Finite Group Databasebeta

← C107×#19034 #41044998

Subgroups — C107×#19034 #41044998

Order 27392.

836 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3563C211yesmaximal, characteristic
2C107×#3218C211yesmaximal, characteristic
3C107×#3165C211yesmaximal, characteristic, complemented
4C2×#501×C107C211yesmaximal, characteristic, complemented
5C107×#1663C214yesmaximal, complemented
6C107×#1660C214yesmaximal, complemented
7C107×#1531C211yesmaximal, characteristic, complemented
8C107×#1528C211yesmaximal, characteristic, complemented
9C107×#1524C211yesmaximal, characteristic
10#564×C107C2212yes—
11#563×C107C2212yes—
12#557×C107—21no—
13#554×C107—21no—
14#552×C107—21no—
15#552×C107—22no—
16#552×C107—21no—
17#544×C107—21no—
18#544×C107—21no—
19#541×C107—21no—
20#541×C107—22no—
21#539×C107—21no—
22#533×C107C2211yescharacteristic
23C2×C4⋊Q8×C107C2211yescharacteristic
24#529×C107C2211yescharacteristic
25C2×#125×C107C2211yescharacteristic
26#501×C107—22no—
27#501×C107C2214yes—
28#501×C107C2214yes—
29#500×C107—21no—
30#498×C107—21no—
31#497×C107C2212yes—
32#491×C107C2212yes—
33#462×C107—21no—
34#461×C107—21no—
35#451×C107—21no—
36#448×C107—21no—
37#432×C107C2211yescharacteristic
38#428×C107—22no—
39C2×#107×C107—21no—
40C2×#106×C107—21no—
41C4×M16×C107C2211yescharacteristic
42C2×#97×C107C2211yescharacteristic
43#330×C107C2214yes—
44#330×C107C2214yes—
45#330×C107C2212yes—
46#329×C107C2212yes—
47C22×Q8×C107—21no—
48C2×Q16×C107—22no—
49C2×SD16×C107—22no—
50C2×M16×C107—21no—
51C22×C8×C107—21no—
52C4⋊Q8×C107—22no—
53C4⋊Q8×C107—21no—
54C4⋊Q8×C107—22no—
55C4⋊Q8×C107—21no—
56C4⋊Q8×C107—21no—
57C4⋊Q8×C107—21no—
58C4⋊Q8×C107D411yescharacteristic
59C4⋊Q8×C107D411yescharacteristic
60C4⋊Q8×C107C2312yes—
61#126×C107—22no—
62#126×C107—22no—
63#126×C107—22no—
64#126×C107—22no—
65#126×C107—21no—
66#125×C107—22no—
67#125×C107—22no—
68#125×C107—21no—
69#125×C107—22no—
70#125×C107—22no—
71#125×C107—22no—
72#125×C107—22no—
73#125×C107—22no—
74#125×C107—22no—
75#125×C107—21no—
76#125×C107—21no—
77#125×C107D412yes—
78#125×C107C2311yescharacteristic
79#125×C107C2312yes—
80#125×C107C2312yes—
81#124×C107C2311yescharacteristic
82#123×C107—22no—
83#123×C107—22no—
84#123×C107—21no—
85C22⋊Q8×C107—22no—
86C22⋊Q8×C107—21no—
87C22⋊Q8×C107—21no—
88C22⋊Q8×C107—22no—
89C22⋊Q8×C107—21no—
90C22⋊Q8×C107—21no—
91C22⋊Q8×C107—22no—
92C22⋊Q8×C107—22no—
93C22⋊Q8×C107D411yescharacteristic
94#121×C107D411yescharacteristic
95C4×Q8×C107—21no—
96C4×Q8×C107—22no—
97C4×Q8×C107—21no—
98C4×Q8×C107—21no—
99C4×Q8×C107—21no—
100C4×Q8×C107D411yescharacteristic
101C4×D4×C107—22no—
102C4×D4×C107—21no—
103C4×D4×C107D411yescharacteristic
104#117×C107—22no—
105#117×C107—21no—
106#117×C107—22no—
107#117×C107—21no—
108#117×C107D412yes—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107—21no—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107D411yescharacteristic
115C2×C4⋊C4×C107D411yescharacteristic
116C2×C42×C107C2311yescharacteristic
117#107×C107—24no—
118#107×C107—24no—
119#106×C107—24no—
120#106×C107—24no—
121C4⋊C8×C107—21no—
122#103×C107—22no—
123#103×C107—22no—
124C22⋊C8×C107—21no—
125#97×C107—21no—
126#97×C107C2312yes—
127#97×C107C2312yes—
128#97×C107C2312yes—
129C4×C8×C107—21no—
130C2×Q8×C107—22no—
131C2×Q8×C107—21no—
132C2×Q8×C107—21no—
133C2×Q8×C107—22no—
134C2×Q8×C107—41no—
135C2×Q8×C107—82no—
136C2×Q8×C107C2×D411yescharacteristic
137C2×D4×C107—21no—
138C2×D4×C107C2×D411yescharacteristic
139C22×C4×C107—21no—
140C22×C4×C107—22no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—41no—
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147Q16×C107—82no—
148SD16×C107—82no—
149M16×C107—24no—
150C2×C8×C107—24no—
151C2×C8×C107—22no—
152C2×C8×C107—22no—
153C2×C8×C107—22no—
154C4⋊C4×C107—22no—
155C4⋊C4×C107—22no—
156C4⋊C4×C107—22no—
157C4⋊C4×C107—22no—
158C4⋊C4×C107—22no—
