Finite Group Databasebeta

← C107×#25131 #41051095

Subgroups — C107×#25131 #41051095

Order 27392.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C107C211yesmaximal, characteristic, complemented
2C2×#449×C107C211yesmaximal, characteristic, complemented
3C2×#435×C107C211yesmaximal, characteristic, complemented
4C2×#416×C107C211yesmaximal, characteristic, complemented
5C107×#2414C211yesmaximal, characteristic, complemented
6C107×#2407C211yesmaximal, characteristic, complemented
7C107×#2067C211yesmaximal, characteristic, complemented
8C107×#2055C211yesmaximal, characteristic, complemented
9C107×#2035C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1972C211yesmaximal, characteristic, complemented
12C107×#1935C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1893C211yesmaximal, characteristic, complemented
15C107×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C23×C8×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×#121×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×C4×D4×C107C2211yescharacteristic
26C2×#117×C107C2211yescharacteristic
27#468×C107—24no—
28#449×C107—24no—
29#435×C107—24no—
30C2×#107×C107C2211yescharacteristic
31C2×#106×C107C2211yescharacteristic
32C2×C4⋊C8×C107C2211yescharacteristic
33#416×C107—24no—
34C2×#103×C107C2211yescharacteristic
35C2×#103×C107C2211yescharacteristic
36C2×#103×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×C22⋊C8×C107C2211yescharacteristic
43C2×C22⋊C8×C107C2211yescharacteristic
44C2×#97×C107C2211yescharacteristic
45#394×C107—21no—
46#394×C107—21no—
47#392×C107—21no—
48#392×C107—21no—
49#391×C107C2211yescharacteristic
50#390×C107—21no—
51#390×C107C2211yescharacteristic
52#390×C107C2211yescharacteristic
53#389×C107C2211yescharacteristic
54#388×C107—21no—
55#386×C107—21no—
56#385×C107—21no—
57#380×C107C2211yescharacteristic
58#380×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C2×#41×C107—22no—
64C2×#41×C107—22no—
65C2×#41×C107—22no—
66C2×#41×C107—22no—
67C2×#41×C107—41no—
68C2×#41×C107—41no—
69C22×Q8×C107C2311yescharacteristic
70C22×D4×C107—21no—
71C22×D4×C107—21no—
72C22×D4×C107—21no—
73C22×D4×C107—21no—
74C22×D4×C107D411yescharacteristic
75C22×D4×C107C2311yescharacteristic
76C22×D4×C107C2311yescharacteristic
77C23×C4×C107—21no—
78C23×C4×C107C2311yescharacteristic
79C23×C4×C107C2311yescharacteristic
80C2×SD16×C107—22no—
81C2×SD16×C107—22no—
82C2×SD16×C107—41no—
83C2×D8×C107—22no—
84C2×D8×C107—22no—
85C2×D8×C107—41no—
86C2×M16×C107—22no—
87C2×M16×C107—22no—
88C2×M16×C107—41no—
89C22×C8×C107—22no—
90C22×C8×C107—22no—
91C22×C8×C107—41no—
92C22×C8×C107C2311yescharacteristic
93C22×C8×C107C2311yescharacteristic
94C22×C8×C107C2311yescharacteristic
95C22×C8×C107C2311yescharacteristic
96C22⋊Q8×C107—22no—
97C22⋊Q8×C107—41no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107—41no—
103#121×C107—41no—
104C4×D4×C107—22no—
105C4×D4×C107—22no—
106#117×C107—22no—
107#117×C107—41no—
108C2×C4⋊C4×C107—21no—
109C2×C4⋊C4×C107—21no—
110C2×C4⋊C4×C107D411yescharacteristic
111C2×C4⋊C4×C107C2311yescharacteristic
112C2×C4⋊C4×C107C2311yescharacteristic
113C2×C4⋊C4×C107C2311yescharacteristic
114C2×C4⋊C4×C107C2311yescharacteristic
115C2×C4⋊C4×C107C2311yescharacteristic
116C2×C22⋊C4×C107—21no—
117C2×C22⋊C4×C107—21no—
118C2×C22⋊C4×C107—21no—
119C2×C22⋊C4×C107—21no—
120C2×C22⋊C4×C107—21no—
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107D411yescharacteristic
128C2×C22⋊C4×C107D411yescharacteristic
129C2×C42×C107—21no—
130C2×C42×C107C2311yescharacteristic
131#107×C107—22no—
132#106×C107—41no—
133C4⋊C8×C107—22no—
134#103×C107—22no—
135#103×C107—22no—
136#103×C107D414yescomplemented
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—41no—
142C22⋊C8×C107—22no—
143C22⋊C8×C107D414yescomplemented
144#97×C107—22no—
145#95×C107—21no—
146#95×C107—21no—
147#95×C107—21no—
148#95×C107—21no—
149#95×C107—21no—
150C24×C107—21no—
151C24×C107—21no—
152C24×C107C2×D411yescharacteristic
153C24×C107C2×D411yescharacteristic
154#41×C107—28no—
155#41×C107—44no—
156#41×C107—44no—
157#41×C107—44no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×Q8×C107—21no—
161C2×Q8×C107—21no—
162C2×Q8×C107—21no—
163C2×Q8×C107C2×D412yes—
164C2×D4×C107—22no—
165C2×D4×C107—21no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—21no—
173C2×D4×C107—21no—
174C2×D4×C107—21no—
