Finite Group Databasebeta

← C107×#19033 #41044997

Subgroups — C107×#19033 #41044997

Order 27392.

948 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3561C211yesmaximal, characteristic
2C107×#3239C211yesmaximal, characteristic, complemented
3C107×#3165C211yesmaximal, characteristic, complemented
4C2×#497×C107C211yesmaximal, characteristic, complemented
5C107×#1661C214yesmaximal, complemented
6C107×#1660C214yesmaximal, complemented
7C107×#1531C211yesmaximal, characteristic, complemented
8C107×#1527C211yesmaximal, characteristic, complemented
9C107×#1524C211yesmaximal, characteristic, complemented
10C22×Q16×C107—21no—
11C22×SD16×C107—21no—
12#563×C107C2212yes—
13#562×C107C2212yes—
14#556×C107—21no—
15#551×C107—22no—
16D4×Q8×C107—21no—
17#548×C107—21no—
18#546×C107—21no—
19#543×C107—21no—
20#542×C107—21no—
21#542×C107—22no—
22#538×C107—21no—
23#536×C107—21no—
24#533×C107C2211yescharacteristic
25C2×C4⋊Q8×C107C2211yescharacteristic
26#529×C107C2211yescharacteristic
27C2×#124×C107C2211yescharacteristic
28#501×C107C2214yescomplemented
29#501×C107C2212yescomplemented
30#500×C107—21no—
31#498×C107—21no—
32#497×C107—22no—
33#497×C107C2214yes—
34#489×C107C2212yescomplemented
35#484×C107—21no—
36#481×C107—21no—
37#475×C107—21no—
38#474×C107—21no—
39#432×C107C2211yescharacteristic
40#428×C107—22no—
41C4×M16×C107C2211yescharacteristic
42C2×#97×C107C2211yescharacteristic
43#330×C107C2212yescomplemented
44#330×C107C2214yescomplemented
45#329×C107C2214yes—
46#329×C107C2212yescomplemented
47C2×#41×C107—21no—
48C22×Q8×C107—21no—
49C22×Q8×C107—21no—
50C22×Q8×C107D411yescharacteristic
51C22×D4×C107D411yescharacteristic
52C2×Q16×C107—24no—
53C2×Q16×C107—44no—
54C2×SD16×C107—24no—
55C2×SD16×C107—44no—
56C2×M16×C107—21no—
57C22×C8×C107—21no—
58C4⋊Q8×C107—21no—
59C4⋊Q8×C107—22no—
60C4⋊Q8×C107—21no—
61C4⋊Q8×C107—21no—
62C4⋊Q8×C107—21no—
63C4⋊Q8×C107D411yescharacteristic
64C4⋊Q8×C107D411yescharacteristic
65C4⋊Q8×C107C2312yes—
66#126×C107—22no—
67#126×C107—22no—
68#126×C107—22no—
69#126×C107—21no—
70#125×C107C2311yescharacteristic
71#125×C107C2312yes—
72#124×C107—21no—
73#124×C107—22no—
74#124×C107—22no—
75#124×C107—21no—
76#124×C107—21no—
77#124×C107D412yes—
78#124×C107C2311yescharacteristic
79#124×C107C2312yes—
80#123×C107—22no—
81#123×C107—22no—
82#123×C107—21no—
83#123×C107—22no—
84#123×C107—22no—
85C22⋊Q8×C107—22no—
86C22⋊Q8×C107—22no—
87C22⋊Q8×C107—21no—
88C22⋊Q8×C107—22no—
89C22⋊Q8×C107—22no—
90C22⋊Q8×C107—22no—
91C22⋊Q8×C107—21no—
92C22⋊Q8×C107—21no—
93C22⋊Q8×C107—22no—
94C22⋊Q8×C107—22no—
95C22⋊Q8×C107D411yescharacteristic
96#121×C107—21no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107D411yescharacteristic
100#120×C107—22no—
101C4×Q8×C107—21no—
102C4×Q8×C107—21no—
103C4×Q8×C107—21no—
104C4×Q8×C107D411yescharacteristic
105C4×D4×C107—22no—
106C4×D4×C107—21no—
107C4×D4×C107—22no—
108C4×D4×C107—21no—
109C4×D4×C107D411yescharacteristic
110#117×C107—22no—
111#117×C107—21no—
112#117×C107D412yes—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107—21no—
115C2×C22⋊C4×C107—22no—
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C42×C107C2311yescharacteristic
