Finite Group Databasebeta

← C107×#32623 #41058587

Subgroups — C107×#32623 #41058587

Order 27392.

846 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2548C211yesmaximal, characteristic, complemented
2C107×#2538C211yesmaximal, characteristic, complemented
3C107×#2094C211yesmaximal, characteristic, complemented
4C107×#2071C211yesmaximal, characteristic, complemented
5C107×#2065C211yesmaximal, characteristic, complemented
6C107×#2054C211yesmaximal, characteristic, complemented
7C107×#2041C211yesmaximal, characteristic, complemented
8C107×#2011C211yesmaximal, characteristic
9C107×#1985C211yesmaximal, characteristic, complemented
10C107×#1972C211yesmaximal, characteristic, complemented
11C107×#1936C211yesmaximal, characteristic, complemented
12C107×#1926C211yesmaximal, characteristic, complemented
13C107×#1919C211yesmaximal, characteristic, complemented
14C107×#1879C211yesmaximal, characteristic, complemented
15C107×#1879C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C2×#127×C107C2211yescharacteristic
19C2×#124×C107—21no—
20C2×C22⋊Q8×C107—21no—
21C2×C4×Q8×C107C2211yescharacteristic
22C2×C4×D4×C107C2211yescharacteristic
23C2×#106×C107C2211yescharacteristic
24C2×#106×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26C2×#102×C107C2211yescharacteristic
27C2×#102×C107C2211yescharacteristic
28C2×#102×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#97×C107C2211yescharacteristic
35#396×C107—21no—
36#396×C107—21no—
37#394×C107—21no—
38#394×C107—21no—
39#390×C107—21no—
40#390×C107C2211yescharacteristic
41#390×C107C2211yescharacteristic
42#390×C107C2211yescharacteristic
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#390×C107C2211yescharacteristic
46#389×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#384×C107C2211yescharacteristic
49#380×C107—21no—
50C4×C4⋊C4×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×C107D411yescharacteristic
60C22×D4×C107—21no—
61C22×D4×C107—21no—
62C22×D4×C107C2311yescharacteristic
63C22×D4×C107C2311yescharacteristic
64C22×D4×C107C2311yescharacteristic
65C23×C4×C107—21no—
66C2×D8×C107—22no—
67C2×D8×C107—22no—
68C2×D8×C107—22no—
69C2×D8×C107—41no—
70C2×D8×C107—41no—
71C2×D8×C107—41no—
72C22×C8×C107C2311yescharacteristic
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76#127×C107—41no—
77#127×C107—41no—
78#124×C107—44no—
79C22⋊Q8×C107—44no—
80C4×Q8×C107—41no—
81C4×Q8×C107—41no—
82C4×D4×C107—41no—
83C4×D4×C107—41no—
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×C107D411yescharacteristic
91C2×C4⋊C4×C107C2311yescharacteristic
92C2×C4⋊C4×C107C2311yescharacteristic
93C2×C4⋊C4×C107C2311yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C22⋊C4×C107—21no—
97C2×C22⋊C4×C107—21no—
98C2×C22⋊C4×C107—21no—
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C42×C107—21no—
110C2×C42×C107C2311yescharacteristic
111C2×C42×C107C2311yescharacteristic
112C2×C42×C107C2311yescharacteristic
113#106×C107—22no—
114#106×C107—41no—
115C4⋊C8×C107—41no—
116#102×C107—22no—
117#102×C107—22no—
118#102×C107—41no—
119#102×C107—41no—
120#102×C107—41no—
121#102×C107—41no—
122#102×C107—41no—
123#102×C107—41no—
124#97×C107—41no—
125#95×C107—21no—
126#95×C107—21no—
127#95×C107—21no—
128C24×C107—21no—
129C24×C107—21no—
130C24×C107—21no—
131C2×Q8×C107—22no—
132C2×Q8×C107—22no—
133C2×Q8×C107—41no—
134C2×D4×C107—21no—
135C2×D4×C107—21no—
136C2×D4×C107—21no—
137C2×D4×C107—21no—
138C2×D4×C107—21no—
139C2×D4×C107—21no—
140C2×D4×C107—21no—
141C2×D4×C107—21no—
142C2×D4×C107—21no—
143C2×D4×C107—21no—
144C2×D4×C107—21no—
145C2×D4×C107—21no—
146C2×D4×C107—21no—
147C2×D4×C107—21no—
148C2×D4×C107—21no—
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×C107—42no—