175C2×D4×C107—21no—
176C2×D4×C107—41no—
177C2×D4×C107—41no—
178C2×D4×C107—42no—
179C2×D4×C107—42no—
180C2×D4×C107—42no—
181C2×D4×C107—42no—
182C2×D4×C107—42no—
183C2×D4×C107—42no—
184C2×D4×C107—42no—
185C2×D4×C107—42no—
186C2×D4×C107—81no—
187C2×D4×C107—81no—
188C2×D4×C107—81no—
189C2×D4×C107—81no—
190C2×D4×C107#4112yes—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—42no—
208C22×C4×C107—42no—
209C22×C4×C107—42no—
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2×D411yescharacteristic
213C22×C4×C107C2×D411yescharacteristic
214C22×C4×C107C2×D412yes—
215C22×C4×C107#4112yes—
216C22×C4×C107C2411yescharacteristic
217SD16×C107—44no—
218D8×C107—44no—
219M16×C107—44no—
220C2×C8×C107—21no—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—44no—
230C2×C8×C107C2×D412yes—
231C2×C8×C107C2×D412yes—
232C2×C8×C107C2×D412yes—
233C4⋊C4×C107—22no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—21no—
243C4⋊C4×C107—42no—
244C4⋊C4×C107—81no—
245C4⋊C4×C107C2×D412yes—
246C22⋊C4×C107—22no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—42no—
254C22⋊C4×C107—42no—
255C22⋊C4×C107—81no—
256C22⋊C4×C107—81no—
257C22⋊C4×C107—81no—
258C22⋊C4×C107—81no—
259C42×C107—21no—
260C42×C107—21no—
261C42×C107—42no—
262C23×C107—21no—
263C23×C107—21no—
264C23×C107—21no—
265C23×C107—21no—
266C23×C107—21no—
267C23×C107—21no—
268C23×C107—21no—
269C23×C107—21no—
270C23×C107—22no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—21no—
274C23×C107—21no—
275C23×C107—21no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107—41no—
284C23×C107—41no—
285C23×C107—41no—
286C23×C107—41no—
287C23×C107—41no—
288C23×C107—41no—
289C23×C107#12112yes—
290C23×C107C22×D411yescharacteristic
291Q8×C107—22no—
292Q8×C107—22no—
293Q8×C107—41no—
294Q8×C107—41no—
295D4×C107—22no—
296D4×C107—22no—
297D4×C107—44no—
298D4×C107—48no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—84no—
306D4×C107—84no—
307D4×C107—84no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—22no—
311C2×C4×C107—22no—
312C2×C4×C107—22no—
313C2×C4×C107—22no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—22no—
318C2×C4×C107—21no—
319C2×C4×C107—22no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—21no—
325C2×C4×C107—48no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—41no—
343C2×C4×C107—41no—
344C2×C4×C107—41no—
345C2×C4×C107—41no—
346C2×C4×C107#12112yes—
347C2×C4×C107C22×D411yescharacteristic
348C2×C4×C107C22×D411yescharacteristic
349C2×C4×C107C2×#4111yescharacteristic
350C2×C4×C107C2×#4111yescharacteristic
351C2×C4×C107H(5,𝔽2)11yescharacteristic
352C2×C4×C107H(5,𝔽2)11yescharacteristic
353C8×C107—22no—
354C8×C107—22no—
355C8×C107—22no—
356C8×C107—41no—
357C22×C107—22no—
358C22×C107—22no—
359C22×C107—22no—
360C22×C107—41no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—41no—
364C22×C107—42no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—41no—
368C22×C107—41no—
369C22×C107—42no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—42no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107—81no—
382C22×C107—81no—
383C22×C107—81no—
384C22×C107—81no—
385C22×C107C2×#12111yescharacteristic
386C22×C107D4211yescharacteristic
387C22×C107#54611yescharacteristic
388C22×C107#57511yescharacteristic
389C22×C107#57511yescharacteristic
390C22×C107#57611yescharacteristic
391C22×C107#57711yescharacteristic
392C4×C107—22no—
393C4×C107—41no—
394C4×C107—42no—
395C4×C107—42no—
396C4×C107—41no—
397C4×C107—41no—
398C4×C107—81no—
399C4×C107—81no—
400C4×C107—81no—
401C4×C107—81no—
402C4×C107#52511yescharacteristic
403C4×C107#53811yescharacteristic
404C4×C107D4211yescharacteristic
405C4×C107#54611yescharacteristic
406#25131C10711yesmaximal, characteristic, direct product factor, Sylow
407C2×C107—42no—
408C2×C107—81no—
409C2×C107—82no—
410C2×C107—161no—
411C2×C107#242411yescharacteristic
412C2×C107#305411yescharacteristic
413C2×C107#306211yescharacteristic
414C2×C107#326811yescharacteristic
415C2×C107#327111yescharacteristic
416C2×C107#330711yescharacteristic
417C2×C107#331911yescharacteristic
418C2×#468C2×C10711yescharacteristic, complemented
419C2×#449C2×C10711yescharacteristic, complemented
420C2×#435C2×C10711yescharacteristic, complemented
421C2×#416C2×C10711yescharacteristic, complemented
422#2414C2×C10711yescharacteristic, complemented
