Finite Group Databasebeta

← C107×#8873 #41034837

Subgroups — C107×#8873 #41034837

Order 27392.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2325C211yesmaximal, characteristic
2C107×#1874C211yesmaximal, characteristic
3C107×#1853C211yesmaximal, characteristic, complemented
4C2×#327×C107C211yesmaximal, characteristic
5C107×#1444C211yesmaximal, characteristic, complemented
6C107×#1294C211yesmaximal, characteristic, complemented
7C107×#1280C211yesmaximal, characteristic, complemented
8C2×#121×C107C2211yescharacteristic
9C2×C4×D4×C107—21no—
10C22×C4⋊C4×C107—21no—
11C22×C4⋊C4×C107C2211yescharacteristic
12C2×#106×C107—21no—
13C2×#102×C107—21no—
14C2×C22⋊C8×C107C2211yescharacteristic
15C2×C22⋊C8×C107C2211yescharacteristic
16#388×C107—21no—
17#387×C107—21no—
18#386×C107—21no—
19#386×C107—21no—
20#385×C107—21no—
21#380×C107C2211yescharacteristic
22C2×#95×C107—21no—
23C2×#95×C107C2211yescharacteristic
24C2×#95×C107C2211yescharacteristic
25#340×C107—21no—
26#340×C107—21no—
27#327×C107C414yescomplemented
28C22×D4×C107—21no—
29C22×D4×C107D411yescharacteristic
30C23×C4×C107—21no—
31C23×C4×C107—21no—
32C23×C4×C107—21no—
33C23×C4×C107D411yescharacteristic
34C23×C4×C107D411yescharacteristic
35C23×C4×C107C2311yescharacteristic
36C22×C8×C107—21no—
37C22×C8×C107—21no—
38#121×C107—21no—
39#121×C107—21no—
40#121×C107C2×C412yes—
41#121×C107Q812yes—
42C4×D4×C107—42no—
43C4×D4×C107—42no—
44C2×C4⋊C4×C107—21no—
45C2×C4⋊C4×C107—21no—
46C2×C4⋊C4×C107—21no—
47C2×C4⋊C4×C107—42no—
48C2×C4⋊C4×C107—42no—
49C2×C4⋊C4×C107—42no—
50C2×C4⋊C4×C107—42no—
51C2×C4⋊C4×C107D411yescharacteristic
52C2×C4⋊C4×C107D411yescharacteristic
53C2×C4⋊C4×C107D411yescharacteristic
54C2×C22⋊C4×C107—21no—
55C2×C22⋊C4×C107—21no—
56C2×C22⋊C4×C107—21no—
57C2×C22⋊C4×C107—21no—
58C2×C22⋊C4×C107—21no—
59C2×C42×C107—21no—
60#106×C107—42no—
61#102×C107—42no—
62C22⋊C8×C107—21no—
63C22⋊C8×C107—21no—
64C22⋊C8×C107—21no—
65C22⋊C8×C107C2×C412yescomplemented
66#95×C107—21no—
67#95×C107—21no—
68#95×C107—21no—
69#95×C107—21no—
70#95×C107—21no—
71#95×C107—21no—
72#95×C107—42no—
73#95×C107C2×C412yescomplemented
74C24×C107—21no—
75C24×C107C2×D411yescharacteristic
76C2×D4×C107—22no—
77C2×D4×C107—22no—
78C2×D4×C107—21no—
79C2×D4×C107—41no—
80C2×D4×C107—41no—
81C2×D4×C107—41no—
82C2×D4×C107—41no—
83C2×D4×C107—41no—
84C2×D4×C107—41no—
85C2×D4×C107C4⋊C412yescomplemented
86C22×C4×C107—22no—
87C22×C4×C107—22no—
88C22×C4×C107—22no—
89C22×C4×C107—21no—
90C22×C4×C107—21no—
91C22×C4×C107—21no—
92C22×C4×C107—22no—
93C22×C4×C107—21no—
94C22×C4×C107—21no—
95C22×C4×C107—21no—
96C22×C4×C107—21no—
97C22×C4×C107—21no—
98C22×C4×C107—41no—
99C22×C4×C107—41no—
100C22×C4×C107—42no—
101C22×C4×C107—41no—
102C22×C4×C107—41no—
103C22×C4×C107—41no—
104C22×C4×C107—41no—
105C22×C4×C107—41no—
106C22×C4×C107—41no—
107C22×C4×C107—41no—
108C22×C4×C107—41no—
109C22×C4×C107—41no—
110C22×C4×C107—41no—
111C22×C4×C107—41no—
112C22×C4×C107—41no—
113C22×C4×C107—41no—
114C22×C4×C107—41no—
115C22×C4×C107—81no—
116C22×C4×C107—81no—
117C22×C4×C107SD1612yes—
118C22×C4×C107C22×C411yescharacteristic
119C22×C4×C107C2×D411yescharacteristic
120C22×C4×C107C2×D411yescharacteristic
121C22×C4×C107C2×Q811yescharacteristic
122C22×C4×C107#4111yescharacteristic
123C22×C4×C107#4111yescharacteristic
124C2×C8×C107—22no—
125C2×C8×C107—41no—
126C2×C8×C107—41no—
127C2×C8×C107—41no—
128C2×C8×C107—41no—
129C2×C8×C107—41no—
130C4⋊C4×C107—21no—
131C4⋊C4×C107—22no—
132C4⋊C4×C107—22no—
133C4⋊C4×C107—41no—
134C4⋊C4×C107—41no—
135C4⋊C4×C107—41no—
136C4⋊C4×C107—41no—
137C4⋊C4×C107—42no—
138C4⋊C4×C107—48no—
139C4⋊C4×C107C4⋊C412yescomplemented
140C22⋊C4×C107—22no—
141C22⋊C4×C107—22no—
142C22⋊C4×C107—42no—
143C22⋊C4×C107—41no—
144C22⋊C4×C107—41no—
145C22⋊C4×C107—81no—
146C22⋊C4×C107—81no—
147C42×C107—42no—
148C23×C107—21no—