119#107×C107—24no—
120#107×C107—22no—
121#106×C107—24no—
122#106×C107—22no—
123C4⋊C8×C107—21no—
124#103×C107—22no—
125#102×C107—22no—
126C22⋊C8×C107—21no—
127#97×C107—21no—
128#97×C107C2312yes—
129#97×C107C2312yes—
130#97×C107C2312yes—
131C4×C8×C107—21no—
132C24×C107—21no—
133#41×C107—82no—
134C2×Q8×C107—22no—
135C2×Q8×C107—21no—
136C2×Q8×C107—21no—
137C2×Q8×C107—21no—
138C2×Q8×C107—22no—
139C2×Q8×C107—42no—
140C2×Q8×C107—42no—
141C2×Q8×C107—42no—
142C2×Q8×C107—41no—
143C2×Q8×C107—82no—
144C2×Q8×C107C2×D411yescharacteristic
145C2×Q8×C107C2×D412yes—
146C2×D4×C107—21no—
147C2×D4×C107—22no—
148C2×D4×C107—22no—
149C2×D4×C107—21no—
150C2×D4×C107—42no—
151C2×D4×C107C2×D411yescharacteristic
152C2×D4×C107C2×D412yes—
153C22×C4×C107—22no—
154C22×C4×C107—22no—
155C22×C4×C107—22no—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—41no—
159C22×C4×C107C2×D411yescharacteristic
160C22×C4×C107C2×D411yescharacteristic
161C22×C4×C107C2×D411yescharacteristic
162Q16×C107—48no—
163SD16×C107—48no—
164M16×C107—24no—
165C2×C8×C107—24no—
166C2×C8×C107—22no—
167C2×C8×C107—22no—
168C2×C8×C107—22no—
169C4⋊C4×C107—22no—
170C4⋊C4×C107—22no—
171C4⋊C4×C107—22no—
172C4⋊C4×C107—22no—
173C4⋊C4×C107—21no—
174C4⋊C4×C107—21no—
175C4⋊C4×C107—21no—
176C4⋊C4×C107—21no—
177C4⋊C4×C107—21no—
178C4⋊C4×C107—21no—
179C4⋊C4×C107—22no—
180C4⋊C4×C107—22no—
181C4⋊C4×C107—22no—
182C4⋊C4×C107—22no—
183C4⋊C4×C107—41no—
184C4⋊C4×C107—41no—
185C4⋊C4×C107C2×D412yes—
186C4⋊C4×C107C2×D411yescharacteristic
187C4⋊C4×C107C2×D412yes—
188C4⋊C4×C107C2×D411yescharacteristic
189C22⋊C4×C107—22no—
190C22⋊C4×C107—22no—
191C22⋊C4×C107—22no—
192C22⋊C4×C107—22no—
193C22⋊C4×C107—22no—
194C22⋊C4×C107—21no—
195C22⋊C4×C107—22no—
196C22⋊C4×C107—22no—
197C22⋊C4×C107—22no—
198C22⋊C4×C107—21no—
199C22⋊C4×C107—21no—
200C22⋊C4×C107—22no—
201C22⋊C4×C107—22no—
202C22⋊C4×C107—21no—
203C22⋊C4×C107—21no—
204C42×C107—22no—
205C42×C107—22no—
206C42×C107—21no—
207C42×C107C2×D411yescharacteristic
208C42×C107C2×D411yescharacteristic
209C42×C107C2×D411yescharacteristic
210C42×C107C2411yescharacteristic
211C23×C107—22no—
212C23×C107—21no—
213C23×C107—42no—
214C23×C107—81no—
215C23×C107—81no—
216C23×C107#12011yescharacteristic
217Q8×C107—42no—
218Q8×C107—41no—
219Q8×C107—42no—
220Q8×C107—42no—
221Q8×C107—42no—
222Q8×C107—42no—
223Q8×C107—81no—
224Q8×C107—82no—
225Q8×C107—82no—
226D4×C107—42no—
227D4×C107—41no—
228D4×C107—42no—
229D4×C107—42no—
230D4×C107—82no—
231D4×C107—82no—
232C2×C4×C107—22no—
233C2×C4×C107—22no—
234C2×C4×C107—21no—
235C2×C4×C107—22no—
236C2×C4×C107—21no—
237C2×C4×C107—22no—
238C2×C4×C107—22no—
239C2×C4×C107—21no—
240C2×C4×C107—41no—
241C2×C4×C107—42no—
242C2×C4×C107—42no—
243C2×C4×C107—81no—
244C2×C4×C107—82no—
245C2×C4×C107—82no—
246C2×C4×C107—82no—
247C2×C4×C107—82no—
248C2×C4×C107#12011yescharacteristic
249C2×C4×C107#12011yescharacteristic
250C2×C4×C107#12011yescharacteristic
251C2×C4×C107C22×D411yescharacteristic
252C2×C4×C107C22×D411yescharacteristic
253C2×C4×C107C22×D411yescharacteristic
254C8×C107—24no—
255C8×C107—24no—
256C8×C107—42no—
257C22×C107—21no—
258C22×C107—21no—
259C22×C107—41no—
260C22×C107—42no—
261C22×C107—41no—
