Finite Group Databasebeta

← C107×#13376 #41039340

Subgroups — C107×#13376 #41039340

Order 27392.

640 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2748C211yesmaximal, characteristic, complemented
2C107×#1792C211yesmaximal, characteristic
3C107×#1790C211yesmaximal, characteristic
4C107×#1790C211yesmaximal, characteristic
5C107×#1393C211yesmaximal, characteristic, complemented
6C107×#1390C211yesmaximal, characteristic, complemented
7C107×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C107C2211yescharacteristic
9C2×#104×C107—21no—
10#417×C107—21no—
11C2×#100×C107C2211yescharacteristic
12C2×#99×C107—21no—
13C2×#99×C107—21no—
14C2×#99×C107C2211yescharacteristic
15C2×#99×C107C2211yescharacteristic
16#399×C107—21no—
17#398×C107—21no—
18#396×C107—21no—
19#390×C107C2211yescharacteristic
20#387×C107—21no—
21#386×C107—21no—
22#386×C107—21no—
23#386×C107C2211yescharacteristic
24#386×C107C2211yescharacteristic
25#385×C107—21no—
26#380×C107—21no—
27H(5,𝔽2)×C107—21no—
28H(5,𝔽2)×C107—21no—
29H(5,𝔽2)×C107—21no—
30H(5,𝔽2)×C107—42no—
31H(5,𝔽2)×C107Q812yes—
32C2×#41×C107—21no—
33C2×#41×C107—41no—
34C22×D4×C107—21no—
35C22×D4×C107—21no—
36C22×D4×C107—41no—
37C22×D4×C107C2311yescharacteristic
38C23×C4×C107D411yescharacteristic
39C23×C4×C107D411yescharacteristic
40C2×M16×C107—21no—
41C2×C4⋊C4×C107—21no—
42C2×C4⋊C4×C107—21no—
43C2×C4⋊C4×C107—21no—
44C2×C4⋊C4×C107—21no—
45C2×C4⋊C4×C107—21no—
46C2×C4⋊C4×C107D411yescharacteristic
47C2×C22⋊C4×C107—21no—
48C2×C22⋊C4×C107—21no—
49C2×C22⋊C4×C107—21no—
50C2×C22⋊C4×C107—21no—
51C2×C22⋊C4×C107—21no—
52C2×C22⋊C4×C107—21no—
53C2×C22⋊C4×C107—41no—
54C2×C22⋊C4×C107—41no—
55C2×C22⋊C4×C107D411yescharacteristic
56C2×C22⋊C4×C107D411yescharacteristic
57C2×C42×C107D411yescharacteristic
58#104×C107—42no—
59#103×C107—41no—
60#102×C107—41no—
61#100×C107—21no—
62#100×C107—21no—
63#99×C107—21no—
64#99×C107—21no—
65#99×C107—21no—
66#99×C107—21no—
67#99×C107—42no—
68#99×C107—42no—
69#95×C107—21no—
70#95×C107—21no—
71#95×C107—21no—
72#95×C107—21no—
73#95×C107—21no—
74#95×C107—41no—
75#95×C107—41no—
76C24×C107—21no—
77C24×C107—21no—
78C24×C107C2×D411yescharacteristic
79C24×C107C2×D411yescharacteristic
80#41×C107—22no—
81#41×C107—22no—
82#41×C107—42no—
83#41×C107—41no—
84#41×C107—42no—
85#41×C107—42no—
86#41×C107—42no—
87#41×C107—41no—
88C2×Q8×C107—21no—
89C2×D4×C107—21no—
90C2×D4×C107—22no—
91C2×D4×C107—22no—
92C2×D4×C107—22no—
93C2×D4×C107—22no—
94C2×D4×C107—41no—
95C2×D4×C107—41no—
96C2×D4×C107—42no—
97C2×D4×C107—42no—
98C2×D4×C107—41no—
99C2×D4×C107—41no—
100C2×D4×C107—41no—
101C2×D4×C107—41no—
102C2×D4×C107—42no—
103C2×D4×C107—42no—
104C2×D4×C107—41no—
105C2×D4×C107—41no—
106C2×D4×C107—41no—
107C2×D4×C107C2×Q811yescharacteristic
108C2×D4×C107#4111yescharacteristic
109C2×D4×C107#4111yescharacteristic
110C2×D4×C107#4111yescharacteristic
111C22×C4×C107—21no—
112C22×C4×C107—21no—
113C22×C4×C107—21no—
114C22×C4×C107—21no—
115C22×C4×C107—21no—
116C22×C4×C107—21no—
117C22×C4×C107—21no—
118C22×C4×C107—21no—
119C22×C4×C107—41no—
120C22×C4×C107—42no—
121C22×C4×C107—41no—
122C22×C4×C107—41no—
123C22×C4×C107—41no—
124C22×C4×C107—41no—
125C22×C4×C107—81no—
126C22×C4×C107C2×D411yescharacteristic
127M16×C107—41no—
128M16×C107—41no—
129C2×C8×C107—41no—
130C4⋊C4×C107—41no—
131C4⋊C4×C107—42no—
132C4⋊C4×C107—81no—
133C4⋊C4×C107—81no—
134C4⋊C4×C107—81no—
135C4⋊C4×C107—81no—