152C2×D4×C107—42no—
153C2×D4×C107—42no—
154C2×D4×C107—42no—
155C2×D4×C107—81no—
156C2×D4×C107—81no—
157C2×D4×C107#4112yes—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—42no—
164C22×C4×C107—42no—
165C22×C4×C107—42no—
166C22×C4×C107C2×D411yescharacteristic
167C22×C4×C107C2×D411yescharacteristic
168C22×C4×C107C2×D411yescharacteristic
169C22×C4×C107C2×D411yescharacteristic
170C22×C4×C107C2×D411yescharacteristic
171C22×C4×C107C2×D411yescharacteristic
172C22×C4×C107C2411yescharacteristic
173D8×C107—44no—
174D8×C107—44no—
175C2×C8×C107—21no—
176C2×C8×C107—21no—
177C2×C8×C107—21no—
178C2×C8×C107—21no—
179C2×C8×C107—21no—
180C2×C8×C107—21no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107#4112yes—
187C4⋊C4×C107—21no—
188C4⋊C4×C107—21no—
189C4⋊C4×C107—21no—
190C4⋊C4×C107—21no—
191C4⋊C4×C107—21no—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—41no—
198C4⋊C4×C107—41no—
199C4⋊C4×C107—41no—
200C4⋊C4×C107—42no—
201C4⋊C4×C107—42no—
202C4⋊C4×C107—42no—
203C4⋊C4×C107—81no—
204C22⋊C4×C107—42no—
205C22⋊C4×C107—42no—
206C22⋊C4×C107—42no—
207C22⋊C4×C107—42no—
208C22⋊C4×C107—42no—
209C22⋊C4×C107—42no—
210C22⋊C4×C107—42no—
211C22⋊C4×C107—81no—
212C22⋊C4×C107—81no—
213C22⋊C4×C107—81no—
214C22⋊C4×C107—81no—
215C22⋊C4×C107—81no—
216C22⋊C4×C107—81no—
217C42×C107—21no—
218C42×C107—21no—
219C42×C107—21no—
220C42×C107—21no—
221C42×C107—21no—
222C42×C107—21no—
223C42×C107—42no—
224C23×C107—22no—
225C23×C107—41no—
226C23×C107—41no—
227C23×C107—41no—
228C23×C107—41no—
229C23×C107—41no—
230C23×C107—41no—
231C23×C107—41no—
232C23×C107—41no—
233C23×C107—41no—
234C23×C107—41no—
235C23×C107—41no—
236C23×C107—41no—
237C23×C107—41no—
238C23×C107—41no—
239C23×C107—41no—
240C23×C107—41no—
241C23×C107—41no—
242C23×C107—41no—
243C23×C107—41no—
244C23×C107—41no—
245C23×C107C22×D411yescharacteristic
246Q8×C107—44no—
247D4×C107—22no—
248D4×C107—22no—
249D4×C107—41no—
250D4×C107—41no—
251D4×C107—41no—
252D4×C107—41no—
253D4×C107—41no—
254D4×C107—41no—
255D4×C107—41no—
256D4×C107—41no—
257D4×C107—41no—
258D4×C107—41no—
259D4×C107—84no—
260D4×C107—84no—
261C2×C4×C107—21no—
262C2×C4×C107—21no—
263C2×C4×C107—21no—
264C2×C4×C107—21no—
265C2×C4×C107—21no—
266C2×C4×C107—21no—
267C2×C4×C107—21no—
268C2×C4×C107—21no—
269C2×C4×C107—21no—
270C2×C4×C107—21no—
271C2×C4×C107—21no—
272C2×C4×C107—21no—
273C2×C4×C107—21no—
274C2×C4×C107—21no—
275C2×C4×C107—21no—
276C2×C4×C107—21no—
277C2×C4×C107—41no—
278C2×C4×C107—41no—
279C2×C4×C107—41no—
280C2×C4×C107—41no—
281C2×C4×C107—41no—
282C2×C4×C107—41no—
283C2×C4×C107—41no—
284C2×C4×C107—41no—
285C2×C4×C107—41no—
286C2×C4×C107—41no—
287C2×C4×C107—41no—
288C2×C4×C107—41no—
289C2×C4×C107—41no—
290C2×C4×C107—41no—
291C2×C4×C107—41no—
292C2×C4×C107—84no—
293C2×C4×C107AGL(1,ℤ/8)12yes—
294C2×C4×C107AGL(1,ℤ/8)12yes—
295C2×C4×C107C2×#4111yescharacteristic
296C2×C4×C107C2×#4111yescharacteristic
297C2×C4×C107H(5,𝔽2)11yescharacteristic
298C2×C4×C107H(5,𝔽2)11yescharacteristic
299C2×C4×C107H(5,𝔽2)11yescharacteristic
300C2×C4×C1072−1+411yescharacteristic
301C8×C107—22no—
302C8×C107—41no—
303C8×C107—41no—
304C8×C107—41no—
305C22×C107—42no—
306C22×C107—42no—
307C22×C107—42no—
308C22×C107—81no—
309C22×C107—81no—
310C22×C107—81no—
311C22×C107—81no—
312C22×C107—81no—
313C22×C107—81no—
314C22×C107—81no—
315C22×C107—81no—
316C22×C107—81no—
317C22×C107—81no—
318C22×C107—81no—
319C22×C107—81no—
320C22×C107—81no—
321C22×C107—81no—
322C22×C107—81no—
323C22×C107—81no—
324C22×C107—81no—
325C22×C107—81no—
326C22×C107#53411yescharacteristic
327C22×C107#54811yescharacteristic
328C22×C107#55011yescharacteristic