262C22×C107—42no—
263C22×C107—42no—
264C22×C107—41no—
265C22×C107—162no—
266C22×C107#45612yes—
267C22×C107C2×#12011yescharacteristic
268C4×C107—21no—
269C4×C107—21no—
270C4×C107—21no—
271C4×C107—21no—
272C4×C107—21no—
273C4×C107—41no—
274C4×C107—42no—
275C4×C107—42no—
276C4×C107—41no—
277C4×C107—41no—
278C4×C107—42no—
279C4×C107—82no—
280C4×C107#45312yes—
281#19033C10711yesmaximal, characteristic, direct product factor, Sylow
282C2×C107—22no—
283C2×C107—81no—
284C2×C107—82no—
285C2×C107C2×#45311yescharacteristic
286C2×C107C2×#45611yescharacteristic
287C2×C107#302211yescharacteristic
288#3561C2×C10711yescharacteristic
289#3239C2×C10711yescharacteristic, complemented
290#3165C2×C10711yescharacteristic, complemented
291C2×#497C2×C10711yescharacteristic, complemented
292#1661C2×C10714yescomplemented
293#1660C2×C10714yescomplemented
294#1531C2×C10711yescharacteristic, complemented
295#1527C2×C10711yescharacteristic, complemented
296#1524C2×C10711yescharacteristic, complemented
297C107#1903311yescharacteristic, direct product factor, Sylow
298C22×Q16—21no—
299C22×SD16—21no—
300#563C22×C10712yes—
301#562C22×C10712yes—
302#556—21no—
303#551—22no—
304D4×Q8—21no—
305#548—21no—
306#546—21no—
307#543—21no—
308#542—21no—
309#542—22no—
310#538—21no—
311#536—21no—
312#533C22×C10711yescharacteristic
313C2×C4⋊Q8C22×C10711yescharacteristic
314#529C22×C10711yescharacteristic
315C2×#124C22×C10711yescharacteristic
316#501C22×C10714yescomplemented
317#501C22×C10712yescomplemented
318#500—21no—
319#498—21no—
320#497—22no—
321#497C22×C10714yes—
322#489C22×C10712yescomplemented
323#484—21no—
324#481—21no—
325#475—21no—
326#474—21no—
327#432C22×C10711yescharacteristic
328#428—22no—
329C4×M16C22×C10711yescharacteristic
330C2×#97C22×C10711yescharacteristic
331#330C22×C10712yescomplemented
332#330C22×C10714yescomplemented
333#329C22×C10714yes—
334#329C22×C10712yescomplemented
335C2×#41—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8D4×C10711yescharacteristic
339C22×D4D4×C10711yescharacteristic
340C2×Q16—24no—
341C2×Q16—44no—
342C2×SD16—24no—
343C2×SD16—44no—
344C2×M16—21no—
345C22×C8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—22no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8D4×C10711yescharacteristic
352C4⋊Q8D4×C10711yescharacteristic
353C4⋊Q8C23×C10712yes—
354#126—22no—
355#126—22no—
356#126—22no—
357#126—21no—
358#125C23×C10711yescharacteristic
359#125C23×C10712yes—
360#124—21no—
361#124—22no—
362#124—22no—
363#124—21no—
364#124—21no—
365#124D4×C10712yes—
366#124C23×C10712yes—
367#124C23×C10711yescharacteristic
368#123—22no—
369#123—22no—
370#123—21no—
371#123—22no—
372#123—22no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8D4×C10711yescharacteristic
384#121—21no—
385#121—22no—
386#121—22no—
387#121D4×C10711yescharacteristic
388#120—22no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8D4×C10711yescharacteristic
393C4×D4—22no—
394C4×D4—21no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4D4×C10711yescharacteristic
398#117—22no—
399#117—21no—
400#117D4×C10712yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42C23×C10711yescharacteristic
407#107—24no—
