C42×C103—21no—
184C2×C42×C103C2311yescharacteristic
185C4⋊C8×C103—21no—
186C4⋊C8×C103—21no—
187C22⋊C8×C103—21no—
188C22⋊C8×C103—21no—
189C22⋊C8×C103—21no—
190C22⋊C8×C103—21no—
191C22⋊C8×C103C2311yescharacteristic
192C22⋊C8×C103C2311yescharacteristic
193C22⋊C8×C103C2311yescharacteristic
194C22⋊C8×C103C2311yescharacteristic
195#97×C103—21no—
196C4×C8×C103—21no—
197#95×C103—21no—
198#95×C103—21no—
199#95×C103—21no—
200#95×C103—21no—
201#95×C103—21no—
202#95×C103C2311yescharacteristic
203#95×C103C2311yescharacteristic
204#95×C103C2311yescharacteristic
205#95×C103C2311yescharacteristic
206C24×C103—21no—
207C24×C103—21no—
208C24×C103C2×D411yescharacteristic
209C24×C103C2×D411yescharacteristic
210#41×C103—81no—
211#41×C103—81no—
212#41×C103—81no—
213#41×C103—81no—
214C2×Q8×C103—21no—
215C2×Q8×C103C22×C411yescharacteristic
216C2×D4×C103—21no—
217C2×D4×C103—21no—
218C2×D4×C103—21no—
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—42no—
232C2×D4×C103—44no—
233C2×D4×C103—81no—
234C2×D4×C103—81no—
235C2×D4×C103—81no—
236C2×D4×C103—81no—
237C2×D4×C103—81no—
238C2×D4×C103—81no—
239C2×D4×C103C22⋊C411yescharacteristic
240C2×D4×C103C22⋊C411yescharacteristic
241C2×D4×C103C22⋊C411yescharacteristic
242C2×D4×C103C22⋊C411yescharacteristic
243C2×D4×C103C22×C411yescharacteristic
244C2×D4×C103C22×C411yescharacteristic
245C2×D4×C103C22×C411yescharacteristic
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—21no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103—21no—
254C22×C4×C103—21no—
255C22×C4×C103—21no—
256C22×C4×C103—21no—
257C22×C4×C103—42no—
258C22×C4×C103—81no—
259C22×C4×C103—81no—
260C22×C4×C103—81no—
261C22×C4×C103—81no—
262C22×C4×C103C22×C411yescharacteristic
263C22×C4×C103C22×C411yescharacteristic
264C22×C4×C103C22×C411yescharacteristic
265C22×C4×C103C22×C411yescharacteristic
266C22×C4×C103C2×D411yescharacteristic
267C22×C4×C103C2×D411yescharacteristic
268C22×C4×C103C2×D411yescharacteristic
269C22×C4×C103C2×D411yescharacteristic
270C22×C4×C103C2×D411yescharacteristic
271C22×C4×C103C2×D411yescharacteristic
272C22×C4×C103C2×D411yescharacteristic
273C22×C4×C103C2×D411yescharacteristic
274C22×C4×C103C2411yescharacteristic
275M16×C103—81no—
276M16×C103—81no—
277C2×C8×C103—21no—
278C2×C8×C103—21no—
279C2×C8×C103—21no—
280C2×C8×C103—21no—
281C2×C8×C103—81no—
282C2×C8×C103—81no—
283C4⋊C4×C103—21no—
284C4⋊C4×C103—21no—
285C4⋊C4×C103—21no—
286C4⋊C4×C103—21no—
287C4⋊C4×C103—21no—
288C4⋊C4×C103—21no—
289C4⋊C4×C103—21no—
290C4⋊C4×C103—21no—
291C4⋊C4×C103—21no—
292C4⋊C4×C103—81no—
293C4⋊C4×C103—81no—
294C4⋊C4×C103C22⋊C411yescharacteristic
295C4⋊C4×C103C22⋊C411yescharacteristic
296C4⋊C4×C103C22⋊C411yescharacteristic
297C4⋊C4×C103C22⋊C411yescharacteristic
298C4⋊C4×C103C22×C411yescharacteristic
299C4⋊C4×C103C22×C411yescharacteristic
300C4⋊C4×C103C22×C411yescharacteristic
301C4⋊C4×C103C22×C411yescharacteristic
302C22⋊C4×C103—21no—
303C22⋊C4×C103—21no—
304C22⋊C4×C103—21no—
305C22⋊C4×C103—21no—
306C22⋊C4×C103—21no—
307C22⋊C4×C103—21no—
308C22⋊C4×C103—21no—
309C22⋊C4×C103—21no—
310C22⋊C4×C103—21no—
311C22⋊C4×C103—21no—
312C22⋊C4×C103—21no—
313C22⋊C4×C103—21no—
314C22⋊C4×C103—21no—
315C22⋊C4×C103—21no—
316C22⋊C4×C103—21no—
317C22⋊C4×C103—21no—
318C22⋊C4×C103—21no—
319C22⋊C4×C103—21no—
320C22⋊C4×C103—21no—
321C22⋊C4×C103—42no—
