Finite Group Databasebeta

← C107×#18434 #41044398

Subgroups — C107×#18434 #41044398

Order 27392.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3560C211yesmaximal, characteristic, complemented
2C107×#3213C211yesmaximal, characteristic, complemented
3C107×#3211C211yesmaximal, characteristic, complemented
4C107×#2662C211yesmaximal, characteristic, complemented
5C107×#1606C211yesmaximal, characteristic, complemented
6C107×#1604C211yesmaximal, characteristic, complemented
7C107×#1603C211yesmaximal, characteristic, complemented
8C107×#1601C211yesmaximal, characteristic, complemented
9C107×#1600C211yesmaximal, characteristic, complemented
10C107×#1598C211yesmaximal, characteristic, complemented
11C107×#1597C211yesmaximal, characteristic, complemented
12C107×#1595C211yesmaximal, characteristic, complemented
13C107×#1509C211yesmaximal, characteristic, complemented
14C107×#1502C211yesmaximal, characteristic, complemented
15C107×#1473C211yesmaximal, characteristic, complemented
16#563×C107—21no—
17#560×C107—21no—
18#553×C107—21no—
19#553×C107—21no—
20#551×C107—21no—
21#547×C107—21no—
22#546×C107—21no—
23#546×C107—21no—
24#542×C107—21no—
25#539×C107—21no—
26#539×C107C2211yescharacteristic
27#538×C107—21no—
28#538×C107—21no—
29#538×C107C2211yescharacteristic
30#537×C107C2211yescharacteristic
31#534×C107C2211yescharacteristic
32#532×C107C2211yescharacteristic
33#529×C107C2211yescharacteristic
34C2×#126×C107C2211yescharacteristic
35C2×#124×C107C2211yescharacteristic, complemented
36#496×C107—21no—
37#495×C107—21no—
38#489×C107—21no—
39#488×C107—21no—
40#464×C107—21no—
41#463×C107—21no—
42#463×C107—21no—
43#463×C107—21no—
44#451×C107C2211yescharacteristic, complemented
45#450×C107C2211yescharacteristic, complemented
46#448×C107C2211yescharacteristic
47#448×C107C2211yescharacteristic
48#448×C107C2211yescharacteristic, complemented
49#447×C107C2211yescharacteristic
50#447×C107C2211yescharacteristic
51#447×C107C2211yescharacteristic, complemented
52#432×C107C2211yescharacteristic, complemented
53#431×C107C2211yescharacteristic, complemented
54#396×C107—21no—
55#395×C107C2211yescharacteristic, complemented
56#394×C107—21no—
57#394×C107C2211yescharacteristic, complemented
58#393×C107C2211yescharacteristic
59#392×C107C2211yescharacteristic
60#390×C107—21no—
61#388×C107—21no—
62C4×C4⋊C4×C107C2211yescharacteristic, complemented
63#328×C107C2211yescharacteristic, complemented
64#328×C107C2211yescharacteristic, complemented
65#327×C107C2211yescharacteristic
66#327×C107C2211yescharacteristic
67#327×C107C2211yescharacteristic
68#327×C107C2211yescharacteristic
69#327×C107C2211yescharacteristic, complemented
70#327×C107C2211yescharacteristic, complemented
71#324×C107C2211yescharacteristic, complemented
72#324×C107C2211yescharacteristic, complemented
73#323×C107C2211yescharacteristic
74#323×C107C2211yescharacteristic
75C2×#41×C107—21no—
76C2×#41×C107—21no—
77C22×Q8×C107C2311yescharacteristic
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107C2311yescharacteristic
81C2×Q16×C107—21no—
82C2×SD16×C107—21no—
83C2×SD16×C107—21no—
84C2×SD16×C107—21no—
85C2×SD16×C107—21no—
86C2×D8×C107—21no—
87C2×D8×C107—21no—
88C2×D8×C107—21no—
89C4⋊Q8×C107—21no—
90C4⋊Q8×C107D411yescharacteristic, complemented
91#127×C107D411yescharacteristic, complemented
92#126×C107—21no—
93#126×C107—21no—
94#126×C107—21no—
95#126×C107—21no—
96#126×C107—21no—
97#126×C107—21no—
98#126×C107—21no—
99#126×C107—21no—
100#126×C107—21no—
101#125×C107—21no—
102#125×C107—21no—
103#125×C107D411yescharacteristic, complemented
104#124×C107—21no—
105#124×C107—21no—