136C22⋊C4×C107—42no—
137C22⋊C4×C107—41no—
138C22⋊C4×C107—41no—
139C22⋊C4×C107—41no—
140C22⋊C4×C107—41no—
141C22⋊C4×C107—41no—
142C22⋊C4×C107—41no—
143C22⋊C4×C107—81no—
144C22⋊C4×C107—81no—
145C22⋊C4×C107—81no—
146C22⋊C4×C107—82no—
147C22⋊C4×C107—82no—
148C42×C107—41no—
149C23×C107—21no—
150C23×C107—21no—
151C23×C107—21no—
152C23×C107—21no—
153C23×C107—22no—
154C23×C107—22no—
155C23×C107—41no—
156C23×C107—41no—
157C23×C107—41no—
158C23×C107—41no—
159C23×C107—41no—
160C23×C107—41no—
161C23×C107—41no—
162C23×C107—81no—
163C23×C107—81no—
164C23×C107—81no—
165C23×C107—81no—
166C23×C107#12011yescharacteristic
167C23×C107C22⋊Q811yescharacteristic
168C23×C107C22⋊Q811yescharacteristic
169C23×C107#12411yescharacteristic
170C23×C107#12411yescharacteristic
171Q8×C107—22no—
172Q8×C107—41no—
173D4×C107—22no—
174D4×C107—41no—
175D4×C107—41no—
176D4×C107—41no—
177D4×C107—41no—
178D4×C107—41no—
179D4×C107—42no—
180D4×C107—42no—
181D4×C107—42no—
182D4×C107—42no—
183D4×C107—42no—
184D4×C107—42no—
185C2×C4×C107—21no—
186C2×C4×C107—21no—
187C2×C4×C107—22no—
188C2×C4×C107—22no—
189C2×C4×C107—22no—
190C2×C4×C107—42no—
191C2×C4×C107—42no—
192C2×C4×C107—41no—
193C2×C4×C107—41no—
194C2×C4×C107—41no—
195C2×C4×C107—41no—
196C2×C4×C107—41no—
197C2×C4×C107—42no—
198C2×C4×C107—41no—
199C2×C4×C107—41no—
200C2×C4×C107—41no—
201C2×C4×C107—41no—
202C2×C4×C107—41no—
203C2×C4×C107—41no—
204C2×C4×C107—41no—
205C2×C4×C107—41no—
206C2×C4×C107—41no—
207C2×C4×C107—41no—
208C2×C4×C107—42no—
209C2×C4×C107—41no—
210C2×C4×C107—41no—
211C2×C4×C107—41no—
212C2×C4×C107—41no—
213C2×C4×C107—41no—
214C2×C4×C107—81no—
215C2×C4×C107—81no—
216C2×C4×C107—81no—
217C2×C4×C107—81no—
218C2×C4×C107—81no—
219C2×C4×C107—81no—
220C2×C4×C107—81no—
221C2×C4×C107—81no—
222C2×C4×C107C22⋊Q811yescharacteristic
223C2×C4×C107#12411yescharacteristic
224C8×C107—81no—
225C22×C107—21no—
226C22×C107—21no—
227C22×C107—21no—
228C22×C107—21no—
229C22×C107—21no—
230C22×C107—21no—
231C22×C107—41no—
232C22×C107—41no—
233C22×C107—41no—
234C22×C107—41no—
235C22×C107—41no—
236C22×C107—41no—
237C22×C107—41no—
238C22×C107—41no—
239C22×C107—42no—
240C22×C107—81no—
241C22×C107—81no—
242C22×C107—82no—
243C22×C107—82no—
244C22×C107—81no—
245C22×C107—81no—
246C22×C107—161no—
247C22×C107—161no—
248C22×C107#39311yescharacteristic
249C22×C107B(4,𝔽2)11yescharacteristic
250C22×C107B(4,𝔽2)11yescharacteristic
251C4×C107—21no—
252C4×C107—21no—
253C4×C107—42no—
254C4×C107—42no—
255C4×C107—81no—
256C4×C107—81no—
257C4×C107—81no—
258C4×C107—81no—
259C4×C107—81no—
260C4×C107—161no—
261C4×C107—161no—
262#13376C10711yesmaximal, characteristic, direct product factor, Sylow
263C2×C107—21no—
264C2×C107—21no—
265C2×C107—41no—
266C2×C107—41no—
267C2×C107—41no—
268C2×C107—41no—
269C2×C107—82no—
270C2×C107#202911yescharacteristic
271C2×C107#219711yescharacteristic
272C2×C107#220011yescharacteristic
273#2748C2×C10711yescharacteristic, complemented
274#1792C2×C10711yescharacteristic
275#1790C2×C10711yescharacteristic
276#1790C2×C10711yescharacteristic
277#1393C2×C10711yescharacteristic, complemented
278#1390C2×C10711yescharacteristic, complemented
279#1390C2×C10711yescharacteristic, complemented
280C107#1337611yescharacteristic, direct product factor, Sylow
281C2×H(5,𝔽2)C22×C10711yescharacteristic
282C2×#104—21no—
283#417—21no—
284C2×#100C22×C10711yescharacteristic
285C2×#99—21no—
286C2×#99—21no—