322C22⋊C4×C103—81no—
323C22⋊C4×C103—81no—
324C22⋊C4×C103C22⋊C411yescharacteristic
325C22⋊C4×C103C22⋊C411yescharacteristic
326C22⋊C4×C103C22⋊C411yescharacteristic
327C22⋊C4×C103C22⋊C411yescharacteristic
328C22⋊C4×C103C22⋊C411yescharacteristic
329C22⋊C4×C103C22⋊C411yescharacteristic
330C22⋊C4×C103C22⋊C411yescharacteristic
331C22⋊C4×C103C22⋊C411yescharacteristic
332C42×C103—21no—
333C42×C103—21no—
334C42×C103—21no—
335C42×C103—81no—
336C42×C103C22×C411yescharacteristic
337C42×C103C22×C411yescharacteristic
338C42×C103C2×D411yescharacteristic
339C42×C103C2×D411yescharacteristic
340C23×C103—21no—
341C23×C103—21no—
342C23×C103—22no—
343C23×C103—21no—
344C23×C103—21no—
345C23×C103—21no—
346C23×C103—21no—
347C23×C103—21no—
348C23×C103—41no—
349C23×C103—41no—
350C23×C103—41no—
351C23×C103—42no—
352C23×C103—42no—
353C23×C103—81no—
354C23×C103—81no—
355C23×C103—81no—
356C23×C103—81no—
357C23×C103C2×C22⋊C411yescharacteristic
358C23×C103C2×C22⋊C411yescharacteristic
359C23×C103C2×C22⋊C411yescharacteristic
360C23×C103C2×C22⋊C411yescharacteristic
361C23×C103C22×D411yescharacteristic
362Q8×C103—41no—
363Q8×C103—81no—
364D4×C103—22no—
365D4×C103—22no—
366D4×C103—41no—
367D4×C103—41no—
368D4×C103—41no—
369D4×C103—41no—
370D4×C103—41no—
371D4×C103—42no—
372D4×C103—42no—
373D4×C103—41no—
374D4×C103—41no—
375D4×C103—41no—
376D4×C103—41no—
377D4×C103—41no—
378D4×C103—41no—
379D4×C103—42no—
380D4×C103—81no—
381D4×C103—81no—
382D4×C103—81no—
383D4×C103—81no—
384D4×C103—81no—
385D4×C103—81no—
386D4×C103—81no—
387D4×C103—81no—
388D4×C103—81no—
389C2×C4×C103—21no—
390C2×C4×C103—21no—
391C2×C4×C103—21no—
392C2×C4×C103—21no—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—21no—
396C2×C4×C103—41no—
397C2×C4×C103—41no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—42no—
409C2×C4×C103—41no—
410C2×C4×C103—41no—
411C2×C4×C103—41no—
412C2×C4×C103—41no—
413C2×C4×C103—41no—
414C2×C4×C103—41no—
415C2×C4×C103—41no—
416C2×C4×C103—41no—
417C2×C4×C103—41no—
418C2×C4×C103—41no—
419C2×C4×C103—41no—
420C2×C4×C103—41no—
421C2×C4×C103—81no—
422C2×C4×C103—81no—
423C2×C4×C103—81no—
424C2×C4×C103—81no—
425C2×C4×C103—81no—
426C2×C4×C103—81no—
427C2×C4×C103—84no—
428C2×C4×C103C2×C22⋊C411yescharacteristic
429C2×C4×C103C2×C22⋊C411yescharacteristic
430C2×C4×C103C2×C22⋊C411yescharacteristic
431C2×C4×C103C2×C22⋊C411yescharacteristic
432C2×C4×C103C2×C22⋊C411yescharacteristic
433C2×C4×C103C2×C22⋊C411yescharacteristic
434C2×C4×C103C2×C22⋊C411yescharacteristic
435C2×C4×C103C2×C22⋊C411yescharacteristic
436C2×C4×C103C23×C411yescharacteristic
437C2×C4×C103C22×D411yescharacteristic
438C8×C103—41no—
439C8×C103—41no—
440C8×C103—41no—
441C8×C103—41no—
442C22×C103—21no—
443C22×C103—21no—
444C22×C103—21no—
445C22×C103—21no—
446C22×C103—21no—
447C22×C103—21no—
448C22×C103—21no—
449C22×C103—21no—
450C22×C103—21no—
451C22×C103—21no—
452C22×C103—21no—
453C22×C103—21no—
454C22×C103—21no—
455C22×C103—42no—
456C22×C103—42no—
457C22×C103—41no—
458C22×C103—41no—
459C22×C103—41no—
460C22×C103—41no—
461C22×C103—41no—
462C22×C103—41no—
463C22×C103—41no—
464C22×C103—41no—
465C22×C103—41no—
466C22×C103—81no—
467C22×C103—81no—
468C22×C103—162no—
469C22×C103—162no—
470C22×C103#42112yes—
471C22×C103C22×C22⋊C411yescharacteristic
472C22×C103#57611yescharacteristic
473C22×C103#57711yescharacteristic