159C4⋊C4×C107—22no—
160C4⋊C4×C107—22no—
161C4⋊C4×C107—22no—
162C4⋊C4×C107—21no—
163C4⋊C4×C107—21no—
164C4⋊C4×C107—22no—
165C4⋊C4×C107—22no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—22no—
171C4⋊C4×C107—22no—
172C4⋊C4×C107—21no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—22no—
175C4⋊C4×C107—22no—
176C4⋊C4×C107—22no—
177C4⋊C4×C107—22no—
178C4⋊C4×C107—41no—
179C4⋊C4×C107—41no—
180C4⋊C4×C107C2×D411yescharacteristic
181C4⋊C4×C107C2×D411yescharacteristic
182C4⋊C4×C107C2×D412yes—
183C4⋊C4×C107C2×D412yes—
184C4⋊C4×C107C2×D412yes—
185C4⋊C4×C107C2×D412yes—
186C22⋊C4×C107—22no—
187C22⋊C4×C107—22no—
188C22⋊C4×C107—22no—
189C22⋊C4×C107—21no—
190C22⋊C4×C107—22no—
191C22⋊C4×C107—21no—
192C22⋊C4×C107—21no—
193C22⋊C4×C107—21no—
194C22⋊C4×C107—21no—
195C42×C107—22no—
196C42×C107—22no—
197C42×C107—22no—
198C42×C107—22no—
199C42×C107—21no—
200C42×C107C2×D411yescharacteristic
201C42×C107C2×D411yescharacteristic
202C42×C107C2×D411yescharacteristic
203C42×C107C2411yescharacteristic
204C23×C107—21no—
205C23×C107#12011yescharacteristic
206Q8×C107—41no—
207Q8×C107—42no—
208Q8×C107—42no—
209Q8×C107—42no—
210Q8×C107—81no—
211Q8×C107—82no—
212Q8×C107—82no—
213D4×C107—41no—
214D4×C107—42no—
215C2×C4×C107—22no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—21no—
219C2×C4×C107—21no—
220C2×C4×C107—21no—
221C2×C4×C107—22no—
222C2×C4×C107—22no—
223C2×C4×C107—22no—
224C2×C4×C107—41no—
225C2×C4×C107—42no—
226C2×C4×C107—42no—
227C2×C4×C107—42no—
228C2×C4×C107—81no—
229C2×C4×C107—82no—
230C2×C4×C107—82no—
231C2×C4×C107#12011yescharacteristic
232C2×C4×C107#12011yescharacteristic
233C2×C4×C107#12011yescharacteristic
234C2×C4×C107C22×D411yescharacteristic
235C2×C4×C107C22×D411yescharacteristic
236C2×C4×C107C22×D411yescharacteristic
237C8×C107—24no—
238C8×C107—24no—
239C8×C107—42no—
240C22×C107—21no—
241C22×C107—21no—
242C22×C107—41no—
243C22×C107—41no—
244C22×C107—41no—
245C22×C107#45612yes—
246C22×C107C2×#12011yescharacteristic
247C4×C107—21no—
248C4×C107—21no—
249C4×C107—21no—
250C4×C107—21no—
251C4×C107—21no—
252C4×C107—42no—
253C4×C107—41no—
254C4×C107—41no—
255C4×C107—42no—
256C4×C107—42no—
257C4×C107—42no—
258C4×C107—41no—
259C4×C107—82no—
260C4×C107#45612yes—
261#19034C10711yesmaximal, characteristic, direct product factor, Sylow
262C2×C107—22no—
263C2×C107—81no—
264C2×C107C2×#45611yescharacteristic
265C2×C107C2×#45611yescharacteristic
266C2×C107#302111yescharacteristic
267#3563C2×C10711yescharacteristic
268#3218C2×C10711yescharacteristic
269#3165C2×C10711yescharacteristic, complemented
270C2×#501C2×C10711yescharacteristic, complemented
271#1663C2×C10714yescomplemented
272#1660C2×C10714yescomplemented
273#1531C2×C10711yescharacteristic, complemented
274#1528C2×C10711yescharacteristic, complemented
275#1524C2×C10711yescharacteristic
276C107#1903411yescharacteristic, direct product factor, Sylow
277#564C22×C10712yes—
278#563C22×C10712yes—
279#557—21no—
280#554—21no—
281#552—21no—
282#552—22no—
283#552—21no—
284#544—21no—
285#544—21no—
286#541—21no—
287#541—22no—
288#539—21no—
289#533C22×C10711yescharacteristic
290C2×C4⋊Q8C22×C10711yescharacteristic
291#529C22×C10711yescharacteristic
292C2×#125C22×C10711yescharacteristic
293#501—22no—
294#501C22×C10714yes—
295#501C22×C10714yes—
296#500—21no—
297#498—21no—
298#497C22×C10712yes—
299#491C22×C10712yes—
300#462—21no—
301#461—21no—
302#451—21no—
303#448—21no—
304#432C22×C10711yescharacteristic
305#428—22no—
306C2×#107—21no—
307C2×#106—21no—
308C4×M16C22×C10711yescharacteristic
309C2×#97C22×C10711yescharacteristic
310#330C22×C10714yes—
311#330C22×C10714yes—
312#330C22×C10712yes—
313#329C22×C10712yes—
314C22×Q8—21no—
315C2×Q16—22no—
316C2×SD16—22no—
317C2×M16—21no—
318C22×C8—21no—
319C4⋊Q8—22no—
320C4⋊Q8—21no—
321C4⋊Q8—22no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8D4×C10711yescharacteristic
