Finite Group Databasebeta

← C107×#18416 #41044380

Subgroups — C107×#18416 #41044380

Order 27392.

978 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3535C211yesmaximal, characteristic, complemented
2C107×#3194C211yesmaximal, characteristic, complemented
3C107×#3187C211yesmaximal, characteristic, complemented
4C107×#2661C211yesmaximal, characteristic, complemented
5C107×#1612C211yesmaximal, characteristic, complemented
6C107×#1611C211yesmaximal, characteristic, complemented
7C107×#1609C211yesmaximal, characteristic, complemented
8C107×#1608C211yesmaximal, characteristic, complemented
9C107×#1600C211yesmaximal, characteristic, complemented
10C107×#1599C211yesmaximal, characteristic, complemented
11C107×#1597C211yesmaximal, characteristic, complemented
12C107×#1596C211yesmaximal, characteristic, complemented
13C107×#1508C211yesmaximal, characteristic, complemented
14C107×#1501C211yesmaximal, characteristic, complemented
15C107×#1468C211yesmaximal, characteristic, complemented
16#563×C107—21no—
17#562×C107—21no—
18#554×C107—21no—
19#552×C107—21no—
20#551×C107—21no—
21#551×C107—21no—
22#547×C107—21no—
23#546×C107—21no—
24#544×C107C2211yescharacteristic
25#543×C107C2211yescharacteristic
26#542×C107—21no—
27#539×C107—21no—
28#539×C107—21no—
29#539×C107C2211yescharacteristic
30#538×C107C2211yescharacteristic
31#536×C107—21no—
32#525×C107C2211yescharacteristic
33C2×#123×C107C2211yescharacteristic
34C2×C22⋊Q8×C107C2211yescharacteristic
35C2×#121×C107C2211yescharacteristic
36#483×C107C2211yescharacteristic
37#483×C107C2211yescharacteristic
38#483×C107C2211yescharacteristic
39#482×C107—21no—
40#481×C107—21no—
41#480×C107C2211yescharacteristic
42#469×C107—21no—
43#468×C107—21no—
44#465×C107—21no—
45#465×C107—21no—
46#450×C107C2211yescharacteristic
47#450×C107C2211yescharacteristic
48#450×C107C2211yescharacteristic
49#449×C107—21no—
50#448×C107—21no—
51#447×C107C2211yescharacteristic
52#407×C107C2211yescharacteristic
53C2×C22⋊C8×C107C2211yescharacteristic
54#398×C107C2211yescharacteristic
55#397×C107C2211yescharacteristic
56#394×C107—21no—
57#394×C107C2211yescharacteristic
58#392×C107—21no—
59#392×C107C2211yescharacteristic
60#390×C107—21no—
61#388×C107—21no—
62C4×C22⋊C4×C107C2211yescharacteristic
63#328×C107C2211yescharacteristic
64#328×C107C2211yescharacteristic
65#328×C107C2211yescharacteristic
66#328×C107C2211yescharacteristic
67#328×C107C2211yescharacteristic
68#328×C107C2211yescharacteristic
69#327×C107C2211yescharacteristic
70#327×C107C2211yescharacteristic
71#324×C107C2211yescharacteristic
72#324×C107C2211yescharacteristic
73#323×C107C2211yescharacteristic
74#323×C107C2211yescharacteristic
75C2×#41×C107—21no—
76C2×#41×C107D411yescharacteristic, complemented
77C22×Q8×C107D411yescharacteristic, complemented
78C22×D4×C107—21no—
79C22×D4×C107—21no—
80C22×D4×C107D411yescharacteristic
81C22×D4×C107C2311yescharacteristic
82C23×C4×C107C2311yescharacteristic
83C2×SD16×C107—21no—
84C2×SD16×C107—21no—
85C2×SD16×C107—21no—
86C2×D8×C107—21no—
87C2×M16×C107—21no—
88C22×C8×C107—21no—
89C4⋊Q8×C107—21no—
90C4⋊Q8×C107—21no—
91C4⋊Q8×C107—21no—
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#125×C107—21no—
99#125×C107—21no—
100#125×C107—21no—
101#125×C107—21no—
102#125×C107—21no—
103#124×C107—21no—
104#124×C107—21no—
105#124×C107—21no—
106#124×C107—21no—
107#123×C107—21no—
108#123×C107—21no—