474C4×C103—21no—
475C4×C103—21no—
476C4×C103—21no—
477C4×C103—21no—
478C4×C103—21no—
479C4×C103—21no—
480C4×C103—21no—
481C4×C103—21no—
482C4×C103—21no—
483C4×C103—21no—
484C4×C103—41no—
485C4×C103—41no—
486C4×C103—41no—
487C4×C103—41no—
488C4×C103—41no—
489C4×C103—81no—
490C4×C103—81no—
491C4×C103—81no—
492C4×C103—81no—
493#17597C10311yesmaximal, characteristic, direct product factor, Sylow
494C2×C103—21no—
495C2×C103—21no—
496C2×C103—22no—
497C2×C103—41no—
498C2×C103—41no—
499C2×C103—41no—
500C2×C103—81no—
501C2×C103—81no—
502C2×C103—81no—
503C2×C103#288311yescharacteristic
504C2×C103#289711yescharacteristic
505C2×C103C2×#42111yescharacteristic
506#3519C2×C10311yescharacteristic
507#2974C2×C10311yescharacteristic, complemented
508#2318C2×C10311yescharacteristic, complemented
509#1521C2×C10311yescharacteristic, complemented
510#1519C2×C10311yescharacteristic, complemented
511#1517C2×C10311yescharacteristic, complemented
512#1516C2×C10311yescharacteristic, complemented
513#1514C2×C10311yescharacteristic, complemented
514#1513C2×C10311yescharacteristic, complemented
515#1512C2×C10311yescharacteristic, complemented
516#1510C2×C10311yescharacteristic, complemented
517#1507C2×C10311yescharacteristic, complemented
518#1504C2×C10311yescharacteristic, complemented
519#1501C2×C10311yescharacteristic, complemented
520C2×#327C2×C10311yescharacteristic, complemented
521C103#1759711yescharacteristic, direct product factor, Sylow
522#555C4×C10311yescharacteristic, complemented
523#554C4×C10311yescharacteristic, complemented
524#553—21no—
525#553C4×C10311yescharacteristic, complemented
526#553C4×C10311yescharacteristic, complemented
527#550C4×C10311yescharacteristic, complemented
528#546—21no—
529#546—21no—
530#546C4×C10311yescharacteristic, complemented
531#546C4×C10311yescharacteristic, complemented
532D42—21no—
533D42C4×C10311yescharacteristic, complemented
534#540—21no—
535#538—21no—
536#538—21no—
537#532C22×C10311yescharacteristic
538#529C22×C10311yescharacteristic
539#525C22×C10311yescharacteristic
540#525C22×C10311yescharacteristic
541C2×#121C22×C10311yescharacteristic
542C2×#121C22×C10311yescharacteristic
543#518—21no—
544C2×C4×D4C22×C10311yescharacteristic
545#436—21no—
546#435—21no—
547#435—21no—
548C8×D4—21no—
549#432C22×C10311yescharacteristic, complemented
550#431C22×C10311yescharacteristic, complemented
551#407C22×C10311yescharacteristic, complemented
552#407C22×C10311yescharacteristic, complemented
553C2×C22⋊C8C22×C10311yescharacteristic, complemented
554C2×C22⋊C8C22×C10311yescharacteristic, complemented
555#388—21no—
556#387—21no—
557#386—21no—
558#385—21no—
559#383C22×C10311yescharacteristic, complemented
560#382C22×C10311yescharacteristic, complemented
561#381C22×C10311yescharacteristic, complemented
562#380C22×C10311yescharacteristic, complemented
563C4×C22⋊C4C22×C10311yescharacteristic, complemented
564C2×#95C22×C10311yescharacteristic, complemented
565#328C22×C10311yescharacteristic, complemented
566#328C22×C10311yescharacteristic, complemented
567#328C22×C10311yescharacteristic, complemented
568#328C22×C10311yescharacteristic, complemented
569#327C22×C10311yescharacteristic
570#327C22×C10311yescharacteristic
571#327C22×C10311yescharacteristic
572#327C22×C10311yescharacteristic