329C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C107C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C107#57611yescharacteristic
332C22×C107#57711yescharacteristic
333C4×C107—22no—
334C4×C107—22no—
335C4×C107—41no—
336C4×C107—41no—
337C4×C107—41no—
338C4×C107—41no—
339C4×C107—81no—
340C4×C107—81no—
341C4×C107—81no—
342C4×C107—81no—
343C4×C107—81no—
344C4×C107#53811yescharacteristic
345C4×C107#54211yescharacteristic
346C4×C107#55111yescharacteristic
347C4×C107#56211yescharacteristic
348#32623C10711yesmaximal, characteristic, direct product factor, Sylow
349C2×C107—82no—
350C2×C107—161no—
351C2×C107—161no—
352C2×C107#273011yescharacteristic
353C2×C107#319211yescharacteristic
354C2×C107#319811yescharacteristic
355C2×C107#336611yescharacteristic
356C2×C107#337311yescharacteristic
357C2×C107#339711yescharacteristic
358C2×C107#339911yescharacteristic
359#2548C2×C10711yescharacteristic, complemented
360#2538C2×C10711yescharacteristic, complemented
361#2094C2×C10711yescharacteristic, complemented
362#2071C2×C10711yescharacteristic, complemented
363#2065C2×C10711yescharacteristic, complemented
364#2054C2×C10711yescharacteristic, complemented
365#2041C2×C10711yescharacteristic, complemented
366#2011C2×C10711yescharacteristic
367#1985C2×C10711yescharacteristic, complemented
368#1972C2×C10711yescharacteristic, complemented
369#1936C2×C10711yescharacteristic, complemented
370#1926C2×C10711yescharacteristic, complemented
371#1919C2×C10711yescharacteristic, complemented
372#1879C2×C10711yescharacteristic, complemented
373#1879C2×C10711yescharacteristic, complemented
374C107#3262311yescharacteristic, direct product factor, Sylow
375C22×D8C22×C10711yescharacteristic
376C22×D8C22×C10711yescharacteristic
377C2×#127C22×C10711yescharacteristic
378C2×#124—21no—
379C2×C22⋊Q8—21no—
380C2×C4×Q8C22×C10711yescharacteristic
381C2×C4×D4C22×C10711yescharacteristic
382C2×#106C22×C10711yescharacteristic
383C2×#106C22×C10711yescharacteristic
384C2×C4⋊C8C22×C10711yescharacteristic
385C2×#102C22×C10711yescharacteristic
386C2×#102C22×C10711yescharacteristic
387C2×#102C22×C10711yescharacteristic
388C2×#102C22×C10711yescharacteristic
389C2×#102C22×C10711yescharacteristic
390C2×#102C22×C10711yescharacteristic
391C2×#102C22×C10711yescharacteristic
392C2×#102C22×C10711yescharacteristic
393C2×#97C22×C10711yescharacteristic
394#396—21no—
395#396—21no—
396#394—21no—
397#394—21no—
398#390—21no—
399#390C22×C10711yescharacteristic
400#390C22×C10711yescharacteristic
401#390C22×C10711yescharacteristic
402#390C22×C10711yescharacteristic
403#390C22×C10711yescharacteristic
404#390C22×C10711yescharacteristic
405#389C22×C10711yescharacteristic
406#389C22×C10711yescharacteristic
407#384C22×C10711yescharacteristic
408#380—21no—
409C4×C4⋊C4C22×C10711yescharacteristic
410#340C22×C10711yescharacteristic
411#340C22×C10711yescharacteristic
412#340C22×C10711yescharacteristic
413#340C22×C10711yescharacteristic
414#336C22×C10711yescharacteristic
415#336C22×C10711yescharacteristic
416#336C22×C10711yescharacteristic
417#336C22×C10711yescharacteristic
418C22×Q8D4×C10711yescharacteristic
419C22×D4—21no—
420C22×D4—21no—
421C22×D4C23×C10711yescharacteristic
422C22×D4C23×C10711yescharacteristic
423C22×D4C23×C10711yescharacteristic
424C23×C4—21no—
425C2×D8—22no—
426C2×D8—22no—
427C2×D8—22no—
428C2×D8—41no—
429C2×D8—41no—
430C2×D8—41no—
431C22×C8C23×C10711yescharacteristic
432C22×C8C23×C10711yescharacteristic
433C22×C8C23×C10711yescharacteristic
434C22×C8C23×C10711yescharacteristic
435#127—41no—
436#127—41no—
437#124—44no—
438C22⋊Q8—44no—
439C4×Q8—41no—
440C4×Q8—41no—
441C4×D4—41no—
442C4×D4—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4D4×C10711yescharacteristic
