Finite Group Databasebeta

← C107×#9520 #41035484

Subgroups — C107×#9520 #41035484

Order 27392.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3003C211yesmaximal, characteristic
2C107×#2976C211yesmaximal, characteristic, complemented
3C107×#1786C211yesmaximal, characteristic, complemented
4C107×#1783C211yesmaximal, characteristic, complemented
5C107×#1513C211yesmaximal, characteristic, complemented
6C107×#1305C211yesmaximal, characteristic, complemented
7C107×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C107C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C107—21no—
10#525×C107C2211yescharacteristic
11#450×C107—21no—
12#450×C107C412yescomplemented
13#447×C107—21no—
14#447×C107C412yescomplemented
15#436×C107—21no—
16#435×C107—21no—
17#435×C107—21no—
18C8×D4×C107—21no—
19#433×C107—21no—
20#418×C107—21no—
21C2×#102×C107—21no—
22C2×#102×C107—21no—
23C2×#100×C107—21no—
24C2×#100×C107—21no—
25#408×C107—21no—
26#407×C107C2211yescharacteristic
27#407×C107C2211yescharacteristic
28#407×C107C2211yescharacteristic
29C2×C22⋊C8×C107C2211yescharacteristic
30#380×C107C2211yescharacteristic
31#328×C107—21no—
32#327×C107—21no—
33C25×C107—21no—
34C2×#41×C107D411yescharacteristic
35C22×D4×C107—21no—
36C22×D4×C107—21no—
37C22×D4×C107—21no—
38C22×D4×C107—21no—
39C22×D4×C107—21no—
40C22×D4×C107—42no—
41C22×D4×C107—42no—
42C22×D4×C107C2×C412yes—
43C23×C4×C107C2311yescharacteristic
44AGL(1,ℤ/8)×C107—42no—
45AGL(1,ℤ/8)×C107—42no—
46C2×SD16×C107—22no—
47C2×D8×C107—22no—
48C2×M16×C107—21no—
49C2×M16×C107—21no—
50C2×M16×C107—21no—
51C2×M16×C107D411yescharacteristic
52C2×M16×C107D411yescharacteristic
53C22×C8×C107—21no—
54C22×C8×C107D411yescharacteristic
55C22×C8×C107D411yescharacteristic
56#123×C107—21no—
57C22⋊Q8×C107C2×C411yescharacteristic
58C22⋊Q8×C107D411yescharacteristic
59#121×C107C2×C411yescharacteristic
60#121×C107D411yescharacteristic
61#120×C107—21no—
62C4×D4×C107—21no—
63C4×D4×C107—21no—
64#117×C107D411yescharacteristic
65C2×C4⋊C4×C107—21no—
66C2×C22⋊C4×C107—21no—
67C4⋊C8×C107—21no—
68C4⋊C8×C107—21no—
69#102×C107—22no—
70#102×C107—22no—
71#102×C107—42no—
72#102×C107—42no—
73#100×C107—42no—
74#100×C107—42no—
75C22⋊C8×C107—21no—
76C22⋊C8×C107—21no—
77C22⋊C8×C107—21no—
78C22⋊C8×C107—21no—
79C22⋊C8×C107—21no—
80C22⋊C8×C107—21no—
81C22⋊C8×C107—21no—
82C22⋊C8×C107—21no—
83C22⋊C8×C107—21no—
84C22⋊C8×C107C2×C412yes—
85#97×C107—21no—
86C4×C8×C107—21no—
87#95×C107—21no—
88C24×C107—22no—
89C24×C107—44no—
90C24×C107—41no—
91C24×C107—41no—
92C24×C107—81no—
93C24×C107—81no—
94C24×C107—82no—
95C24×C107#4111yescharacteristic
96#41×C107—41no—
97#41×C107—41no—
98C2×Q8×C107C22⋊C411yescharacteristic
99C2×D4×C107—22no—
100C2×D4×C107—22no—
101C2×D4×C107—22no—
102C2×D4×C107—22no—
103C2×D4×C107—22no—
104C2×D4×C107—22no—
105C2×D4×C107—21no—
106C2×D4×C107—21no—
107C2×D4×C107—21no—
108C2×D4×C107—22no—
109C2×D4×C107—22no—
110C2×D4×C107—41no—
111C2×D4×C107—41no—
112C2×D4×C107—41no—
113C2×D4×C107—41no—
114C2×D4×C107—41no—
115C2×D4×C107—41no—
116C2×D4×C107—44no—
117C2×D4×C107—44no—
118C2×D4×C107—44no—
119C2×D4×C107—41no—
120C2×D4×C107—41no—
121C2×D4×C107C22⋊C411yescharacteristic
122C22×C4×C107—21no—
123C22×C4×C107—41no—
124C22×C4×C107—41no—
125C22×C4×C107—41no—
126C22×C4×C107C22×C411yescharacteristic