573#327C22×C10311yescharacteristic, complemented
574#327C22×C10311yescharacteristic, complemented
575#327C22×C10311yescharacteristic, complemented
576#327C22×C10311yescharacteristic, complemented
577#327C22×C10311yescharacteristic, complemented
578#327C22×C10311yescharacteristic, complemented
579#327C22×C10311yescharacteristic, complemented
580#327C22×C10311yescharacteristic, complemented
581C2×#41—21no—
582C2×#41C2×C4×C10311yescharacteristic
583C2×#41C2×C4×C10311yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×C4×C10311yescharacteristic
588C22×D4C2×C4×C10311yescharacteristic, complemented
589C22×D4D4×C10311yescharacteristic
590C23×C4—21no—
591C23×C4C23×C10311yescharacteristic
592C23×C4C23×C10311yescharacteristic
593C2×M16—21no—
594C2×M16—21no—
595C22×C8—21no—
596C22×C8—21no—
597C4⋊Q8C2×C4×C10311yescharacteristic, complemented
598#127—21no—
599#127C2×C4×C10311yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×C4×C10311yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×C4×C10311yescharacteristic, 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×C10311yescharacteristic
619C22⋊Q8C2×C4×C10311yescharacteristic, complemented
620C22⋊Q8C23×C10311yescharacteristic
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×C10311yescharacteristic
635#121C2×C4×C10311yescharacteristic
636#121C2×C4×C10311yescharacteristic
637#121C2×C4×C10311yescharacteristic, complemented
638#121C2×C4×C10311yescharacteristic, complemented
639#121C2×C4×C10311yescharacteristic, complemented
640#121C23×C10311yescharacteristic
641#121C23×C10311yescharacteristic
642#121C23×C10311yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×C4×C10311yescharacteristic, 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×C10311yescharacteristic
661C4×D4C2×C4×C10311yescharacteristic
662C4×D4C2×C4×C10311yescharacteristic
663C4×D4C2×C4×C10311yescharacteristic
664C4×D4C2×C4×C10311yescharacteristic, complemented
665C4×D4C2×C4×C10311yescharacteristic, complemented
666C4×D4C2×C4×C10311yescharacteristic, complemented
667C4×D4D4×C10311yescharacteristic
668C4×D4D4×C10311yescharacteristic
669C4×D4D4×C10311yescharacteristic
670C4×D4D4×C10311yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×C4×C10311yescharacteristic
674#117C2×C4×C10311yescharacteristic, complemented
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4C2×C4×C10311yescharacteristic
678C2×C4⋊C4C2×C4×C10311yescharacteristic, complemented
679C2×C4⋊C4D4×C10311yescharacteristic
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×C10311yescharacteristic
688C2×C22⋊C4D4×C10311yescharacteristic
689C2×C42—21no—
690C2×C42C23×C10311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8C23×C10311yescharacteristic
698C22⋊C8C23×C10311yescharacteristic
699C22⋊C8C23×C10311yescharacteristic
700C22⋊C8C23×C10311yescharacteristic
701#97—21no—
702C4×C8—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C23×C10311yescharacteristic
709#95C23×C10311yescharacteristic
710#95C23×C10311yescharacteristic
711#95C23×C10311yescharacteristic
712C24—21no—
713C24—21no—
714C24C2×D4×C10311yescharacteristic
715C24C2×D4×C10311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C10311yescharacteristic
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×C10311yescharacteristic
746C2×D4C22⋊C4×C10311yescharacteristic