106#124×C107—21no—
107#124×C107—21no—
108#124×C107—21no—
109#124×C107—21no—
110#124×C107—21no—
111#124×C107—21no—
112#124×C107D411yescharacteristic, complemented
113#123×C107—21no—
114#123×C107—21no—
115#123×C107—21no—
116#123×C107—21no—
117#123×C107—21no—
118#123×C107—21no—
119#123×C107—21no—
120#123×C107—21no—
121#123×C107—21no—
122#123×C107—21no—
123#123×C107—21no—
124#123×C107—21no—
125C22⋊Q8×C107—21no—
126C22⋊Q8×C107—21no—
127C22⋊Q8×C107—21no—
128C22⋊Q8×C107—21no—
129C22⋊Q8×C107—21no—
130C22⋊Q8×C107—21no—
131C22⋊Q8×C107—21no—
132C22⋊Q8×C107C2311yescharacteristic
133#121×C107—21no—
134#121×C107—21no—
135#121×C107—21no—
136#121×C107—21no—
137#121×C107—21no—
138#121×C107—21no—
139#121×C107—21no—
140#121×C107—21no—
141#121×C107—21no—
142#121×C107—21no—
143#121×C107—21no—
144#121×C107—21no—
145#121×C107C2311yescharacteristic
146#121×C107C2311yescharacteristic
147#121×C107C2311yescharacteristic
148#120×C107—21no—
149#120×C107—21no—
150#120×C107—21no—
151#120×C107—21no—
152#120×C107—21no—
153C4×Q8×C107D411yescharacteristic, complemented
154C4×D4×C107—21no—
155C4×D4×C107—21no—
156C4×D4×C107—21no—
157C4×D4×C107—21no—
158C4×D4×C107—21no—
159C4×D4×C107—21no—
160C4×D4×C107—21no—
161C4×D4×C107—21no—
162C4×D4×C107D411yescharacteristic, complemented
163C4×D4×C107D411yescharacteristic, complemented
164C4×D4×C107D411yescharacteristic, complemented
165#117×C107—21no—
166#117×C107—21no—
167C2×C4⋊C4×C107—21no—
168C2×C4⋊C4×C107—21no—
169C2×C4⋊C4×C107—21no—
170C2×C4⋊C4×C107D411yescharacteristic
171C2×C4⋊C4×C107D411yescharacteristic
172C2×C4⋊C4×C107C2311yescharacteristic
173C2×C22⋊C4×C107—21no—
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×C22⋊C4×C107C2311yescharacteristic
184C2×C42×C107—21no—
185C2×C42×C107C2311yescharacteristic
186C4⋊C8×C107—21no—
187C4⋊C8×C107—21no—
188#103×C107—21no—
189#103×C107—21no—
190#103×C107—21no—
191#103×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#102×C107—21no—
196C22⋊C8×C107C2311yescharacteristic
197C22⋊C8×C107C2311yescharacteristic
198C22⋊C8×C107C2311yescharacteristic
199C22⋊C8×C107C2311yescharacteristic
200#97×C107—21no—
201C4×C8×C107—21no—
202#95×C107—21no—
203#95×C107—21no—
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107—21no—
208C24×C107C2×D411yescharacteristic
209#41×C107—81no—
210#41×C107—81no—
211#41×C107—81no—
212#41×C107—81no—
213C2×Q8×C107—21no—
214C2×Q8×C107—21no—
215C2×Q8×C107—21no—
216C2×Q8×C107—21no—
217C2×Q8×C107—81no—
218C2×Q8×C107C2×D411yescharacteristic
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—21no—
232C2×D4×C107—21no—
233C2×D4×C107—42no—
234C2×D4×C107—81no—
235C2×D4×C107—81no—
236C2×D4×C107—81no—
237C2×D4×C107—81no—
238C2×D4×C107—81no—
239C2×D4×C107C2×D411yescharacteristic
240C2×D4×C107C2×D411yescharacteristic
241C2×D4×C107C2×D411yescharacteristic
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
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×C107C2×D411yescharacteristic
254C22×C4×C107C2×D411yescharacteristic
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2×D411yescharacteristic
257C22×C4×C107C2×D411yescharacteristic
258C22×C4×C107C2411yescharacteristic
259Q16×C107—81no—
260SD16×C107—81no—
261SD16×C107—81no—
262SD16×C107—81no—
263SD16×C107—81no—
264D8×C107—81no—
265D8×C107—81no—
266D8×C107—81no—
267C2×C8×C107—21no—
268C2×C8×C107—21no—
269C2×C8×C107—21no—
270C2×C8×C107—21no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—42no—
289C4⋊C4×C107—81no—
290C4⋊C4×C107C2×D411yescharacteristic
291C4⋊C4×C107C2×D411yescharacteristic
292C4⋊C4×C107C2×D411yescharacteristic
293C4⋊C4×C107C2×D411yescharacteristic