326C4⋊Q8D4×C10711yescharacteristic
327C4⋊Q8C23×C10712yes—
328#126—22no—
329#126—22no—
330#126—22no—
331#126—22no—
332#126—21no—
333#125—22no—
334#125—22no—
335#125—21no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—22no—
340#125—22no—
341#125—22no—
342#125—21no—
343#125—21no—
344#125D4×C10712yes—
345#125C23×C10712yes—
346#125C23×C10711yescharacteristic
347#125C23×C10712yes—
348#124C23×C10711yescharacteristic
349#123—22no—
350#123—22no—
351#123—21no—
352C22⋊Q8—22no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—22no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8D4×C10711yescharacteristic
361#121D4×C10711yescharacteristic
362C4×Q8—21no—
363C4×Q8—22no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8D4×C10711yescharacteristic
368C4×D4—22no—
369C4×D4—21no—
370C4×D4D4×C10711yescharacteristic
371#117—22no—
372#117—21no—
373#117—22no—
374#117—21no—
375#117D4×C10712yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4D4×C10711yescharacteristic
382C2×C4⋊C4D4×C10711yescharacteristic
383C2×C42C23×C10711yescharacteristic
384#107—24no—
385#107—24no—
386#106—24no—
387#106—24no—
388C4⋊C8—21no—
389#103—22no—
390#103—22no—
391C22⋊C8—21no—
392#97—21no—
393#97C23×C10712yes—
394#97C23×C10712yes—
395#97C23×C10712yes—
396C4×C8—21no—
397C2×Q8—22no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—41no—
402C2×Q8—82no—
403C2×Q8C2×D4×C10711yescharacteristic
404C2×D4—21no—
405C2×D4C2×D4×C10711yescharacteristic
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—41no—
411C22×C4C2×D4×C10711yescharacteristic
412C22×C4C2×D4×C10711yescharacteristic
413C22×C4C2×D4×C10711yescharacteristic
414Q16—82no—
415SD16—82no—
416M16—24no—
417C2×C8—24no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4C2×D4×C10711yescharacteristic
448C4⋊C4C2×D4×C10711yescharacteristic
449C4⋊C4C2×D4×C10712yes—
450C4⋊C4C2×D4×C10712yes—
451C4⋊C4C2×D4×C10712yes—
452C4⋊C4C2×D4×C10712yes—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—21no—
457C22⋊C4—22no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C42—22no—
463C42—22no—
464C42—22no—
465C42—22no—
466C42—21no—
467C42C2×D4×C10711yescharacteristic
468C42C2×D4×C10711yescharacteristic
469C42C2×D4×C10711yescharacteristic
470C42C24×C10711yescharacteristic
471C23—21no—
472C23#120×C10711yescharacteristic
473Q8—41no—
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—81no—
478Q8—82no—
479Q8—82no—
480D4—41no—
481D4—42no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—81no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4#120×C10711yescharacteristic
499C2×C4#120×C10711yescharacteristic
500C2×C4#120×C10711yescharacteristic
501C2×C4C22×D4×C10711yescharacteristic
502C2×C4C22×D4×C10711yescharacteristic
503C2×C4C22×D4×C10711yescharacteristic
504C8—24no—
505C8—24no—
506C8—42no—
507C22—21no—
508C22—21no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22#456×C10712yes—
513C22C2×#120×C10711yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—42no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—82no—
527C4#456×C10712yes—
528C2—22no—
529C2—81no—
530C2C2×#456×C10711yescharacteristic
531C2C2×#456×C10711yescharacteristic
532C2C107×#302111yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radical#121×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#3165C2semidirect
4. C2×#501×C107C2semidirect
5. C107×#1663C2semidirect
6. C107×#1660C2semidirect
7. C107×#1531C2semidirect
8. C107×#1528C2semidirect
261. #19034C107direct (N × H)
269. #3165C2×C107semidirect
270. C2×#501C2×C107semidirect
271. #1663C2×C107semidirect
272. #1660C2×C107semidirect
273. #1531C2×C107semidirect
274. #1528C2×C107semidirect
276. C107#19034direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35632
C107×#32182
C107×#31652
C2×#501×C1072
C107×#16632
C107×#16602
C107×#15312
C107×#15282
C107×#15242
#19034107