149C23×C107—21no—
150C23×C107—21no—
151C23×C107—21no—
152C23×C107—22no—
153C23×C107—41no—
154C23×C107—41no—
155C23×C107—41no—
156C23×C107—41no—
157C23×C107—41no—
158C23×C107—41no—
159C23×C107C4×D411yescharacteristic
160C23×C107#12011yescharacteristic
161C23×C107C22⋊Q811yescharacteristic
162C23×C107C2×SD1611yescharacteristic
163C23×C107#13511yescharacteristic
164C23×C107AGL(1,ℤ/8)11yescharacteristic
165C23×C107AGL(1,ℤ/8)11yescharacteristic
166D4×C107—42no—
167D4×C107—42no—
168D4×C107—42no—
169D4×C107—42no—
170D4×C107—42no—
171D4×C107—81no—
172C2×C4×C107—21no—
173C2×C4×C107—21no—
174C2×C4×C107—21no—
175C2×C4×C107—21no—
176C2×C4×C107—24no—
177C2×C4×C107—22no—
178C2×C4×C107—22no—
179C2×C4×C107—41no—
180C2×C4×C107—41no—
181C2×C4×C107—41no—
182C2×C4×C107—41no—
183C2×C4×C107—42no—
184C2×C4×C107—42no—
185C2×C4×C107—42no—
186C2×C4×C107—42no—
187C2×C4×C107—42no—
188C2×C4×C107—42no—
189C2×C4×C107—41no—
190C2×C4×C107—41no—
191C2×C4×C107—41no—
192C2×C4×C107—41no—
193C2×C4×C107—42no—
194C2×C4×C107—42no—
195C2×C4×C107—42no—
196C2×C4×C107—42no—
197C2×C4×C107—41no—
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—42no—
206C2×C4×C107—41no—
207C2×C4×C107—81no—
208C2×C4×C107—84no—
209C2×C4×C107—81no—
210C2×C4×C107—81no—
211C2×C4×C107—81no—
212C2×C4×C107—81no—
213C2×C4×C107—81no—
214C2×C4×C107C2×C4⋊C411yescharacteristic
215C2×C4×C107C4×D411yescharacteristic
216C2×C4×C107C22⋊Q811yescharacteristic
217C2×C4×C107#12311yescharacteristic
218C8×C107—42no—
219C8×C107—81no—
220C22×C107—21no—
221C22×C107—21no—
222C22×C107—21no—
223C22×C107—21no—
224C22×C107—21no—
225C22×C107—21no—
226C22×C107—21no—
227C22×C107—21no—
228C22×C107—21no—
229C22×C107—21no—
230C22×C107—21no—
231C22×C107—21no—
232C22×C107—42no—
233C22×C107—42no—
234C22×C107—42no—
235C22×C107—81no—
236C22×C107—81no—
237C22×C107—81no—
238C22×C107—81no—
239C22×C107#38511yescharacteristic
240C22×C107C4×SD1611yescharacteristic
241C22×C107#44211yescharacteristic
242C22×C107#44911yescharacteristic
243C22×C107#45011yescharacteristic
244C22×C107#45311yescharacteristic
245C22×C107#45611yescharacteristic
246C22×C107B(4,𝔽2)11yescharacteristic
247C22×C107#45811yescharacteristic
248C22×C107#47611yescharacteristic
249C22×C107#47811yescharacteristic
250C4×C107—21no—
251C4×C107—21no—
252C4×C107—21no—
253C4×C107—21no—
254C4×C107—44no—
255C4×C107—42no—
256C4×C107—42no—
257C4×C107—81no—
258C4×C107—82no—
259C4×C107—81no—
260C4×C107—81no—
261#8873C10711yesmaximal, characteristic, direct product factor, Sylow
262C2×C107—21no—
263C2×C107—21no—
264C2×C107—21no—
265C2×C107—21no—
266C2×C107—82no—
267C2×C107#160011yescharacteristic
268C2×C107#160411yescharacteristic
269C2×C107#160911yescharacteristic
270C2×C107#161311yescharacteristic
271C2×C107#185911yescharacteristic
272C2×C107#186411yescharacteristic
273C2×C107#186711yescharacteristic
274#2325C2×C10711yescharacteristic
275#1874C2×C10711yescharacteristic
276#1853C2×C10711yescharacteristic, complemented
277C2×#327C2×C10711yescharacteristic
278#1444C2×C10711yescharacteristic, complemented
279#1294C2×C10711yescharacteristic, complemented
280#1280C2×C10711yescharacteristic, complemented
281C107#887311yescharacteristic, direct product factor, Sylow
282C2×#121C22×C10711yescharacteristic
283C2×C4×D4—21no—
284C22×C4⋊C4—21no—
285C22×C4⋊C4C22×C10711yescharacteristic
286C2×#106—21no—
287C2×#102—21no—
288C2×C22⋊C8C22×C10711yescharacteristic
289C2×C22⋊C8C22×C10711yescharacteristic
290#388—21no—
291#387—21no—
292#386—21no—
293#386—21no—
294#385—21no—
295#380C22×C10711yescharacteristic
296C2×#95—21no—
297C2×#95C22×C10711yescharacteristic
298C2×#95C22×C10711yescharacteristic
299#340—21no—
300#340—21no—
301#327C4×C10714yescomplemented
302C22×D4—21no—
303C22×D4D4×C10711yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4D4×C10711yescharacteristic