294C22⋊C4×C107—21no—
295C22⋊C4×C107—21no—
296C22⋊C4×C107—21no—
297C22⋊C4×C107—21no—
298C22⋊C4×C107—21no—
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
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—42no—
320C22⋊C4×C107—41no—
321C22⋊C4×C107—41no—
322C22⋊C4×C107—41no—
323C22⋊C4×C107—41no—
324C22⋊C4×C107—81no—
325C22⋊C4×C107—81no—
326C22⋊C4×C107—81no—
327C42×C107—21no—
328C42×C107—21no—
329C42×C107—21no—
330C42×C107—81no—
331C42×C107C2×D411yescharacteristic
332C42×C107C2×D411yescharacteristic
333C42×C107C2×D411yescharacteristic
334C42×C107C2×D411yescharacteristic
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—21no—
339C23×C107—21no—
340C23×C107—21no—
341C23×C107—41no—
342C23×C107—41no—
343C23×C107—41no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—41no—
347C23×C107—41no—
348C23×C107—41no—
349C23×C107—41no—
350C23×C107—81no—
351C23×C107—81no—
352C23×C107—81no—
353C23×C107C22×D411yescharacteristic
354Q8×C107—41no—
355Q8×C107—41no—
356Q8×C107—41no—
357Q8×C107—41no—
358Q8×C107—41no—
359Q8×C107—81no—
360Q8×C107—81no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—41no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—41no—
369D4×C107—41no—
370D4×C107—41no—
371D4×C107—41no—
372D4×C107—41no—
373D4×C107—41no—
374D4×C107—81no—
375D4×C107—81no—
376D4×C107—81no—
377D4×C107—81no—
378D4×C107—81no—
379D4×C107—81no—
380D4×C107—81no—
381D4×C107—81no—
382D4×C107—81no—
383D4×C107—84no—
384C2×C4×C107—21no—
385C2×C4×C107—21no—
386C2×C4×C107—22no—
387C2×C4×C107—21no—
388C2×C4×C107—21no—
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—21no—
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—41no—
409C2×C4×C107—81no—
410C2×C4×C107—81no—
411C2×C4×C107—81no—
412C2×C4×C107—81no—
413C2×C4×C107—81no—
414C2×C4×C107—81no—
415C2×C4×C107—81no—
416C2×C4×C107—81no—
417C2×C4×C107#12011yescharacteristic
418C2×C4×C107#12011yescharacteristic
419C2×C4×C107#12011yescharacteristic
420C2×C4×C107#12011yescharacteristic
421C2×C4×C107C22×D411yescharacteristic
422C2×C4×C107C22×D411yescharacteristic
423C8×C107—41no—
424C8×C107—41no—
425C8×C107—41no—
426C8×C107—41no—
427C22×C107—21no—
428C22×C107—21no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—41no—
434C22×C107—41no—
435C22×C107—41no—
436C22×C107—41no—
437C22×C107—41no—
438C22×C107—41no—
439C22×C107—41no—
440C22×C107—41no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107—81no—
448C22×C107—81no—
449C22×C107—81no—
450C22×C107—162no—
451C22×C107C2×#12011yescharacteristic
452C22×C107#57611yescharacteristic
453C22×C107#57711yescharacteristic
454C4×C107—21no—
455C4×C107—21no—
456C4×C107—21no—
457C4×C107—21no—
458C4×C107—21no—
459C4×C107—21no—
460C4×C107—42no—
461C4×C107—41no—
462C4×C107—41no—
463C4×C107—41no—
464C4×C107—41no—
465C4×C107—41no—
466C4×C107—41no—
467C4×C107—41no—
468C4×C107—41no—
469C4×C107—81no—
470C4×C107—81no—
471#18434C10711yesmaximal, characteristic, direct product factor, Sylow
472C2×C107—21no—
473C2×C107—21no—
474C2×C107—81no—
475C2×C107—81no—
476C2×C107—81no—
477C2×C107—81no—
478C2×C107—161no—
479C2×C107#301211yescharacteristic
480C2×C107#301811yescharacteristic
481C2×C107#302711yescharacteristic
482#3560C2×C10711yescharacteristic, complemented
483#3213C2×C10711yescharacteristic, complemented
484#3211C2×C10711yescharacteristic, complemented
485#2662C2×C10711yescharacteristic, complemented
486#1606C2×C10711yescharacteristic, complemented
487#1604C2×C10711yescharacteristic, complemented
488#1603C2×C10711yescharacteristic, complemented
489#1601C2×C10711yescharacteristic, complemented
490#1600C2×C10711yescharacteristic, complemented
