Finite Group Databasebeta

← C107×#29172 #41055136

Subgroups — C107×#29172 #41055136

Order 27392.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2629C211yesmaximal, characteristic
2C107×#2323C211yesmaximal, characteristic
3C107×#2100C211yesmaximal, characteristic, complemented
4C107×#2096C211yesmaximal, characteristic, complemented
5C107×#2059C211yesmaximal, characteristic, complemented
6C107×#2026C211yesmaximal, characteristic, complemented
7C107×#1920C211yesmaximal, characteristic, complemented
8C107×#1919C211yesmaximal, characteristic, complemented
9C107×#1894C211yesmaximal, characteristic
10C107×#1892C211yesmaximal, characteristic
11C107×#1865C211yesmaximal, characteristic, complemented
12C107×#1863C211yesmaximal, characteristic, complemented
13C107×#1809C211yesmaximal, characteristic
14C107×#1807C211yesmaximal, characteristic
15C107×#1729C211yesmaximal, characteristic
16C22×M16×C107C2211yescharacteristic
17C23×C8×C107C2211yescharacteristic
18C2×#125×C107C2211yescharacteristic
19C2×C22⋊Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22C2×#107×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×#106×C107C2211yescharacteristic
26C2×#103×C107C2211yescharacteristic
27C2×#103×C107C2211yescharacteristic
28C2×#103×C107C2211yescharacteristic
29C2×#103×C107C2211yescharacteristic
30#398×C107—21no—
31#398×C107—21no—
32#396×C107—21no—
33#396×C107—21no—
34#391×C107C2211yescharacteristic
35#389×C107—21no—
36#389×C107C2211yescharacteristic
37#389×C107C2211yescharacteristic
38#389×C107C2211yescharacteristic
39#388×C107—21no—
40#388×C107—21no—
41#387×C107—21no—
42#384×C107C2211yescharacteristic
43#380×C107C2211yescharacteristic
44#380×C107C2211yescharacteristic
45#380×C107C2211yescharacteristic
46C4×C4⋊C4×C107C2211yescharacteristic
47#340×C107C2211yescharacteristic
48#340×C107C2211yescharacteristic
49#340×C107C2211yescharacteristic
50#340×C107C2211yescharacteristic
51#340×C107C2211yescharacteristic
52#340×C107C2211yescharacteristic
53#340×C107C2211yescharacteristic
54#340×C107C2211yescharacteristic
55#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59C22×Q8×C107C2311yescharacteristic
60C23×C4×C107C2311yescharacteristic
61C2×M16×C107—22no—
62C2×M16×C107—22no—
63C2×M16×C107—41no—
64C22×C8×C107—22no—
65C22×C8×C107—22no—
66C22×C8×C107—41no—
67C22×C8×C107C2311yescharacteristic
68C22×C8×C107C2311yescharacteristic
69C22×C8×C107C2311yescharacteristic
70C22×C8×C107C2311yescharacteristic
71#125×C107—41no—
72#125×C107—41no—
73C22⋊Q8×C107—22no—
74C22⋊Q8×C107Q814yes—
75C4×Q8×C107—41no—
76C4×Q8×C107—41no—
77#117×C107—41no—
78#117×C107—41no—
79C2×C4⋊C4×C107—21no—
80C2×C4⋊C4×C107—21no—
81C2×C4⋊C4×C107—21no—
82C2×C4⋊C4×C107—21no—
83C2×C4⋊C4×C107—21no—
84C2×C4⋊C4×C107—21no—
85C2×C4⋊C4×C107—21no—
86C2×C4⋊C4×C107—21no—
87C2×C4⋊C4×C107—21no—
88C2×C4⋊C4×C107D411yescharacteristic
89C2×C4⋊C4×C107D411yescharacteristic
90C2×C4⋊C4×C107C2311yescharacteristic
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107D411yescharacteristic
102C2×C22⋊C4×C107D411yescharacteristic
103C2×C42×C107—21no—
104C2×C42×C107—21no—
105C2×C42×C107C2311yescharacteristic
106C2×C42×C107C2311yescharacteristic
107#107×C107—41no—
108#106×C107—22no—
109#106×C107—22no—
110#106×C107—41no—
111#103×C107—22no—
112#103×C107—22no—
113#103×C107—41no—
114#103×C107—41no—
115#95×C107—21no—
116#95×C107—21no—
117#95×C107—21no—
118#95×C107—21no—
119#95×C107—21no—
120#95×C107—21no—
