Finite Group Databasebeta

← C107×#25961 #41051925

Subgroups — C107×#25961 #41051925

Order 27392.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#479×C107C211yesmaximal, characteristic, complemented
2C2×#416×C107C211yesmaximal, characteristic
3C107×#2441C211yesmaximal, characteristic, complemented
4C107×#2341C211yesmaximal, characteristic
5C107×#2093C211yesmaximal, characteristic, complemented
6C107×#2067C211yesmaximal, characteristic, complemented
7C107×#2065C211yesmaximal, characteristic, complemented
8C107×#2025C211yesmaximal, characteristic, complemented
9C107×#1863C211yesmaximal, characteristic, complemented
10C107×#1863C211yesmaximal, characteristic, complemented
11C107×#1854C211yesmaximal, characteristic, complemented
12C107×#1850C211yesmaximal, characteristic, complemented
13C107×#1808C211yesmaximal, characteristic, complemented
14C107×#1803C211yesmaximal, characteristic, complemented
15C107×#1788C211yesmaximal, characteristic
16C22×#41×C107C2211yescharacteristic
17C23×C8×C107C2211yescharacteristic
18C2×#125×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22#479×C107—24no—
23C2×#107×C107C2211yescharacteristic
24C2×#107×C107C2211yescharacteristic
25C2×#107×C107C2211yescharacteristic
26C2×#106×C107C2211yescharacteristic
27C2×C4⋊C8×C107C2211yescharacteristic
28C2×C4⋊C8×C107C2211yescharacteristic
29#416×C107—24no—
30C2×#103×C107C2211yescharacteristic
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#103×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic
35C2×#102×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39#399×C107—21no—
40#396×C107—21no—
41#390×C107—21no—
42#390×C107—21no—
43#390×C107C2211yescharacteristic
44#390×C107C2211yescharacteristic
45#389×C107—21no—
46#389×C107C2211yescharacteristic
47#389×C107C2211yescharacteristic
48#387×C107—21no—
49#384×C107C2211yescharacteristic
50#380×C107—21no—
51#380×C107C2211yescharacteristic
52#380×C107C2211yescharacteristic
53C4×C22⋊C4×C107—21no—
54C4×C22⋊C4×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61C2×#41×C107—22no—
62C2×#41×C107—22no—
63C2×#41×C107—22no—
64C2×#41×C107—41no—
65C2×#41×C107—41no—
66C2×#41×C107Q814yes—
67C22×Q8×C107C2311yescharacteristic
68C22×D4×C107—21no—
69C22×D4×C107C2311yescharacteristic
70C23×C4×C107—21no—
71C23×C4×C107C2311yescharacteristic
72C22×C8×C107—22no—
73C22×C8×C107—22no—
74C22×C8×C107—41no—
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79#125×C107—22no—
80#125×C107—41no—
81C4×Q8×C107—22no—
82C4×Q8×C107—22no—
83C4×Q8×C107—41no—
84C4×Q8×C107—41no—
85#117×C107—22no—
86#117×C107—41no—
87C2×C4⋊C4×C107—21no—
88C2×C4⋊C4×C107—21no—
89C2×C4⋊C4×C107—21no—
90C2×C4⋊C4×C107—21no—
91C2×C4⋊C4×C107—21no—
92C2×C4⋊C4×C107—21no—
93C2×C4⋊C4×C107—21no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
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×C107D411yescharacteristic
109C2×C22⋊C4×C107D411yescharacteristic
110C2×C42×C107—21no—
111C2×C42×C107—21no—
112C2×C42×C107—21no—
113C2×C42×C107C2311yescharacteristic
114C2×C42×C107C2311yescharacteristic
115#107×C107—22no—
116#107×C107—41no—
117#107×C107—41no—
118#106×C107—22no—
119C4⋊C8×C107—22no—
120C4⋊C8×C107—41no—
121#103×C107—22no—
122#103×C107—22no—
123#103×C107—22no—
124#103×C107D414yes—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—41no—
128#102×C107—41no—
129C22⋊C8×C107—22no—
130#95×C107—21no—
131#95×C107—21no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107D411yescharacteristic
135#95×C107D411yescharacteristic
136C24×C107—21no—
137C24×C107C2×D411yescharacteristic
138#41×C107—28no—
139#41×C107—44no—
140#41×C107—44no—
141#41×C107—44no—