491#1598C2×C10711yescharacteristic, complemented
492#1597C2×C10711yescharacteristic, complemented
493#1595C2×C10711yescharacteristic, complemented
494#1509C2×C10711yescharacteristic, complemented
495#1502C2×C10711yescharacteristic, complemented
496#1473C2×C10711yescharacteristic, complemented
497C107#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C10711yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C10711yescharacteristic
512#537C22×C10711yescharacteristic
513#534C22×C10711yescharacteristic
514#532C22×C10711yescharacteristic
515#529C22×C10711yescharacteristic
516C2×#126C22×C10711yescharacteristic
517C2×#124C22×C10711yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C10711yescharacteristic, complemented
527#450C22×C10711yescharacteristic, complemented
528#448C22×C10711yescharacteristic
529#448C22×C10711yescharacteristic
530#448C22×C10711yescharacteristic, complemented
531#447C22×C10711yescharacteristic
532#447C22×C10711yescharacteristic
533#447C22×C10711yescharacteristic, complemented
534#432C22×C10711yescharacteristic, complemented
535#431C22×C10711yescharacteristic, complemented
536#396—21no—
537#395C22×C10711yescharacteristic, complemented
538#394—21no—
539#394C22×C10711yescharacteristic, complemented
540#393C22×C10711yescharacteristic
541#392C22×C10711yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C10711yescharacteristic, complemented
545#328C22×C10711yescharacteristic, complemented
546#328C22×C10711yescharacteristic, complemented
547#327C22×C10711yescharacteristic
548#327C22×C10711yescharacteristic
549#327C22×C10711yescharacteristic
550#327C22×C10711yescharacteristic
551#327C22×C10711yescharacteristic, complemented
552#327C22×C10711yescharacteristic, complemented
553#324C22×C10711yescharacteristic, complemented
554#324C22×C10711yescharacteristic, complemented
555#323C22×C10711yescharacteristic
556#323C22×C10711yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C10711yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C10711yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C10711yescharacteristic, complemented
573#127D4×C10711yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C10711yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C10711yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C10711yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C10711yescharacteristic
628#121C23×C10711yescharacteristic
629#121C23×C10711yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C10711yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C10711yescharacteristic, complemented
645C4×D4D4×C10711yescharacteristic, complemented
646C4×D4D4×C10711yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10711yescharacteristic
653C2×C4⋊C4D4×C10711yescharacteristic
654C2×C4⋊C4C23×C10711yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10711yescharacteristic
664C2×C22⋊C4D4×C10711yescharacteristic
665C2×C22⋊C4C23×C10711yescharacteristic
666C2×C42—21no—
667C2×C42C23×C10711yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C10711yescharacteristic
679C22⋊C8C23×C10711yescharacteristic
680C22⋊C8C23×C10711yescharacteristic
681C22⋊C8C23×C10711yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C10711yescharacteristic
687#95C23×C10711yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C10711yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C10711yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C10711yescharacteristic
722C2×D4C2×D4×C10711yescharacteristic
723C2×D4C2×D4×C10711yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C10711yescharacteristic