287C2×#99C22×C10711yescharacteristic
288C2×#99C22×C10711yescharacteristic
289#399—21no—
290#398—21no—
291#396—21no—
292#390C22×C10711yescharacteristic
293#387—21no—
294#386—21no—
295#386—21no—
296#386C22×C10711yescharacteristic
297#386C22×C10711yescharacteristic
298#385—21no—
299#380—21no—
300H(5,𝔽2)—21no—
301H(5,𝔽2)—21no—
302H(5,𝔽2)—21no—
303H(5,𝔽2)—42no—
304H(5,𝔽2)Q8×C10712yes—
305C2×#41—21no—
306C2×#41—41no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4—41no—
310C22×D4C23×C10711yescharacteristic
311C23×C4D4×C10711yescharacteristic
312C23×C4D4×C10711yescharacteristic
313C2×M16—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C10711yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4D4×C10711yescharacteristic
329C2×C22⋊C4D4×C10711yescharacteristic
330C2×C42D4×C10711yescharacteristic
331#104—42no—
332#103—41no—
333#102—41no—
334#100—21no—
335#100—21no—
336#99—21no—
337#99—21no—
338#99—21no—
339#99—21no—
340#99—42no—
341#99—42no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—41no—
348#95—41no—
349C24—21no—
350C24—21no—
351C24C2×D4×C10711yescharacteristic
352C24C2×D4×C10711yescharacteristic
353#41—22no—
354#41—22no—
355#41—42no—
356#41—41no—
357#41—42no—
358#41—42no—
359#41—42no—
360#41—41no—
361C2×Q8—21no—
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—42no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4C2×Q8×C10711yescharacteristic
381C2×D4#41×C10711yescharacteristic
382C2×D4#41×C10711yescharacteristic
383C2×D4#41×C10711yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—81no—
399C22×C4C2×D4×C10711yescharacteristic
400M16—41no—
401M16—41no—
402C2×C8—41no—
403C4⋊C4—41no—
404C4⋊C4—42no—
405C4⋊C4—81no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C4⋊C4—81no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C22⋊C4—82no—
420C22⋊C4—82no—
421C42—41no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—81no—
436C23—81no—
437C23—81no—
438C23—81no—
439C23#120×C10711yescharacteristic
440C23C22⋊Q8×C10711yescharacteristic
441C23C22⋊Q8×C10711yescharacteristic
442C23#124×C10711yescharacteristic
443C23#124×C10711yescharacteristic
444Q8—22no—
445Q8—41no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4C22⋊Q8×C10711yescharacteristic
496C2×C4#124×C10711yescharacteristic
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—82no—
516C22—82no—
517C22—81no—
518C22—81no—
519C22—161no—
520C22—161no—
521C22#393×C10711yescharacteristic
522C22B(4,𝔽2)×C10711yescharacteristic
523C22B(4,𝔽2)×C10711yescharacteristic
524C4—21no—
525C4—21no—
526C4—42no—
527C4—42no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—161no—
534C4—161no—
535C2—21no—
536C2—21no—
537C2—41no—
538C2—41no—
539C2—41no—
540C2—41no—
541C2—82no—
542C2C107×#202911yescharacteristic
543C2C107×#219711yescharacteristic
544C2C107×#220011yescharacteristic
subgroupG/H
center, socleC22×C107B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C107
prime radicalC2×H(5,𝔽2)×C107C22
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2748C2semidirect
5. C107×#1393C2semidirect
6. C107×#1390C2semidirect
7. C107×#1390C2semidirect
262. #13376C107direct (N × H)
273. #2748C2×C107semidirect
277. #1393C2×C107semidirect
278. #1390C2×C107semidirect
279. #1390C2×C107semidirect
280. C107#13376direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#27482
C107×#17922
C107×#17902
C107×#13932
C107×#13902
#13376107