121#95×C107—21no—
122#95×C107—21no—
123#95×C107—21no—
124C24×C107C2×D411yescharacteristic
125C2×Q8×C107—21no—
126C2×Q8×C107—21no—
127C2×Q8×C107—21no—
128C2×Q8×C107—21no—
129C2×Q8×C107—21no—
130C2×Q8×C107C2×Q812yes—
131C22×C4×C107—21no—
132C22×C4×C107—21no—
133C22×C4×C107—21no—
134C22×C4×C107—21no—
135C22×C4×C107—21no—
136C22×C4×C107—21no—
137C22×C4×C107—21no—
138C22×C4×C107—21no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107C2×D411yescharacteristic
144C22×C4×C107C2×D411yescharacteristic
145C22×C4×C107C2×D411yescharacteristic
146C22×C4×C107C2×D411yescharacteristic
147C22×C4×C107C2×D411yescharacteristic
148C22×C4×C107C2×Q812yes—
149C22×C4×C107#4112yes—
150C22×C4×C107C2411yescharacteristic
151M16×C107—44no—
152C2×C8×C107—21no—
153C2×C8×C107—21no—
154C2×C8×C107—21no—
155C2×C8×C107—21no—
156C2×C8×C107—21no—
157C2×C8×C107—21no—
158C2×C8×C107—21no—
159C2×C8×C107—21no—
160C2×C8×C107—21no—
161C2×C8×C107—21no—
162C2×C8×C107—44no—
163C2×C8×C107#4112yes—
164C2×C8×C107#4112yes—
165C4⋊C4×C107—24no—
166C4⋊C4×C107—21no—
167C4⋊C4×C107—21no—
168C4⋊C4×C107—21no—
169C4⋊C4×C107—21no—
170C4⋊C4×C107—21no—
171C4⋊C4×C107—21no—
172C4⋊C4×C107—21no—
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—41no—
180C4⋊C4×C107—41no—
181C4⋊C4×C107—42no—
182C4⋊C4×C107—42no—
183C4⋊C4×C107—42no—
184C4⋊C4×C107—81no—
185C4⋊C4×C107—81no—
186C4⋊C4×C107—81no—
187C4⋊C4×C107—81no—
188C4⋊C4×C107—81no—
189C4⋊C4×C107C2×Q812yes—
190C22⋊C4×C107—24no—
191C22⋊C4×C107—41no—
192C22⋊C4×C107—41no—
193C22⋊C4×C107—81no—
194C22⋊C4×C107—81no—
195C22⋊C4×C107—81no—
196C42×C107—21no—
197C42×C107—21no—
198C42×C107—21no—
199C42×C107—21no—
200C42×C107—42no—
201C42×C107—81no—
202C23×C107—21no—
203C23×C107—21no—
204C23×C107—21no—
205C23×C107—21no—
206C23×C107—21no—
207C23×C107—21no—
208C23×C107C22⋊Q812yes—
209C23×C107C22×D411yescharacteristic
210Q8×C107—22no—
211Q8×C107—22no—
212Q8×C107—41no—
213Q8×C107—41no—
214C2×C4×C107—21no—
215C2×C4×C107—21no—
216C2×C4×C107—22no—
217C2×C4×C107—22no—
218C2×C4×C107—22no—
219C2×C4×C107—22no—
220C2×C4×C107—22no—
221C2×C4×C107—22no—
222C2×C4×C107—21no—
223C2×C4×C107—21no—
224C2×C4×C107—21no—
225C2×C4×C107—21no—
226C2×C4×C107—21no—
227C2×C4×C107—21no—
228C2×C4×C107—21no—
229C2×C4×C107—21no—
230C2×C4×C107—21no—
231C2×C4×C107—21no—
232C2×C4×C107—21no—
233C2×C4×C107—21no—
234C2×C4×C107—41no—
235C2×C4×C107—41no—
236C2×C4×C107—41no—
237C2×C4×C107—41no—
238C2×C4×C107—41no—
239C2×C4×C107—41no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—41no—
243C2×C4×C107—41no—
244C2×C4×C107—41no—
245C2×C4×C107—41no—
246C2×C4×C107—41no—
247C2×C4×C107—41no—
248C2×C4×C107—41no—
249C2×C4×C107—41no—
250C2×C4×C107—41no—
251C2×C4×C107—41no—
252C2×C4×C107—41no—
253C2×C4×C107—41no—
254C2×C4×C107—41no—
255C2×C4×C107—41no—
256C2×C4×C107C22⋊Q812yes—
257C2×C4×C107C22×Q811yescharacteristic
258C2×C4×C107C2×#4111yescharacteristic
259C2×C4×C107C2×#4111yescharacteristic
260C2×C4×C107C2×#4111yescharacteristic
261C2×C4×C107H(5,𝔽2)11yescharacteristic
262C2×C4×C107H(5,𝔽2)11yescharacteristic
263C8×C107—22no—
264C8×C107—22no—
265C8×C107—41no—
266C8×C107—41no—
267C22×C107—22no—
268C22×C107—22no—
269C22×C107—22no—
270C22×C107—41no—
271C22×C107—41no—
272C22×C107—41no—
273C22×C107—41no—
274C22×C107C2×C22⋊Q811yescharacteristic
275C22×C107#53211yescharacteristic
276C22×C107#53411yescharacteristic
277C22×C107#57711yescharacteristic
278C22×C107#57711yescharacteristic
279C22×C107#57711yescharacteristic