736C22×C4C2×D4×C10711yescharacteristic
737C22×C4C2×D4×C10711yescharacteristic
738C22×C4C2×D4×C10711yescharacteristic
739C22×C4C2×D4×C10711yescharacteristic
740C22×C4C24×C10711yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C10711yescharacteristic
773C4⋊C4C2×D4×C10711yescharacteristic
774C4⋊C4C2×D4×C10711yescharacteristic
775C4⋊C4C2×D4×C10711yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C10711yescharacteristic
814C42C2×D4×C10711yescharacteristic
815C42C2×D4×C10711yescharacteristic
816C42C2×D4×C10711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C10711yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C10711yescharacteristic
900C2×C4#120×C10711yescharacteristic
901C2×C4#120×C10711yescharacteristic
902C2×C4#120×C10711yescharacteristic
903C2×C4C22×D4×C10711yescharacteristic
904C2×C4C22×D4×C10711yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C10711yescharacteristic
934C22#576×C10711yescharacteristic
935C22#577×C10711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C107×#301211yescharacteristic
961C2C107×#301811yescharacteristic
962C2C107×#302711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3560C2semidirect
2. C107×#3213C2semidirect
3. C107×#3211C2semidirect
4. C107×#2662C2semidirect
5. C107×#1606C2semidirect
6. C107×#1604C2semidirect
7. C107×#1603C2semidirect
8. C107×#1601C2semidirect
9. C107×#1600C2semidirect
10. C107×#1598C2semidirect
11. C107×#1597C2semidirect
12. C107×#1595C2semidirect
13. C107×#1509C2semidirect
14. C107×#1502C2semidirect
15. C107×#1473C2semidirect
35. C2×#124×C107C22semidirect
44. #451×C107C22semidirect
45. #450×C107C22semidirect
48. #448×C107C22semidirect
51. #447×C107C22semidirect
52. #432×C107C22semidirect
53. #431×C107C22semidirect
55. #395×C107C22semidirect
57. #394×C107C22semidirect
62. C4×C4⋊C4×C107C22semidirect
63. #328×C107C22semidirect
64. #328×C107C22semidirect
69. #327×C107C22semidirect
70. #327×C107C22semidirect
71. #324×C107C22semidirect
72. #324×C107C22semidirect
90. C4⋊Q8×C107D4semidirect
91. #127×C107D4semidirect
103. #125×C107D4semidirect
112. #124×C107D4semidirect
153. C4×Q8×C107D4semidirect
162. C4×D4×C107D4semidirect
163. C4×D4×C107D4semidirect
164. C4×D4×C107D4semidirect
471. #18434C107direct (N × H)
482. #3560C2×C107semidirect
483. #3213C2×C107semidirect
484. #3211C2×C107semidirect
485. #2662C2×C107semidirect
486. #1606C2×C107semidirect
487. #1604C2×C107semidirect
488. #1603C2×C107semidirect
489. #1601C2×C107semidirect
490. #1600C2×C107semidirect
491. #1598C2×C107semidirect
492. #1597C2×C107semidirect
493. #1595C2×C107semidirect
494. #1509C2×C107semidirect
495. #1502C2×C107semidirect
496. #1473C2×C107semidirect
497. C107#18434direct (N × H)
517. C2×#124C22×C107semidirect
526. #451C22×C107semidirect
527. #450C22×C107semidirect
530. #448C22×C107semidirect
533. #447C22×C107semidirect
534. #432C22×C107semidirect
535. #431C22×C107semidirect
537. #395C22×C107semidirect
539. #394C22×C107semidirect
544. C4×C4⋊C4C22×C107semidirect
545. #328C22×C107semidirect
546. #328C22×C107semidirect
551. #327C22×C107semidirect
552. #327C22×C107semidirect
553. #324C22×C107semidirect
554. #324C22×C107semidirect
572. C4⋊Q8D4×C107semidirect
573. #127D4×C107semidirect
585. #125D4×C107semidirect
594. #124D4×C107semidirect
635. C4×Q8D4×C107semidirect
644. C4×D4D4×C107semidirect
645. C4×D4D4×C107semidirect
646. C4×D4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35602
C107×#32132
C107×#32112
C107×#26622
C107×#16062
C107×#16042
C107×#16032
C107×#16012
C107×#16002
C107×#15982
C107×#15972
C107×#15952
C107×#15092
C107×#15022
C107×#14732
#18434107