Finite Group Databasebeta

← C107×#9938 #41035902

Subgroups — C107×#9938 #41035902

Order 27392.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3006C211yesmaximal, characteristic, complemented
2C107×#2539C211yesmaximal, characteristic, complemented
3C107×#2404C211yesmaximal, characteristic, complemented
4C107×#1789C211yesmaximal, characteristic, complemented
5C107×#1510C211yesmaximal, characteristic, complemented
6C107×#1462C211yesmaximal, characteristic, complemented
7C107×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C107C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C107—21no—
10C2×#123×C107—21no—
11C2×#121×C107C2211yescharacteristic
12C2×#120×C107—21no—
13C2×#120×C107—21no—
14C22×C22⋊C4×C107C2211yescharacteristic
15#449×C107—22no—
16#448×C107—21no—
17#447×C107—21no—
18C2×#104×C107—22no—
19#417×C107—21no—
20#407×C107C2211yescharacteristic
21#407×C107C2211yescharacteristic
22#399×C107—21no—
23#393×C107—21no—
24#392×C107—21no—
25#392×C107—21no—
26#390×C107—22no—
27#386×C107—21no—
28#386×C107—22no—
29#381×C107C2211yescharacteristic
30C4×C22⋊C4×C107C2211yescharacteristic
31#327×C107—22no—
32#323×C107—22no—
33C25×C107D411yescharacteristic
34C2×#41×C107—21no—
35C2×#41×C107—21no—
36C2×#41×C107—21no—
37C2×#41×C107—21no—
38C2×#41×C107—44no—
39C22×Q8×C107D411yescharacteristic, complemented
40C22×D4×C107—21no—
41C22×D4×C107—21no—
42C22×D4×C107—22no—
43C22×D4×C107—22no—
44C22×D4×C107D411yescharacteristic, complemented
45C22×D4×C107D411yescharacteristic, complemented
46C23×C4×C107—21no—
47C23×C4×C107D411yescharacteristic
48C23×C4×C107C2311yescharacteristic
49AGL(1,ℤ/8)×C107—44no—
50C2×SD16×C107—22no—
51C2×D8×C107—22no—
52C2×M16×C107—21no—
53C2×M16×C107—21no—
54#123×C107—44no—
55#121×C107—21no—
56#121×C107—21no—
57#121×C107—21no—
58#121×C107—21no—
59#120×C107—44no—
60#120×C107—44no—
61C2×C4⋊C4×C107—22no—
62C2×C4⋊C4×C107D411yescharacteristic, complemented
63C2×C22⋊C4×C107—21no—
64C2×C22⋊C4×C107—22no—
65C2×C22⋊C4×C107—22no—
66C2×C22⋊C4×C107—22no—
67C2×C22⋊C4×C107—21no—
68C2×C22⋊C4×C107—21no—
69C2×C22⋊C4×C107—21no—
70C2×C22⋊C4×C107—21no—
71C2×C22⋊C4×C107—21no—
72C2×C22⋊C4×C107—21no—
73C2×C22⋊C4×C107—21no—
74C2×C22⋊C4×C107—21no—
75C2×C22⋊C4×C107—22no—
76C2×C42×C107D412yescomplemented
77#104×C107—44no—
78#103×C107—22no—
79#102×C107—22no—
80C22⋊C8×C107—21no—
81C22⋊C8×C107—21no—
82C22⋊C8×C107—21no—
83C22⋊C8×C107D412yescomplemented
84#95×C107—22no—
85#95×C107—21no—
86#95×C107—21no—
87#95×C107D412yescomplemented
88C24×C107—21no—
89C24×C107—21no—
90C24×C107—21no—
91C24×C107—21no—
92C24×C107—21no—
93C24×C107—42no—
94C24×C107—42no—
95C24×C107—42no—
96C24×C107C2×D411yescharacteristic
97#41×C107—24no—
98#41×C107—24no—
99#41×C107—42no—
100#41×C107—42no—
101#41×C107—42no—
102#41×C107—42no—
103#41×C107—42no—
104#41×C107—42no—
105C2×Q8×C107—21no—
106C2×Q8×C107—21no—
107C2×Q8×C107—42no—
108C2×D4×C107—24no—
109C2×D4×C107—21no—
110C2×D4×C107—21no—
111C2×D4×C107—21no—
112C2×D4×C107—21no—
113C2×D4×C107—42no—
114C2×D4×C107—44no—
115C2×D4×C107—42no—
116C2×D4×C107—42no—
117C2×D4×C107—41no—
118C2×D4×C107—41no—
119C2×D4×C107—42no—
120C2×D4×C107—44no—
121C2×D4×C107—42no—
122C2×D4×C107—44no—
123C2×D4×C107—44no—
124C2×D4×C107—41no—
125C2×D4×C107—41no—
126C2×D4×C107—82no—
127C2×D4×C107—82no—
128C22×C4×C107—21no—
129C22×C4×C107—22no—
130C22×C4×C107—22no—
131C22×C4×C107—21no—