109#123×C107—21no—
110#123×C107—21no—
111#123×C107—21no—
112#123×C107—21no—
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—
121C22⋊Q8×C107—21no—
122C22⋊Q8×C107—21no—
123C22⋊Q8×C107—21no—
124C22⋊Q8×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×C107—21no—
133C22⋊Q8×C107—21no—
134C22⋊Q8×C107—21no—
135C22⋊Q8×C107D411yescharacteristic, complemented
136C22⋊Q8×C107D411yescharacteristic, complemented
137C22⋊Q8×C107D411yescharacteristic, complemented
138C22⋊Q8×C107C2311yescharacteristic
139C22⋊Q8×C107C2311yescharacteristic
140C22⋊Q8×C107C2311yescharacteristic
141#121×C107—21no—
142#121×C107—21no—
143#121×C107—21no—
144#121×C107—21no—
145#121×C107—21no—
146#121×C107—21no—
147#121×C107—21no—
148#121×C107—21no—
149#121×C107D411yescharacteristic, complemented
150#121×C107C2311yescharacteristic
151#120×C107—21no—
152#120×C107—21no—
153C4×Q8×C107—21no—
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—
161#117×C107—21no—
162#117×C107—21no—
163#117×C107—21no—
164#117×C107D411yescharacteristic, complemented
165C2×C4⋊C4×C107—21no—
166C2×C4⋊C4×C107—21no—
167C2×C4⋊C4×C107—21no—
168C2×C4⋊C4×C107D411yescharacteristic
169C2×C4⋊C4×C107D411yescharacteristic, complemented
170C2×C4⋊C4×C107C2311yescharacteristic
171C2×C4⋊C4×C107C2311yescharacteristic
172C2×C22⋊C4×C107—21no—
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×C107D411yescharacteristic
181C2×C22⋊C4×C107D411yescharacteristic
182C2×C22⋊C4×C107C2311yescharacteristic
183C2×C42×C107—21no—
184#107×C107—21no—
185#106×C107—21no—
186#106×C107—21no—
187#106×C107—21no—
188#103×C107—21no—
189#103×C107—21no—
190#103×C107—21no—
191#102×C107—21no—
192#102×C107—21no—
193#102×C107—21no—
194#102×C107—21no—
195#102×C107—21no—
196C22⋊C8×C107—21no—
197C22⋊C8×C107—21no—
198C22⋊C8×C107C2311yescharacteristic
199C22⋊C8×C107C2311yescharacteristic
200C22⋊C8×C107C2311yescharacteristic
201C22⋊C8×C107C2311yescharacteristic
202#95×C107—21no—
203#95×C107—21no—
204#95×C107C2311yescharacteristic
205#95×C107C2311yescharacteristic
206C24×C107—21no—
207C24×C107C2×D411yescharacteristic
208C24×C107C2×D411yescharacteristic
209#41×C107—82no—
210#41×C107—81no—
211C2×Q8×C107—21no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107—81no—
215C2×Q8×C107C2×D411yescharacteristic
216C2×Q8×C107C2×D411yescharacteristic
217C2×Q8×C107C2×D411yescharacteristic
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—42no—
228C2×D4×C107—41no—
229C2×D4×C107—41no—
230C2×D4×C107—81no—
231C2×D4×C107—81no—
232C2×D4×C107—81no—
233C2×D4×C107—81no—
234C2×D4×C107—81no—
235C2×D4×C107—81no—
236C2×D4×C107C2×D411yescharacteristic
237C22×C4×C107—21no—
238C22×C4×C107—21no—
239C22×C4×C107—21no—
240C22×C4×C107—21no—
241C22×C4×C107—21no—
242C22×C4×C107—21no—
243C22×C4×C107—21no—
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—81no—
248C22×C4×C107C2×D411yescharacteristic
249C22×C4×C107C2×D411yescharacteristic
250C22×C4×C107C2×D411yescharacteristic
251C22×C4×C107C2×D411yescharacteristic
252C22×C4×C107C2×D411yescharacteristic
253C22×C4×C107C2×D411yescharacteristic
254C22×C4×C107C2×D411yescharacteristic
255C22×C4×C107C2×D411yescharacteristic
256C22×C4×C107C2411yescharacteristic
257SD16×C107—81no—
258SD16×C107—81no—
259SD16×C107—81no—
260D8×C107—81no—
261M16×C107—81no—
262C2×C8×C107—21no—
263C2×C8×C107—21no—
264C2×C8×C107—21no—
265C2×C8×C107—21no—
266C2×C8×C107—81no—
267C4⋊C4×C107—21no—