448C2×C4⋊C4D4×C10711yescharacteristic
449C2×C4⋊C4D4×C10711yescharacteristic
450C2×C4⋊C4C23×C10711yescharacteristic
451C2×C4⋊C4C23×C10711yescharacteristic
452C2×C4⋊C4C23×C10711yescharacteristic
453C2×C4⋊C4C23×C10711yescharacteristic
454C2×C4⋊C4C23×C10711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C42—21no—
469C2×C42C23×C10711yescharacteristic
470C2×C42C23×C10711yescharacteristic
471C2×C42C23×C10711yescharacteristic
472#106—22no—
473#106—41no—
474C4⋊C8—41no—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479#102—41no—
480#102—41no—
481#102—41no—
482#102—41no—
483#97—41no—
484#95—21no—
485#95—21no—
486#95—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—81no—
515C2×D4—81no—
516C2×D4#41×C10712yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4C2×D4×C10711yescharacteristic
526C22×C4C2×D4×C10711yescharacteristic
527C22×C4C2×D4×C10711yescharacteristic
528C22×C4C2×D4×C10711yescharacteristic
529C22×C4C2×D4×C10711yescharacteristic
530C22×C4C2×D4×C10711yescharacteristic
531C22×C4C24×C10711yescharacteristic
532D8—44no—
533D8—44no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8#41×C10712yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C10711yescharacteristic
605Q8—44no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619D4—84no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4AGL(1,ℤ/8)×C10712yes—
653C2×C4AGL(1,ℤ/8)×C10712yes—
654C2×C4C2×#41×C10711yescharacteristic
655C2×C4C2×#41×C10711yescharacteristic
656C2×C4H(5,𝔽2)×C10711yescharacteristic
657C2×C4H(5,𝔽2)×C10711yescharacteristic
658C2×C4H(5,𝔽2)×C10711yescharacteristic
659C2×C42−1+4×C10711yescharacteristic
660C8—22no—
661C8—41no—
662C8—41no—
663C8—41no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22#534×C10711yescharacteristic
686C22#548×C10711yescharacteristic
687C22#550×C10711yescharacteristic
688C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
689C22C2×AGL(1,ℤ/8)×C10711yescharacteristic
690C22#576×C10711yescharacteristic
691C22#577×C10711yescharacteristic
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4#538×C10711yescharacteristic
704C4#542×C10711yescharacteristic
705C4#551×C10711yescharacteristic
706C4#562×C10711yescharacteristic
707C2—82no—
708C2—161no—
709C2—161no—
710C2C107×#273011yescharacteristic
711C2C107×#319211yescharacteristic
712C2C107×#319811yescharacteristic
713C2C107×#336611yescharacteristic
714C2C107×#337311yescharacteristic
715C2C107×#339711yescharacteristic
716C2C107×#339911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC107×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×Q8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#2548C2semidirect
2. C107×#2538C2semidirect
3. C107×#2094C2semidirect
4. C107×#2071C2semidirect
5. C107×#2065C2semidirect
6. C107×#2054C2semidirect
7. C107×#2041C2semidirect
9. C107×#1985C2semidirect
10. C107×#1972C2semidirect
11. C107×#1936C2semidirect
12. C107×#1926C2semidirect
13. C107×#1919C2semidirect
14. C107×#1879C2semidirect
15. C107×#1879C2semidirect
348. #32623C107direct (N × H)
359. #2548C2×C107semidirect
360. #2538C2×C107semidirect
361. #2094C2×C107semidirect
362. #2071C2×C107semidirect
363. #2065C2×C107semidirect
364. #2054C2×C107semidirect
365. #2041C2×C107semidirect
367. #1985C2×C107semidirect
368. #1972C2×C107semidirect
369. #1936C2×C107semidirect
370. #1926C2×C107semidirect
371. #1919C2×C107semidirect
372. #1879C2×C107semidirect
373. #1879C2×C107semidirect
374. C107#32623direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#25482
C107×#25382
C107×#20942
C107×#20712
C107×#20652
C107×#20542
C107×#20412
C107×#20112
C107×#19852
C107×#19722
C107×#19362
C107×#19262
C107×#19192
C107×#18792
#32623107