308C23×C4D4×C10711yescharacteristic
309C23×C4C23×C10711yescharacteristic
310C22×C8—21no—
311C22×C8—21no—
312#121—21no—
313#121—21no—
314#121C2×C4×C10712yes—
315#121Q8×C10712yes—
316C4×D4—42no—
317C4×D4—42no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4D4×C10711yescharacteristic
326C2×C4⋊C4D4×C10711yescharacteristic
327C2×C4⋊C4D4×C10711yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C42—21no—
334#106—42no—
335#102—42no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8C2×C4×C10712yescomplemented
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—42no—
347#95C2×C4×C10712yescomplemented
348C24—21no—
349C24C2×D4×C10711yescharacteristic
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—21no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4C4⋊C4×C10712yescomplemented
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—42no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4SD16×C10712yes—
392C22×C4C22×C4×C10711yescharacteristic
393C22×C4C2×D4×C10711yescharacteristic
394C22×C4C2×D4×C10711yescharacteristic
395C22×C4C2×Q8×C10711yescharacteristic
396C22×C4#41×C10711yescharacteristic
397C22×C4#41×C10711yescharacteristic
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—42no—
412C4⋊C4—48no—
413C4⋊C4C4⋊C4×C10712yescomplemented
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—42no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—81no—
420C22⋊C4—81no—
421C42—42no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23C4×D4×C10711yescharacteristic
434C23#120×C10711yescharacteristic
435C23C22⋊Q8×C10711yescharacteristic
436C23C2×SD16×C10711yescharacteristic
437C23#135×C10711yescharacteristic
438C23AGL(1,ℤ/8)×C10711yescharacteristic
439C23AGL(1,ℤ/8)×C10711yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—81no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
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—42no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—84no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C2×C4⋊C4×C10711yescharacteristic
489C2×C4C4×D4×C10711yescharacteristic
490C2×C4C22⋊Q8×C10711yescharacteristic
491C2×C4#123×C10711yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22#385×C10711yescharacteristic
514C22C4×SD16×C10711yescharacteristic
515C22#442×C10711yescharacteristic
516C22#449×C10711yescharacteristic
517C22#450×C10711yescharacteristic
518C22#453×C10711yescharacteristic
519C22#456×C10711yescharacteristic
520C22B(4,𝔽2)×C10711yescharacteristic
521C22#458×C10711yescharacteristic
522C22#476×C10711yescharacteristic
523C22#478×C10711yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—42no—
530C4—42no—
531C4—81no—
532C4—81no—
533C4—82no—
534C4—81no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—82no—
540C2C107×#160011yescharacteristic
541C2C107×#160411yescharacteristic
542C2C107×#160911yescharacteristic
543C2C107×#161311yescharacteristic
544C2C107×#185911yescharacteristic
545C2C107×#186411yescharacteristic
546C2C107×#186711yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC2×#121×C107C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1853C2semidirect
5. C107×#1444C2semidirect
6. C107×#1294C2semidirect
7. C107×#1280C2semidirect
27. #327×C107C4semidirect
65. C22⋊C8×C107C2×C4semidirect
73. #95×C107C2×C4semidirect
85. C2×D4×C107C4⋊C4semidirect
139. C4⋊C4×C107C4⋊C4semidirect
261. #8873C107direct (N × H)
276. #1853C2×C107semidirect
278. #1444C2×C107semidirect
279. #1294C2×C107semidirect
280. #1280C2×C107semidirect
281. C107#8873direct (N × H)
301. #327C4×C107semidirect
339. C22⋊C8C2×C4×C107semidirect
347. #95C2×C4×C107semidirect
359. C2×D4C4⋊C4×C107semidirect
413. C4⋊C4C4⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#23252
C107×#18742
C107×#18532
C2×#327×C1072
C107×#14442
C107×#12942
C107×#12802
#8873107