268C4⋊C4×C107—21no—
269C4⋊C4×C107—21no—
270C4⋊C4×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—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—21no—
291C4⋊C4×C107—21no—
292C4⋊C4×C107—81no—
293C4⋊C4×C107C2×D411yescharacteristic
294C4⋊C4×C107C2×D411yescharacteristic
295C4⋊C4×C107C2×D411yescharacteristic
296C4⋊C4×C107C2×D411yescharacteristic
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—21no—
320C22⋊C4×C107—42no—
321C22⋊C4×C107—42no—
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—21no—
331C42×C107—21no—
332C42×C107—81no—
333C23×C107—21no—
334C23×C107—21no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—21no—
339C23×C107—41no—
340C23×C107—41no—
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#12011yescharacteristic
351C23×C107#12011yescharacteristic
352C23×C107C22×D411yescharacteristic
353Q8×C107—41no—
354Q8×C107—41no—
355Q8×C107—41no—
356Q8×C107—81no—
357Q8×C107—81no—
358Q8×C107—81no—
359D4×C107—41no—
360D4×C107—41no—
361D4×C107—41no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—42no—
365D4×C107—42no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—81no—
369D4×C107—81no—
370D4×C107—81no—
371D4×C107—81no—
372D4×C107—84no—
373D4×C107—82no—
374D4×C107—82no—
375C2×C4×C107—22no—
376C2×C4×C107—21no—
377C2×C4×C107—21no—
378C2×C4×C107—21no—
379C2×C4×C107—21no—
380C2×C4×C107—21no—
381C2×C4×C107—21no—
382C2×C4×C107—21no—
383C2×C4×C107—21no—
384C2×C4×C107—21no—
385C2×C4×C107—21no—
386C2×C4×C107—21no—
387C2×C4×C107—21no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—42no—
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—81no—
406C2×C4×C107—81no—
407C2×C4×C107—81no—
408C2×C4×C107—81no—
409C2×C4×C107—81no—
410C2×C4×C107—81no—
411C2×C4×C107#12011yescharacteristic
412C2×C4×C107#12011yescharacteristic
413C2×C4×C107C22×D411yescharacteristic
414C2×C4×C107C22×D411yescharacteristic
415C8×C107—41no—
416C8×C107—41no—
417C8×C107—41no—
418C8×C107—41no—
419C22×C107—21no—
420C22×C107—21no—
421C22×C107—21no—
422C22×C107—21no—
423C22×C107—21no—
424C22×C107—21no—
425C22×C107—21no—
426C22×C107—21no—
427C22×C107—41no—
428C22×C107—41no—
429C22×C107—41no—
430C22×C107—41no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—81no—
434C22×C107—81no—
435C22×C107—81no—
436C22×C107—81no—
437C22×C107—81no—
438C22×C107—81no—
439C22×C107—81no—
440C22×C107—81no—
441C22×C107—81no—
442C22×C107—81no—
443C22×C107—81no—
444C22×C107C2×#12011yescharacteristic
445C22×C107#57711yescharacteristic
446C22×C107#57711yescharacteristic
447C4×C107—21no—
448C4×C107—21no—
449C4×C107—21no—
450C4×C107—21no—
451C4×C107—42no—
452C4×C107—41no—
453C4×C107—41no—
454C4×C107—41no—
455C4×C107—41no—
456C4×C107—41no—
457C4×C107—41no—
458C4×C107—41no—
459C4×C107—41no—
460C4×C107—41no—
461C4×C107—41no—
462C4×C107—81no—
463C4×C107—81no—
464#18416C10711yesmaximal, characteristic, direct product factor, Sylow
465C2×C107—21no—
466C2×C107—21no—
467C2×C107—41no—
468C2×C107—41no—
469C2×C107—81no—
470C2×C107—81no—
471C2×C107—161no—
472C2×C107#301011yescharacteristic
473C2×C107#301811yescharacteristic
474C2×C107#302611yescharacteristic
475#3535C2×C10711yescharacteristic, complemented
476#3194C2×C10711yescharacteristic, complemented
477#3187C2×C10711yescharacteristic, complemented
478#2661C2×C10711yescharacteristic, complemented
479#1612C2×C10711yescharacteristic, complemented