747C2×D4C22⋊C4×C10311yescharacteristic
748C2×D4C22⋊C4×C10311yescharacteristic
749C2×D4C22×C4×C10311yescharacteristic
750C2×D4C22×C4×C10311yescharacteristic
751C2×D4C22×C4×C10311yescharacteristic
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×C10311yescharacteristic
769C22×C4C22×C4×C10311yescharacteristic
770C22×C4C22×C4×C10311yescharacteristic
771C22×C4C22×C4×C10311yescharacteristic
772C22×C4C2×D4×C10311yescharacteristic
773C22×C4C2×D4×C10311yescharacteristic
774C22×C4C2×D4×C10311yescharacteristic
775C22×C4C2×D4×C10311yescharacteristic
776C22×C4C2×D4×C10311yescharacteristic
777C22×C4C2×D4×C10311yescharacteristic
778C22×C4C2×D4×C10311yescharacteristic
779C22×C4C2×D4×C10311yescharacteristic
780C22×C4C24×C10311yescharacteristic
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×C10311yescharacteristic
801C4⋊C4C22⋊C4×C10311yescharacteristic
802C4⋊C4C22⋊C4×C10311yescharacteristic
803C4⋊C4C22⋊C4×C10311yescharacteristic
804C4⋊C4C22×C4×C10311yescharacteristic
805C4⋊C4C22×C4×C10311yescharacteristic
806C4⋊C4C22×C4×C10311yescharacteristic
807C4⋊C4C22×C4×C10311yescharacteristic
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×C10311yescharacteristic
831C22⋊C4C22⋊C4×C10311yescharacteristic
832C22⋊C4C22⋊C4×C10311yescharacteristic
833C22⋊C4C22⋊C4×C10311yescharacteristic
834C22⋊C4C22⋊C4×C10311yescharacteristic
835C22⋊C4C22⋊C4×C10311yescharacteristic
836C22⋊C4C22⋊C4×C10311yescharacteristic
837C22⋊C4C22⋊C4×C10311yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C10311yescharacteristic
843C42C22×C4×C10311yescharacteristic
844C42C2×D4×C10311yescharacteristic
845C42C2×D4×C10311yescharacteristic
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×C10311yescharacteristic
864C23C2×C22⋊C4×C10311yescharacteristic
865C23C2×C22⋊C4×C10311yescharacteristic
866C23C2×C22⋊C4×C10311yescharacteristic
867C23C22×D4×C10311yescharacteristic
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×C10311yescharacteristic
935C2×C4C2×C22⋊C4×C10311yescharacteristic
936C2×C4C2×C22⋊C4×C10311yescharacteristic
937C2×C4C2×C22⋊C4×C10311yescharacteristic
938C2×C4C2×C22⋊C4×C10311yescharacteristic
939C2×C4C2×C22⋊C4×C10311yescharacteristic
940C2×C4C2×C22⋊C4×C10311yescharacteristic
941C2×C4C2×C22⋊C4×C10311yescharacteristic
942C2×C4C23×C4×C10311yescharacteristic
943C2×C4C22×D4×C10311yescharacteristic
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×C10312yes—
977C22C22×C22⋊C4×C10311yescharacteristic
978C22#576×C10311yescharacteristic
979C22#577×C10311yescharacteristic
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—
1008C2C103×#288311yescharacteristic
1009C2C103×#289711yescharacteristic
1010C2C2×#421×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C22×C22⋊C4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2974C2semidirect
3. C103×#2318C2semidirect
4. C103×#1521C2semidirect
5. C103×#1519C2semidirect
6. C103×#1517C2semidirect
7. C103×#1516C2semidirect
8. C103×#1514C2semidirect
9. C103×#1513C2semidirect
10. C103×#1512C2semidirect
11. C103×#1510C2semidirect
12. C103×#1507C2semidirect
13. C103×#1504C2semidirect
14. C103×#1501C2semidirect
15. C2×#327×C103C2semidirect
16. #555×C103C4semidirect
17. #554×C103C4semidirect
19. #553×C103C4semidirect
20. #553×C103C4semidirect
21. #550×C103C4semidirect
24. #546×C103C4semidirect