142C2×Q8×C107—21no—
143C2×Q8×C107—21no—
144C2×Q8×C107—21no—
145C2×Q8×C107C2×D412yes—
146C2×Q8×C107C2×Q812yes—
147C2×Q8×C107#4112yes—
148C2×D4×C107—24no—
149C2×D4×C107—21no—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—42no—
155C2×D4×C107—42no—
156C2×D4×C107C2×Q812yes—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—24no—
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—21no—
167C22×C4×C107—21no—
168C22×C4×C107—21no—
169C22×C4×C107—42no—
170C22×C4×C107—42no—
171C22×C4×C107C2×D411yescharacteristic
172C22×C4×C107C2×D411yescharacteristic
173C22×C4×C107C2×D411yescharacteristic
174C22×C4×C107C2×D411yescharacteristic
175C22×C4×C107C2×D411yescharacteristic
176C22×C4×C107C2×Q812yes—
177C22×C4×C107#4112yes—
178C22×C4×C107C2411yescharacteristic
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—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107—21no—
190C2×C8×C107—44no—
191C2×C8×C107C2×D412yes—
192C4⋊C4×C107—21no—
193C4⋊C4×C107—21no—
194C4⋊C4×C107—21no—
195C4⋊C4×C107—21no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—21no—
199C4⋊C4×C107—21no—
200C4⋊C4×C107—21no—
201C4⋊C4×C107—21no—
202C4⋊C4×C107—21no—
203C4⋊C4×C107—42no—
204C4⋊C4×C107—42no—
205C4⋊C4×C107—42no—
206C4⋊C4×C107—42no—
207C4⋊C4×C107—42no—
208C4⋊C4×C107—42no—
209C4⋊C4×C107—81no—
210C4⋊C4×C107—81no—
211C4⋊C4×C107C2×D412yes—
212C22⋊C4×C107—22no—
213C22⋊C4×C107—41no—
214C22⋊C4×C107—42no—
215C22⋊C4×C107—42no—
216C22⋊C4×C107—42no—
217C22⋊C4×C107—81no—
218C22⋊C4×C107—81no—
219C22⋊C4×C107—81no—
220C22⋊C4×C107—81no—
221C42×C107—21no—
222C42×C107—21no—
223C42×C107—21no—
224C42×C107—21no—
225C42×C107—42no—
226C42×C107—42no—
227C42×C107—42no—
228C23×C107—21no—
229C23×C107—21no—
230C23×C107—21no—
231C23×C107—21no—
232C23×C107—21no—
233C23×C107—21no—
234C23×C107—22no—
235C23×C107—41no—
236C23×C107—41no—
237C23×C107—41no—
238C23×C107—41no—
239C23×C107—41no—
240C23×C107—41no—
241C23×C107C22⋊Q812yes—
242C23×C107C22×D411yescharacteristic
243Q8×C107—22no—
244Q8×C107—22no—
245Q8×C107—22no—
246Q8×C107C22⋊Q814yes—
247D4×C107—22no—
248D4×C107—22no—
249D4×C107—48no—
250D4×C107—41no—
251D4×C107—41no—
252C2×C4×C107—22no—
253C2×C4×C107—21no—
254C2×C4×C107—22no—
255C2×C4×C107—21no—
256C2×C4×C107—22no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—22no—
260C2×C4×C107—22no—
261C2×C4×C107—22no—
262C2×C4×C107—22no—
263C2×C4×C107—21no—
264C2×C4×C107—21no—
265C2×C4×C107—22no—
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—48no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—41no—
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×C107C22⋊Q812yes—
292C2×C4×C107#13512yes—
293C2×C4×C107C22×D411yescharacteristic
294C2×C4×C107C22×Q811yescharacteristic
295C2×C4×C107C2×#4111yescharacteristic
296C2×C4×C107C2×#4111yescharacteristic
297C2×C4×C107H(5,𝔽2)11yescharacteristic
298C2×C4×C107H(5,𝔽2)11yescharacteristic
299C8×C107—22no—
300C8×C107—41no—
301C8×C107—41no—
302C8×C107—41no—
303C22×C107—22no—
304C22×C107—22no—
305C22×C107—22no—
306C22×C107—41no—
307C22×C107—41no—
308C22×C107—41no—
309C22×C107—41no—
310C22×C107—42no—
311C22×C107—42no—
312C22×C107—42no—
313C22×C107—81no—
314C22×C107—81no—
315C22×C107—81no—
316C22×C107—81no—
317C22×C107C2×C22⋊Q811yescharacteristic
318C22×C107D4211yescharacteristic
319C22×C107#54611yescharacteristic
320C22×C107C2×#13511yescharacteristic
321C22×C107#57511yescharacteristic
322C22×C107#57611yescharacteristic
323C22×C107#57811yescharacteristic
324C4×C107—22no—
325C4×C107—24no—
326C4×C107—22no—
327C4×C107—41no—
328C4×C107—42no—
329C4×C107—41no—
330C4×C107—41no—
331C4×C107—81no—
332C4×C107—81no—
333C4×C107—81no—
334C4×C107—81no—