132C22×C4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—42no—
136C22×C4×C107—42no—
137C22×C4×C107—42no—
138C22×C4×C107—41no—
139C22×C4×C107—41no—
140C22×C4×C107—42no—
141C22×C4×C107C2×D411yescharacteristic
142C22×C4×C107C2×D411yescharacteristic
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107#4111yescharacteristic
147SD16×C107—44no—
148D8×C107—44no—
149M16×C107—42no—
150M16×C107—42no—
151C2×C8×C107—22no—
152C2×C8×C107—41no—
153C4⋊C4×C107—21no—
154C4⋊C4×C107—21no—
155C4⋊C4×C107—44no—
156C22⋊C4×C107—24no—
157C22⋊C4×C107—44no—
158C22⋊C4×C107—44no—
159C22⋊C4×C107—44no—
160C22⋊C4×C107—42no—
161C22⋊C4×C107—41no—
162C22⋊C4×C107—41no—
163C22⋊C4×C107—41no—
164C22⋊C4×C107—41no—
165C22⋊C4×C107—41no—
166C22⋊C4×C107—41no—
167C22⋊C4×C107—82no—
168C42×C107—42no—
169C23×C107—22no—
170C23×C107—22no—
171C23×C107—22no—
172C23×C107—22no—
173C23×C107—22no—
174C23×C107—22no—
175C23×C107—41no—
176C23×C107—42no—
177C23×C107—42no—
178C23×C107—41no—
179C23×C107—42no—
180C23×C107—41no—
181C23×C107—41no—
182C23×C107—41no—
183C23×C107—41no—
184C23×C107—41no—
185C23×C107—42no—
186C23×C107—41no—
187C23×C107—41no—
188C23×C107—42no—
189C23×C107—42no—
190C23×C107—42no—
191C23×C107—41no—
192C23×C107—42no—
193C23×C107—81no—
194C23×C107—81no—
195C23×C107—88no—
196C23×C107#12011yescharacteristic
197C23×C107#12011yescharacteristic
198C23×C107#12111yescharacteristic
199Q8×C107—22no—
200Q8×C107—22no—
201Q8×C107—41no—
202Q8×C107—41no—
203D4×C107—22no—
204D4×C107—22no—
205D4×C107—41no—
206D4×C107—41no—
207D4×C107—42no—
208D4×C107—44no—
209D4×C107—44no—
210D4×C107—81no—
211D4×C107—88no—
212D4×C107—82no—
213D4×C107—88no—
214D4×C107—82no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—24no—
218C2×C4×C107—22no—
219C2×C4×C107—41no—
220C2×C4×C107—41no—
221C2×C4×C107—41no—
222C2×C4×C107—41no—
223C2×C4×C107—44no—
224C2×C4×C107—44no—
225C2×C4×C107—41no—
226C2×C4×C107—42no—
227C2×C4×C107—41no—
228C2×C4×C107—42no—
229C2×C4×C107—42no—
230C2×C4×C107—41no—
231C2×C4×C107—42no—
232C2×C4×C107—41no—
233C2×C4×C107—42no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—42no—
237C2×C4×C107—42no—
238C2×C4×C107—81no—
239C2×C4×C107#12011yescharacteristic
240C2×C4×C107#12111yescharacteristic
241C2×C4×C107#12111yescharacteristic
242C2×C4×C107#12711yescharacteristic
243C8×C107—42no—
244C8×C107—81no—
245C22×C107—21no—
246C22×C107—21no—
247C22×C107—21no—
248C22×C107—21no—
249C22×C107—21no—
250C22×C107—21no—
251C22×C107—21no—
252C22×C107—44no—
253C22×C107—44no—
254C22×C107—44no—
255C22×C107—44no—
256C22×C107—42no—
257C22×C107—42no—
258C22×C107—82no—
259C22×C107—82no—
260C22×C107—82no—
261C22×C107—82no—
262C22×C107—82no—
263C22×C107—82no—
264C22×C107—82no—
265C22×C107—81no—
266C22×C107—81no—
267C22×C107—81no—
268C22×C107—81no—
269C22×C107—81no—
270C22×C107—81no—
271C22×C107—81no—
272C22×C107#39211yescharacteristic
273C22×C107#45312yes—
274C22×C107B(4,𝔽2)12yes—
275C4×C107—21no—
276C4×C107—21no—
277C4×C107—21no—
278C4×C107—21no—
279C4×C107—44no—
280C4×C107—42no—
281C4×C107—82no—
282C4×C107—81no—
283C4×C107—81no—
284#9938C10711yesmaximal, characteristic, direct product factor, Sylow
285C2×C107—22no—
286C2×C107—22no—
287C2×C107—41no—
288C2×C107—82no—
289C2×C107—82no—
290C2×C107—161no—
291C2×C107#200211yescharacteristic
292C2×C107#201011yescharacteristic
293C2×C107#202111yescharacteristic
294#3006C2×C10711yescharacteristic, complemented
295#2539C2×C10711yescharacteristic, complemented