408#107—22no—
409#106—24no—
410#106—22no—
411C4⋊C8—21no—
412#103—22no—
413#102—22no—
414C22⋊C8—21no—
415#97—21no—
416#97C23×C10712yes—
417#97C23×C10712yes—
418#97C23×C10712yes—
419C4×C8—21no—
420C24—21no—
421#41—82no—
422C2×Q8—22no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—41no—
431C2×Q8—82no—
432C2×Q8C2×D4×C10711yescharacteristic
433C2×Q8C2×D4×C10712yes—
434C2×D4—21no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4—42no—
439C2×D4C2×D4×C10711yescharacteristic
440C2×D4C2×D4×C10712yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C10711yescharacteristic
448C22×C4C2×D4×C10711yescharacteristic
449C22×C4C2×D4×C10711yescharacteristic
450Q16—48no—
451SD16—48no—
452M16—24no—
453C2×C8—24no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C10712yes—
474C4⋊C4C2×D4×C10711yescharacteristic
475C4⋊C4C2×D4×C10712yes—
476C4⋊C4C2×D4×C10711yescharacteristic
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42C2×D4×C10711yescharacteristic
496C42C2×D4×C10711yescharacteristic
497C42C2×D4×C10711yescharacteristic
498C42C24×C10711yescharacteristic
499C23—22no—
500C23—21no—
501C23—42no—
502C23—81no—
503C23—81no—
504C23#120×C10711yescharacteristic
505Q8—42no—
506Q8—41no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—42no—
511Q8—81no—
512Q8—82no—
513Q8—82no—
514D4—42no—
515D4—41no—
516D4—42no—
517D4—42no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4#120×C10711yescharacteristic
537C2×C4#120×C10711yescharacteristic
538C2×C4#120×C10711yescharacteristic
539C2×C4C22×D4×C10711yescharacteristic
540C2×C4C22×D4×C10711yescharacteristic
541C2×C4C22×D4×C10711yescharacteristic
542C8—24no—
543C8—24no—
544C8—42no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—42no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—41no—
553C22—162no—
554C22#456×C10712yes—
555C22C2×#120×C10711yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—82no—
568C4#453×C10712yes—
569C2—22no—
570C2—82no—
571C2—81no—
572C2C2×#453×C10711yescharacteristic
573C2C2×#456×C10711yescharacteristic
574C2C107×#302211yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#3561C2
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
2. C107×#3239C2semidirect
3. C107×#3165C2semidirect
4. C2×#497×C107C2semidirect
5. C107×#1661C2semidirect
6. C107×#1660C2semidirect
7. C107×#1531C2semidirect
8. C107×#1527C2semidirect
9. C107×#1524C2semidirect
28. #501×C107C22semidirect
29. #501×C107C22semidirect
34. #489×C107C22semidirect
43. #330×C107C22semidirect
44. #330×C107C22semidirect
46. #329×C107C22semidirect
281. #19033C107direct (N × H)
289. #3239C2×C107semidirect
290. #3165C2×C107semidirect
291. C2×#497C2×C107semidirect
292. #1661C2×C107semidirect
293. #1660C2×C107semidirect
294. #1531C2×C107semidirect
295. #1527C2×C107semidirect
296. #1524C2×C107semidirect
297. C107#19033direct (N × H)
316. #501C22×C107semidirect
317. #501C22×C107semidirect
322. #489C22×C107semidirect
331. #330C22×C107semidirect
332. #330C22×C107semidirect
334. #329C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35612
C107×#32392
C107×#31652
C2×#497×C1072
C107×#16612
C107×#16602
C107×#15312
C107×#15272
C107×#15242
#19033107