335C4×C107—81no—
336C4×C107C2×C22⋊Q811yescharacteristic
337C4×C107#54311yescharacteristic
338C4×C107#54611yescharacteristic
339C4×C107#55111yescharacteristic
340#25961C10711yesmaximal, characteristic, direct product factor, Sylow
341C2×C107—42no—
342C2×C107—82no—
343C2×C107#243711yescharacteristic
344C2×C107#307611yescharacteristic
345C2×C107#308311yescharacteristic
346C2×C107#326911yescharacteristic
347C2×C107#328711yescharacteristic
348C2×C107#330011yescharacteristic
349C2×C107#330911yescharacteristic
350C2×#479C2×C10711yescharacteristic, complemented
351C2×#416C2×C10711yescharacteristic
352#2441C2×C10711yescharacteristic, complemented
353#2341C2×C10711yescharacteristic
354#2093C2×C10711yescharacteristic, complemented
355#2067C2×C10711yescharacteristic, complemented
356#2065C2×C10711yescharacteristic, complemented
357#2025C2×C10711yescharacteristic, complemented
358#1863C2×C10711yescharacteristic, complemented
359#1863C2×C10711yescharacteristic, complemented
360#1854C2×C10711yescharacteristic, complemented
361#1850C2×C10711yescharacteristic, complemented
362#1808C2×C10711yescharacteristic, complemented
363#1803C2×C10711yescharacteristic, complemented
364#1788C2×C10711yescharacteristic
365C107#2596111yescharacteristic, direct product factor, Sylow
366C22×#41C22×C10711yescharacteristic
367C23×C8C22×C10711yescharacteristic
368C2×#125C22×C10711yescharacteristic
369C2×C4×Q8C22×C10711yescharacteristic
370C2×C4×Q8C22×C10711yescharacteristic
371C2×#117C22×C10711yescharacteristic
372#479—24no—
373C2×#107C22×C10711yescharacteristic
374C2×#107C22×C10711yescharacteristic
375C2×#107C22×C10711yescharacteristic
376C2×#106C22×C10711yescharacteristic
377C2×C4⋊C8C22×C10711yescharacteristic
378C2×C4⋊C8C22×C10711yescharacteristic
379#416—24no—
380C2×#103C22×C10711yescharacteristic
381C2×#103C22×C10711yescharacteristic
382C2×#103C22×C10711yescharacteristic
383C2×#103C22×C10711yescharacteristic
384C2×#102C22×C10711yescharacteristic
385C2×#102C22×C10711yescharacteristic
386C2×#102C22×C10711yescharacteristic
387C2×#102C22×C10711yescharacteristic
388C2×C22⋊C8C22×C10711yescharacteristic
389#399—21no—
390#396—21no—
391#390—21no—
392#390—21no—
393#390C22×C10711yescharacteristic
394#390C22×C10711yescharacteristic
395#389—21no—
396#389C22×C10711yescharacteristic
397#389C22×C10711yescharacteristic
398#387—21no—
399#384C22×C10711yescharacteristic
400#380—21no—
401#380C22×C10711yescharacteristic
402#380C22×C10711yescharacteristic
403C4×C22⋊C4—21no—
404C4×C22⋊C4C22×C10711yescharacteristic
405#340C22×C10711yescharacteristic
406#340C22×C10711yescharacteristic
407#340C22×C10711yescharacteristic
408#340C22×C10711yescharacteristic
409#336C22×C10711yescharacteristic
410#336C22×C10711yescharacteristic
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—41no—
415C2×#41—41no—
416C2×#41Q8×C10714yes—
417C22×Q8C23×C10711yescharacteristic
418C22×D4—21no—
419C22×D4C23×C10711yescharacteristic
420C23×C4—21no—
421C23×C4C23×C10711yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—41no—
425C22×C8C23×C10711yescharacteristic
426C22×C8C23×C10711yescharacteristic
427C22×C8C23×C10711yescharacteristic
428C22×C8C23×C10711yescharacteristic
429#125—22no—
430#125—41no—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×Q8—41no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C10711yescharacteristic
446C2×C4⋊C4C23×C10711yescharacteristic
447C2×C4⋊C4C23×C10711yescharacteristic
448C2×C4⋊C4C23×C10711yescharacteristic
449C2×C4⋊C4C23×C10711yescharacteristic
450C2×C4⋊C4C23×C10711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C10711yescharacteristic