480#1611C2×C10711yescharacteristic, complemented
481#1609C2×C10711yescharacteristic, complemented
482#1608C2×C10711yescharacteristic, complemented
483#1600C2×C10711yescharacteristic, complemented
484#1599C2×C10711yescharacteristic, complemented
485#1597C2×C10711yescharacteristic, complemented
486#1596C2×C10711yescharacteristic, complemented
487#1508C2×C10711yescharacteristic, complemented
488#1501C2×C10711yescharacteristic, complemented
489#1468C2×C10711yescharacteristic, complemented
490C107#1841611yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C10711yescharacteristic
500#543C22×C10711yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C10711yescharacteristic
505#538C22×C10711yescharacteristic
506#536—21no—
507#525C22×C10711yescharacteristic
508C2×#123C22×C10711yescharacteristic
509C2×C22⋊Q8C22×C10711yescharacteristic
510C2×#121C22×C10711yescharacteristic
511#483C22×C10711yescharacteristic
512#483C22×C10711yescharacteristic
513#483C22×C10711yescharacteristic
514#482—21no—
515#481—21no—
516#480C22×C10711yescharacteristic
517#469—21no—
518#468—21no—
519#465—21no—
520#465—21no—
521#450C22×C10711yescharacteristic
522#450C22×C10711yescharacteristic
523#450C22×C10711yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C10711yescharacteristic
527#407C22×C10711yescharacteristic
528C2×C22⋊C8C22×C10711yescharacteristic
529#398C22×C10711yescharacteristic
530#397C22×C10711yescharacteristic
531#394—21no—
532#394C22×C10711yescharacteristic
533#392—21no—
534#392C22×C10711yescharacteristic
535#390—21no—
536#388—21no—
537C4×C22⋊C4C22×C10711yescharacteristic
538#328C22×C10711yescharacteristic
539#328C22×C10711yescharacteristic
540#328C22×C10711yescharacteristic
541#328C22×C10711yescharacteristic
542#328C22×C10711yescharacteristic
543#328C22×C10711yescharacteristic
544#327C22×C10711yescharacteristic
545#327C22×C10711yescharacteristic
546#324C22×C10711yescharacteristic
547#324C22×C10711yescharacteristic
548#323C22×C10711yescharacteristic
549#323C22×C10711yescharacteristic
550C2×#41—21no—
551C2×#41D4×C10711yescharacteristic, complemented
552C22×Q8D4×C10711yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C10711yescharacteristic
556C22×D4C23×C10711yescharacteristic
557C23×C4C23×C10711yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C10711yescharacteristic, complemented
611C22⋊Q8D4×C10711yescharacteristic, complemented
612C22⋊Q8D4×C10711yescharacteristic, complemented
613C22⋊Q8C23×C10711yescharacteristic
614C22⋊Q8C23×C10711yescharacteristic
615C22⋊Q8C23×C10711yescharacteristic
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#121D4×C10711yescharacteristic, complemented
625#121C23×C10711yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C10711yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C10711yescharacteristic
644C2×C4⋊C4D4×C10711yescharacteristic, complemented
645C2×C4⋊C4C23×C10711yescharacteristic
646C2×C4⋊C4C23×C10711yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C10711yescharacteristic
656C2×C22⋊C4D4×C10711yescharacteristic
657C2×C22⋊C4C23×C10711yescharacteristic
658C2×C42—21no—
659#107—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10711yescharacteristic
674C22⋊C8C23×C10711yescharacteristic
675C22⋊C8C23×C10711yescharacteristic
676C22⋊C8C23×C10711yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C10711yescharacteristic
680#95C23×C10711yescharacteristic
681C24—21no—