127C22×C4×C107C2×D411yescharacteristic
128C22×C4×C107C2×D411yescharacteristic
129C22×C4×C107C2×D411yescharacteristic
130C22×C4×C107C2×D411yescharacteristic
131C22×C4×C107#4111yescharacteristic
132SD16×C107—44no—
133D8×C107—44no—
134M16×C107—41no—
135M16×C107—41no—
136M16×C107—41no—
137M16×C107—41no—
138M16×C107—41no—
139M16×C107—41no—
140M16×C107—81no—
141C2×C8×C107—22no—
142C2×C8×C107—21no—
143C2×C8×C107—21no—
144C2×C8×C107—21no—
145C2×C8×C107—21no—
146C2×C8×C107—41no—
147C2×C8×C107—41no—
148C2×C8×C107—41no—
149C2×C8×C107—81no—
150C4⋊C4×C107—21no—
151C4⋊C4×C107—21no—
152C4⋊C4×C107—41no—
153C4⋊C4×C107—41no—
154C4⋊C4×C107C22⋊C411yescharacteristic
155C4⋊C4×C107C22⋊C411yescharacteristic
156C22⋊C4×C107—21no—
157C22⋊C4×C107—21no—
158C22⋊C4×C107—21no—
159C22⋊C4×C107—21no—
160C22⋊C4×C107—21no—
161C22⋊C4×C107—81no—
162C42×C107—21no—
163C23×C107—21no—
164C23×C107—21no—
165C23×C107—24no—
166C23×C107—21no—
167C23×C107—41no—
168C23×C107—41no—
169C23×C107—42no—
170C23×C107—42no—
171C23×C107—42no—
172C23×C107—42no—
173C23×C107—42no—
174C23×C107—42no—
175C23×C107—82no—
176C23×C107—82no—
177C23×C107—82no—
178C23×C107—81no—
179C23×C107—81no—
180C23×C107—82no—
181C23×C107—88no—
182C23×C107—88no—
183C23×C107—81no—
184C23×C107—81no—
185C23×C107C4×D411yescharacteristic
186C23×C107#12111yescharacteristic
187C23×C107#12311yescharacteristic
188Q8×C107—41no—
189D4×C107—24no—
190D4×C107—24no—
191D4×C107—41no—
192D4×C107—42no—
193D4×C107—42no—
194D4×C107—42no—
195D4×C107—42no—
196D4×C107—41no—
197D4×C107—41no—
198D4×C107—42no—
199D4×C107—42no—
200D4×C107—81no—
201D4×C107—81no—
202C2×C4×C107—21no—
203C2×C4×C107—21no—
204C2×C4×C107—21no—
205C2×C4×C107—21no—
206C2×C4×C107—21no—
207C2×C4×C107—21no—
208C2×C4×C107—21no—
209C2×C4×C107—21no—
210C2×C4×C107—21no—
211C2×C4×C107—41no—
212C2×C4×C107—41no—
213C2×C4×C107—41no—
214C2×C4×C107—41no—
215C2×C4×C107—41no—
216C2×C4×C107—81no—
217C2×C4×C107—81no—
218C2×C4×C107—81no—
219C2×C4×C107C2×C22⋊C411yescharacteristic
220C2×C4×C107C4×D411yescharacteristic
221C2×C4×C107#12011yescharacteristic
222C2×C4×C107#12111yescharacteristic
223C8×C107—42no—
224C8×C107—41no—
225C8×C107—41no—
226C8×C107—41no—
227C8×C107—41no—
228C8×C107—81no—
229C22×C107—21no—
230C22×C107—21no—
231C22×C107—21no—
232C22×C107—21no—
233C22×C107—21no—
234C22×C107—21no—
235C22×C107—21no—
236C22×C107—21no—
237C22×C107—42no—
238C22×C107—42no—
239C22×C107—41no—
240C22×C107—44no—
241C22×C107—41no—
242C22×C107—41no—
243C22×C107—82no—
244C22×C107—82no—
245C22×C107—82no—
246C22×C107—82no—
247C22×C107—84no—
248C22×C107—84no—
249C22×C107—84no—
250C22×C107—84no—
251C22×C107—82no—
252C22×C107—82no—
253C22×C107#38611yescharacteristic
254C22×C107#47111yescharacteristic
255C22×C107#47211yescharacteristic
256C4×C107—21no—
257C4×C107—21no—
258C4×C107—21no—
259C4×C107—41no—
260C4×C107—41no—
261C4×C107—41no—
262C4×C107—161no—
263C4×C107B(4,𝔽2)11yescharacteristic
264C4×C107B(4,𝔽2)11yescharacteristic
265#9520C10711yesmaximal, characteristic, direct product factor, Sylow
266C2×C107—21no—
267C2×C107—21no—
268C2×C107—41no—
269C2×C107—41no—
270C2×C107—81no—
271C2×C107—84no—
272C2×C107#188911yescharacteristic
273C2×C107#190311yescharacteristic
274C2×C107#190711yescharacteristic
275#3003C2×C10711yescharacteristic
276#2976C2×C10711yescharacteristic, complemented