280C22×C107#57811yescharacteristic
281C4×C107—22no—
282C4×C107—42no—
283C4×C107—42no—
284C4×C107—41no—
285C4×C107—41no—
286C4×C107—41no—
287C4×C107—41no—
288C4×C107—81no—
289C4×C107—81no—
290C4×C107—81no—
291C4×C107—81no—
292C4×C107—81no—
293C4×C107—81no—
294C4×C107#55111yescharacteristic
295C4×C107#55111yescharacteristic
296C4×C107#55411yescharacteristic
297C4×C107#55411yescharacteristic
298#29172C10711yesmaximal, characteristic, direct product factor, Sylow
299C2×C107—42no—
300C2×C107#256411yescharacteristic
301C2×C107#308211yescharacteristic
302C2×C107#308411yescharacteristic
303C2×C107#317411yescharacteristic
304C2×C107#317811yescharacteristic
305C2×C107#320111yescharacteristic
306C2×C107#320411yescharacteristic
307#2629C2×C10711yescharacteristic
308#2323C2×C10711yescharacteristic
309#2100C2×C10711yescharacteristic, complemented
310#2096C2×C10711yescharacteristic, complemented
311#2059C2×C10711yescharacteristic, complemented
312#2026C2×C10711yescharacteristic, complemented
313#1920C2×C10711yescharacteristic, complemented
314#1919C2×C10711yescharacteristic, complemented
315#1894C2×C10711yescharacteristic
316#1892C2×C10711yescharacteristic
317#1865C2×C10711yescharacteristic, complemented
318#1863C2×C10711yescharacteristic, complemented
319#1809C2×C10711yescharacteristic
320#1807C2×C10711yescharacteristic
321#1729C2×C10711yescharacteristic
322C107#2917211yescharacteristic, direct product factor, Sylow
323C22×M16C22×C10711yescharacteristic
324C23×C8C22×C10711yescharacteristic
325C2×#125C22×C10711yescharacteristic
326C2×C22⋊Q8C22×C10711yescharacteristic
327C2×C4×Q8C22×C10711yescharacteristic
328C2×#117C22×C10711yescharacteristic
329C2×#107C22×C10711yescharacteristic
330C2×#106C22×C10711yescharacteristic
331C2×#106C22×C10711yescharacteristic
332C2×#106C22×C10711yescharacteristic
333C2×#103C22×C10711yescharacteristic
334C2×#103C22×C10711yescharacteristic
335C2×#103C22×C10711yescharacteristic
336C2×#103C22×C10711yescharacteristic
337#398—21no—
338#398—21no—
339#396—21no—
340#396—21no—
341#391C22×C10711yescharacteristic
342#389—21no—
343#389C22×C10711yescharacteristic
344#389C22×C10711yescharacteristic
345#389C22×C10711yescharacteristic
346#388—21no—
347#388—21no—
348#387—21no—
349#384C22×C10711yescharacteristic
350#380C22×C10711yescharacteristic
351#380C22×C10711yescharacteristic
352#380C22×C10711yescharacteristic
353C4×C4⋊C4C22×C10711yescharacteristic
354#340C22×C10711yescharacteristic
355#340C22×C10711yescharacteristic
356#340C22×C10711yescharacteristic
357#340C22×C10711yescharacteristic
358#340C22×C10711yescharacteristic
359#340C22×C10711yescharacteristic
360#340C22×C10711yescharacteristic
361#340C22×C10711yescharacteristic
362#336C22×C10711yescharacteristic
363#336C22×C10711yescharacteristic
364#336C22×C10711yescharacteristic
365#336C22×C10711yescharacteristic
366C22×Q8C23×C10711yescharacteristic
367C23×C4C23×C10711yescharacteristic
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—41no—
371C22×C8—22no—
372C22×C8—22no—
373C22×C8—41no—
374C22×C8C23×C10711yescharacteristic
375C22×C8C23×C10711yescharacteristic
376C22×C8C23×C10711yescharacteristic
377C22×C8C23×C10711yescharacteristic
378#125—41no—
379#125—41no—
380C22⋊Q8—22no—
381C22⋊Q8Q8×C10714yes—
382C4×Q8—41no—
383C4×Q8—41no—
384#117—41no—
385#117—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C10711yescharacteristic
396C2×C4⋊C4D4×C10711yescharacteristic