25. #546×C103C4semidirect
27. D42×C103C4semidirect
43. #432×C103C22semidirect
44. #431×C103C22semidirect
45. #407×C103C22semidirect
46. #407×C103C22semidirect
47. C2×C22⋊C8×C103C22semidirect
48. C2×C22⋊C8×C103C22semidirect
53. #383×C103C22semidirect
54. #382×C103C22semidirect
55. #381×C103C22semidirect
56. #380×C103C22semidirect
57. C4×C22⋊C4×C103C22semidirect
58. C2×#95×C103C22semidirect
59. #328×C103C22semidirect
60. #328×C103C22semidirect
61. #328×C103C22semidirect
62. #328×C103C22semidirect
67. #327×C103C22semidirect
68. #327×C103C22semidirect
69. #327×C103C22semidirect
70. #327×C103C22semidirect
71. #327×C103C22semidirect
72. #327×C103C22semidirect
73. #327×C103C22semidirect
74. #327×C103C22semidirect
77. C2×#41×C103C2×C4semidirect
82. C22×D4×C103C2×C4semidirect
91. C4⋊Q8×C103C2×C4semidirect
93. #127×C103C2×C4semidirect
98. #125×C103C2×C4semidirect
102. #124×C103C2×C4semidirect
113. C22⋊Q8×C103C2×C4semidirect
131. #121×C103C2×C4semidirect
132. #121×C103C2×C4semidirect
133. #121×C103C2×C4semidirect
143. C4×Q8×C103C2×C4semidirect
158. C4×D4×C103C2×C4semidirect
159. C4×D4×C103C2×C4semidirect
160. C4×D4×C103C2×C4semidirect
168. #117×C103C2×C4semidirect
172. C2×C4⋊C4×C103C2×C4semidirect
493. #17597C103direct (N × H)
507. #2974C2×C103semidirect
508. #2318C2×C103semidirect
509. #1521C2×C103semidirect
510. #1519C2×C103semidirect
511. #1517C2×C103semidirect
512. #1516C2×C103semidirect
513. #1514C2×C103semidirect
514. #1513C2×C103semidirect
515. #1512C2×C103semidirect
516. #1510C2×C103semidirect
517. #1507C2×C103semidirect
518. #1504C2×C103semidirect
519. #1501C2×C103semidirect
520. C2×#327C2×C103semidirect
521. C103#17597direct (N × H)
522. #555C4×C103semidirect
523. #554C4×C103semidirect
525. #553C4×C103semidirect
526. #553C4×C103semidirect
527. #550C4×C103semidirect
530. #546C4×C103semidirect
531. #546C4×C103semidirect
533. D42C4×C103semidirect
549. #432C22×C103semidirect
550. #431C22×C103semidirect
551. #407C22×C103semidirect
552. #407C22×C103semidirect
553. C2×C22⋊C8C22×C103semidirect
554. C2×C22⋊C8C22×C103semidirect
559. #383C22×C103semidirect
560. #382C22×C103semidirect
561. #381C22×C103semidirect
562. #380C22×C103semidirect
563. C4×C22⋊C4C22×C103semidirect
564. C2×#95C22×C103semidirect
565. #328C22×C103semidirect
566. #328C22×C103semidirect
567. #328C22×C103semidirect
568. #328C22×C103semidirect
573. #327C22×C103semidirect
574. #327C22×C103semidirect
575. #327C22×C103semidirect
576. #327C22×C103semidirect
577. #327C22×C103semidirect
578. #327C22×C103semidirect
579. #327C22×C103semidirect
580. #327C22×C103semidirect
583. C2×#41C2×C4×C103semidirect
588. C22×D4C2×C4×C103semidirect
597. C4⋊Q8C2×C4×C103semidirect
599. #127C2×C4×C103semidirect
604. #125C2×C4×C103semidirect
608. #124C2×C4×C103semidirect
619. C22⋊Q8C2×C4×C103semidirect
637. #121C2×C4×C103semidirect
638. #121C2×C4×C103semidirect
639. #121C2×C4×C103semidirect
649. C4×Q8C2×C4×C103semidirect
664. C4×D4C2×C4×C103semidirect
665. C4×D4C2×C4×C103semidirect
666. C4×D4C2×C4×C103semidirect
674. #117C2×C4×C103semidirect
678. C2×C4⋊C4C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35192
C103×#29742
C103×#23182
C103×#15212
C103×#15192
C103×#15172
C103×#15162
C103×#15142
C103×#15132
C103×#15122
C103×#15102
C103×#15072
C103×#15042
C103×#15012
C2×#327×C1032
#17597103