277#1786C2×C10711yescharacteristic, complemented
278#1783C2×C10711yescharacteristic, complemented
279#1513C2×C10711yescharacteristic, complemented
280#1305C2×C10711yescharacteristic, complemented
281#1293C2×C10711yescharacteristic, complemented
282C107#952011yescharacteristic, direct product factor, Sylow
283C23×D4C22×C10711yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C10711yescharacteristic
286#450—21no—
287#450C4×C10712yescomplemented
288#447—21no—
289#447C4×C10712yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C10711yescharacteristic
302#407C22×C10711yescharacteristic
303#407C22×C10711yescharacteristic
304C2×C22⋊C8C22×C10711yescharacteristic
305#380C22×C10711yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C10711yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C10712yes—
318C23×C4C23×C10711yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C10711yescharacteristic
327C2×M16D4×C10711yescharacteristic
328C22×C8—21no—
329C22×C8D4×C10711yescharacteristic
330C22×C8D4×C10711yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C10711yescharacteristic
333C22⋊Q8D4×C10711yescharacteristic
334#121C2×C4×C10711yescharacteristic
335#121D4×C10711yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C10711yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C10712yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C10711yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C10711yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C10711yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C10711yescharacteristic
402C22×C4C2×D4×C10711yescharacteristic
403C22×C4C2×D4×C10711yescharacteristic
404C22×C4C2×D4×C10711yescharacteristic
405C22×C4C2×D4×C10711yescharacteristic
406C22×C4#41×C10711yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C10711yescharacteristic
430C4⋊C4C22⋊C4×C10711yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C10711yescharacteristic
461C23#121×C10711yescharacteristic
462C23#123×C10711yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C10711yescharacteristic
495C2×C4C4×D4×C10711yescharacteristic
496C2×C4#120×C10711yescharacteristic
497C2×C4#121×C10711yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C10711yescharacteristic
529C22#471×C10711yescharacteristic
530C22#472×C10711yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C10711yescharacteristic
539C4B(4,𝔽2)×C10711yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C107×#188911yescharacteristic
547C2C107×#190311yescharacteristic
548C2C107×#190711yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC107×#3003C2
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
2. C107×#2976C2semidirect
3. C107×#1786C2semidirect
4. C107×#1783C2semidirect
5. C107×#1513C2semidirect
6. C107×#1305C2semidirect
7. C107×#1293C2semidirect
12. #450×C107C4semidirect
14. #447×C107C4semidirect
265. #9520C107direct (N × H)
276. #2976C2×C107semidirect
277. #1786C2×C107semidirect
278. #1783C2×C107semidirect
279. #1513C2×C107semidirect
280. #1305C2×C107semidirect
281. #1293C2×C107semidirect
282. C107#9520direct (N × H)
287. #450C4×C107semidirect
289. #447C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#30032
C107×#29762
C107×#17862
C107×#17832
C107×#15132
C107×#13052
C107×#12932
#9520107