397C2×C4⋊C4C23×C10711yescharacteristic
398C2×C4⋊C4C23×C10711yescharacteristic
399C2×C4⋊C4C23×C10711yescharacteristic
400C2×C4⋊C4C23×C10711yescharacteristic
401C2×C4⋊C4C23×C10711yescharacteristic
402C2×C4⋊C4C23×C10711yescharacteristic
403C2×C4⋊C4C23×C10711yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4D4×C10711yescharacteristic
409C2×C22⋊C4D4×C10711yescharacteristic
410C2×C42—21no—
411C2×C42—21no—
412C2×C42C23×C10711yescharacteristic
413C2×C42C23×C10711yescharacteristic
414#107—41no—
415#106—22no—
416#106—22no—
417#106—41no—
418#103—22no—
419#103—22no—
420#103—41no—
421#103—41no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431C24C2×D4×C10711yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×Q8×C10712yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4C2×D4×C10711yescharacteristic
451C22×C4C2×D4×C10711yescharacteristic
452C22×C4C2×D4×C10711yescharacteristic
453C22×C4C2×D4×C10711yescharacteristic
454C22×C4C2×D4×C10711yescharacteristic
455C22×C4C2×Q8×C10712yes—
456C22×C4#41×C10712yes—
457C22×C4C24×C10711yescharacteristic
458M16—44no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—44no—
470C2×C8#41×C10712yes—
471C2×C8#41×C10712yes—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—81no—
495C4⋊C4—81no—
496C4⋊C4C2×Q8×C10712yes—
497C22⋊C4—24no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—81no—
501C22⋊C4—81no—
502C22⋊C4—81no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—81no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23C22⋊Q8×C10712yes—
516C23C22×D4×C10711yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4C22⋊Q8×C10712yes—
564C2×C4C22×Q8×C10711yescharacteristic
565C2×C4C2×#41×C10711yescharacteristic
566C2×C4C2×#41×C10711yescharacteristic
567C2×C4C2×#41×C10711yescharacteristic
568C2×C4H(5,𝔽2)×C10711yescharacteristic
569C2×C4H(5,𝔽2)×C10711yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×C22⋊Q8×C10711yescharacteristic
582C22#532×C10711yescharacteristic
583C22#534×C10711yescharacteristic
584C22#577×C10711yescharacteristic
585C22#577×C10711yescharacteristic
586C22#577×C10711yescharacteristic
587C22#578×C10711yescharacteristic
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—81no—
601C4#551×C10711yescharacteristic
602C4#551×C10711yescharacteristic
603C4#554×C10711yescharacteristic
604C4#554×C10711yescharacteristic
605C2—42no—
606C2C107×#256411yescharacteristic
607C2C107×#308211yescharacteristic
608C2C107×#308411yescharacteristic
609C2C107×#317411yescharacteristic
610C2C107×#317811yescharacteristic
611C2C107×#320111yescharacteristic
612C2C107×#320411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC24×C107C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#2100C2semidirect
4. C107×#2096C2semidirect
5. C107×#2059C2semidirect
6. C107×#2026C2semidirect
7. C107×#1920C2semidirect
8. C107×#1919C2semidirect
11. C107×#1865C2semidirect
12. C107×#1863C2semidirect
298. #29172C107direct (N × H)
309. #2100C2×C107semidirect
310. #2096C2×C107semidirect
311. #2059C2×C107semidirect
312. #2026C2×C107semidirect
313. #1920C2×C107semidirect
314. #1919C2×C107semidirect
317. #1865C2×C107semidirect
318. #1863C2×C107semidirect
322. C107#29172direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#26292
C107×#23232
C107×#21002
C107×#20962
C107×#20592
C107×#20262
C107×#19202
C107×#19192
C107×#18942
C107×#18922
C107×#18652
C107×#18632
C107×#18092
C107×#18072
C107×#17292
#29172107