296#2404C2×C10711yescharacteristic, complemented
297#1789C2×C10711yescharacteristic, complemented
298#1510C2×C10711yescharacteristic, complemented
299#1462C2×C10711yescharacteristic, complemented
300#1284C2×C10711yescharacteristic, complemented
301C107#993811yescharacteristic, direct product factor, Sylow
302C22×#41C22×C10711yescharacteristic
303C2×AGL(1,ℤ/8)—21no—
304C2×#123—21no—
305C2×#121C22×C10711yescharacteristic
306C2×#120—21no—
307C2×#120—21no—
308C22×C22⋊C4C22×C10711yescharacteristic
309#449—22no—
310#448—21no—
311#447—21no—
312C2×#104—22no—
313#417—21no—
314#407C22×C10711yescharacteristic
315#407C22×C10711yescharacteristic
316#399—21no—
317#393—21no—
318#392—21no—
319#392—21no—
320#390—22no—
321#386—21no—
322#386—22no—
323#381C22×C10711yescharacteristic
324C4×C22⋊C4C22×C10711yescharacteristic
325#327—22no—
326#323—22no—
327C25D4×C10711yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C10711yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C10711yescharacteristic, complemented
339C22×D4D4×C10711yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C10711yescharacteristic
342C23×C4C23×C10711yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C10711yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C10712yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C10712yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C10712yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C10711yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C10711yescharacteristic
436C22×C4C2×D4×C10711yescharacteristic
437C22×C4C2×D4×C10711yescharacteristic
438C22×C4C2×D4×C10711yescharacteristic
439C22×C4C2×D4×C10711yescharacteristic
440C22×C4#41×C10711yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C10711yescharacteristic
491C23#120×C10711yescharacteristic
492C23#121×C10711yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C10711yescharacteristic
534C2×C4#121×C10711yescharacteristic
535C2×C4#121×C10711yescharacteristic
536C2×C4#127×C10711yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22#392×C10711yescharacteristic
567C22#453×C10712yes—
568C22B(4,𝔽2)×C10712yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C107×#200211yescharacteristic
585C2C107×#201011yescharacteristic
586C2C107×#202111yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC23×C4C23×C107
LCSG ▷ C23×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×#3006C2semidirect
2. C107×#2539C2semidirect
3. C107×#2404C2semidirect
4. C107×#1789C2semidirect
5. C107×#1510C2semidirect
6. C107×#1462C2semidirect
7. C107×#1284C2semidirect
39. C22×Q8×C107D4semidirect
44. C22×D4×C107D4semidirect
45. C22×D4×C107D4semidirect
62. C2×C4⋊C4×C107D4semidirect
76. C2×C42×C107D4semidirect
83. C22⋊C8×C107D4semidirect
87. #95×C107D4semidirect
284. #9938C107direct (N × H)
294. #3006C2×C107semidirect
295. #2539C2×C107semidirect
296. #2404C2×C107semidirect
297. #1789C2×C107semidirect
298. #1510C2×C107semidirect
299. #1462C2×C107semidirect
300. #1284C2×C107semidirect
301. C107#9938direct (N × H)
333. C22×Q8D4×C107semidirect
338. C22×D4D4×C107semidirect
339. C22×D4D4×C107semidirect
356. C2×C4⋊C4D4×C107semidirect
370. C2×C42D4×C107semidirect
377. C22⋊C8D4×C107semidirect
381. #95D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30062
C107×#25392
C107×#24042
C107×#17892
C107×#15102
C107×#14622
C107×#12842
#9938107