682C24C2×D4×C10711yescharacteristic
683C24C2×D4×C10711yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C10711yescharacteristic
691C2×Q8C2×D4×C10711yescharacteristic
692C2×Q8C2×D4×C10711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C10711yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C10711yescharacteristic
724C22×C4C2×D4×C10711yescharacteristic
725C22×C4C2×D4×C10711yescharacteristic
726C22×C4C2×D4×C10711yescharacteristic
727C22×C4C2×D4×C10711yescharacteristic
728C22×C4C2×D4×C10711yescharacteristic
729C22×C4C2×D4×C10711yescharacteristic
730C22×C4C2×D4×C10711yescharacteristic
731C22×C4C24×C10711yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—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—81no—
768C4⋊C4C2×D4×C10711yescharacteristic
769C4⋊C4C2×D4×C10711yescharacteristic
770C4⋊C4C2×D4×C10711yescharacteristic
771C4⋊C4C2×D4×C10711yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
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—42no—
796C22⋊C4—42no—
797C22⋊C4—41no—
798C22⋊C4—41no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—81no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C10711yescharacteristic
826C23#120×C10711yescharacteristic
827C23C22×D4×C10711yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—84no—
848D4—82no—
849D4—82no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C10711yescharacteristic
887C2×C4#120×C10711yescharacteristic
888C2×C4C22×D4×C10711yescharacteristic
889C2×C4C22×D4×C10711yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C10711yescharacteristic
920C22#577×C10711yescharacteristic
921C22#577×C10711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C107×#301011yescharacteristic
947C2C107×#301811yescharacteristic
948C2C107×#302611yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3535C2semidirect
2. C107×#3194C2semidirect
3. C107×#3187C2semidirect
4. C107×#2661C2semidirect
5. C107×#1612C2semidirect
6. C107×#1611C2semidirect
7. C107×#1609C2semidirect
8. C107×#1608C2semidirect
9. C107×#1600C2semidirect
10. C107×#1599C2semidirect
11. C107×#1597C2semidirect
12. C107×#1596C2semidirect
13. C107×#1508C2semidirect
14. C107×#1501C2semidirect
15. C107×#1468C2semidirect
76. C2×#41×C107D4semidirect
77. C22×Q8×C107D4semidirect
135. C22⋊Q8×C107D4semidirect
136. C22⋊Q8×C107D4semidirect
137. C22⋊Q8×C107D4semidirect
149. #121×C107D4semidirect
164. #117×C107D4semidirect
169. C2×C4⋊C4×C107D4semidirect
464. #18416C107direct (N × H)
475. #3535C2×C107semidirect
476. #3194C2×C107semidirect
477. #3187C2×C107semidirect
478. #2661C2×C107semidirect
479. #1612C2×C107semidirect
480. #1611C2×C107semidirect
481. #1609C2×C107semidirect
482. #1608C2×C107semidirect
483. #1600C2×C107semidirect
484. #1599C2×C107semidirect
485. #1597C2×C107semidirect
486. #1596C2×C107semidirect
487. #1508C2×C107semidirect
488. #1501C2×C107semidirect
489. #1468C2×C107semidirect
490. C107#18416direct (N × H)
551. C2×#41D4×C107semidirect
552. C22×Q8D4×C107semidirect
610. C22⋊Q8D4×C107semidirect
611. C22⋊Q8D4×C107semidirect
612. C22⋊Q8D4×C107semidirect
624. #121D4×C107semidirect
639. #117D4×C107semidirect
644. C2×C4⋊C4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35352
C107×#31942
C107×#31872
C107×#26612
C107×#16122
C107×#16112
C107×#16092
C107×#16082
C107×#16002
C107×#15992
C107×#15972
C107×#15962
C107×#15082
C107×#15012
C107×#14682
#18416107