459C2×C22⋊C4D4×C10711yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42C23×C10711yescharacteristic
464C2×C42C23×C10711yescharacteristic
465#107—22no—
466#107—41no—
467#107—41no—
468#106—22no—
469C4⋊C8—22no—
470C4⋊C8—41no—
471#103—22no—
472#103—22no—
473#103—22no—
474#103D4×C10714yes—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479C22⋊C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C10711yescharacteristic
485#95D4×C10711yescharacteristic
486C24—21no—
487C24C2×D4×C10711yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×D4×C10712yes—
496C2×Q8C2×Q8×C10712yes—
497C2×Q8#41×C10712yes—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×Q8×C10712yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4C2×D4×C10711yescharacteristic
522C22×C4C2×D4×C10711yescharacteristic
523C22×C4C2×D4×C10711yescharacteristic
524C22×C4C2×D4×C10711yescharacteristic
525C22×C4C2×D4×C10711yescharacteristic
526C22×C4C2×Q8×C10712yes—
527C22×C4#41×C10712yes—
528C22×C4C24×C10711yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—44no—
541C2×C8C2×D4×C10712yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4C2×D4×C10712yes—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—42no—
577C42—42no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23C22⋊Q8×C10712yes—
592C23C22×D4×C10711yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8C22⋊Q8×C10714yes—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4C22⋊Q8×C10712yes—
642C2×C4#135×C10712yes—
643C2×C4C22×D4×C10711yescharacteristic
644C2×C4C22×Q8×C10711yescharacteristic
645C2×C4C2×#41×C10711yescharacteristic
646C2×C4C2×#41×C10711yescharacteristic
647C2×C4H(5,𝔽2)×C10711yescharacteristic
648C2×C4H(5,𝔽2)×C10711yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22C2×C22⋊Q8×C10711yescharacteristic
668C22D42×C10711yescharacteristic
669C22#546×C10711yescharacteristic
670C22C2×#135×C10711yescharacteristic
671C22#575×C10711yescharacteristic
672C22#576×C10711yescharacteristic
673C22#578×C10711yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—41no—
678C4—42no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4C2×C22⋊Q8×C10711yescharacteristic
687C4#543×C10711yescharacteristic
688C4#546×C10711yescharacteristic
689C4#551×C10711yescharacteristic
690C2—42no—
691C2—82no—
692C2C107×#243711yescharacteristic
693C2C107×#307611yescharacteristic
694C2C107×#308311yescharacteristic
695C2C107×#326911yescharacteristic
696C2C107×#328711yescharacteristic
697C2C107×#330011yescharacteristic
698C2C107×#330911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC22×#41×C107C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C22⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#479×C107C2semidirect
3. C107×#2441C2semidirect
5. C107×#2093C2semidirect
6. C107×#2067C2semidirect
7. C107×#2065C2semidirect
8. C107×#2025C2semidirect
9. C107×#1863C2semidirect
10. C107×#1863C2semidirect
11. C107×#1854C2semidirect
12. C107×#1850C2semidirect
13. C107×#1808C2semidirect
14. C107×#1803C2semidirect
340. #25961C107direct (N × H)
350. C2×#479C2×C107semidirect
352. #2441C2×C107semidirect
354. #2093C2×C107semidirect
355. #2067C2×C107semidirect
356. #2065C2×C107semidirect
357. #2025C2×C107semidirect
358. #1863C2×C107semidirect
359. #1863C2×C107semidirect
360. #1854C2×C107semidirect
361. #1850C2×C107semidirect
362. #1808C2×C107semidirect
363. #1803C2×C107semidirect
365. C107#25961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#479×C1072
C2×#416×C1072
C107×#24412
C107×#23412
C107×#20932
C107×#20672
C107×#20652
C107×#20252
C107×#18632
C107×#18542
C107×#18502
C107×#18082
C107×#18032
C107×#17882
#25961107