423#2407C2×C10711yescharacteristic, complemented
424#2067C2×C10711yescharacteristic, complemented
425#2055C2×C10711yescharacteristic, complemented
426#2035C2×C10711yescharacteristic, complemented
427#1999C2×C10711yescharacteristic, complemented
428#1972C2×C10711yescharacteristic, complemented
429#1935C2×C10711yescharacteristic, complemented
430#1895C2×C10711yescharacteristic, complemented
431#1893C2×C10711yescharacteristic, complemented
432#1854C2×C10711yescharacteristic, complemented
433C107#2513111yescharacteristic, direct product factor, Sylow
434C22×#41C22×C10711yescharacteristic
435C22×SD16C22×C10711yescharacteristic
436C22×D8C22×C10711yescharacteristic
437C22×M16C22×C10711yescharacteristic
438C23×C8C22×C10711yescharacteristic
439C2×C22⋊Q8C22×C10711yescharacteristic
440C2×#121C22×C10711yescharacteristic
441C2×#121C22×C10711yescharacteristic
442C2×#121C22×C10711yescharacteristic
443C2×C4×D4C22×C10711yescharacteristic
444C2×#117C22×C10711yescharacteristic
445#468—24no—
446#449—24no—
447#435—24no—
448C2×#107C22×C10711yescharacteristic
449C2×#106C22×C10711yescharacteristic
450C2×C4⋊C8C22×C10711yescharacteristic
451#416—24no—
452C2×#103C22×C10711yescharacteristic
453C2×#103C22×C10711yescharacteristic
454C2×#103C22×C10711yescharacteristic
455C2×#102C22×C10711yescharacteristic
456C2×#102C22×C10711yescharacteristic
457C2×#102C22×C10711yescharacteristic
458C2×#102C22×C10711yescharacteristic
459C2×#102C22×C10711yescharacteristic
460C2×C22⋊C8C22×C10711yescharacteristic
461C2×C22⋊C8C22×C10711yescharacteristic
462C2×#97C22×C10711yescharacteristic
463#394—21no—
464#394—21no—
465#392—21no—
466#392—21no—
467#391C22×C10711yescharacteristic
468#390—21no—
469#390C22×C10711yescharacteristic
470#390C22×C10711yescharacteristic
471#389C22×C10711yescharacteristic
472#388—21no—
473#386—21no—
474#385—21no—
475#380C22×C10711yescharacteristic
476#380C22×C10711yescharacteristic
477#340C22×C10711yescharacteristic
478#340C22×C10711yescharacteristic
479#340C22×C10711yescharacteristic
480#340C22×C10711yescharacteristic
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C10711yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C10711yescharacteristic
493C22×D4C23×C10711yescharacteristic
494C22×D4C23×C10711yescharacteristic
495C23×C4—21no—
496C23×C4C23×C10711yescharacteristic
497C23×C4C23×C10711yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C10711yescharacteristic
511C22×C8C23×C10711yescharacteristic
512C22×C8C23×C10711yescharacteristic
513C22×C8C23×C10711yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C10711yescharacteristic
529C2×C4⋊C4C23×C10711yescharacteristic
530C2×C4⋊C4C23×C10711yescharacteristic
531C2×C4⋊C4C23×C10711yescharacteristic
532C2×C4⋊C4C23×C10711yescharacteristic
533C2×C4⋊C4C23×C10711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C10711yescharacteristic
546C2×C22⋊C4D4×C10711yescharacteristic
547C2×C42—21no—
548C2×C42C23×C10711yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C10714yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C10714yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C10711yescharacteristic
571C24C2×D4×C10711yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C10712yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C10712yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C10711yescharacteristic
629C22×C4C2×D4×C10711yescharacteristic
630C22×C4C2×D4×C10711yescharacteristic
631C22×C4C2×D4×C10711yescharacteristic
632C22×C4C2×D4×C10712yes—
633C22×C4#41×C10712yes—
634C22×C4C24×C10711yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C10712yes—
649C2×C8C2×D4×C10712yes—
650C2×C8C2×D4×C10712yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C10712yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C10712yes—
708C23C22×D4×C10711yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C10712yes—
765C2×C4C22×D4×C10711yescharacteristic
766C2×C4C22×D4×C10711yescharacteristic
767C2×C4C2×#41×C10711yescharacteristic
768C2×C4C2×#41×C10711yescharacteristic
769C2×C4H(5,𝔽2)×C10711yescharacteristic
770C2×C4H(5,𝔽2)×C10711yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C10711yescharacteristic
804C22D42×C10711yescharacteristic
805C22#546×C10711yescharacteristic
806C22#575×C10711yescharacteristic
807C22#575×C10711yescharacteristic
808C22#576×C10711yescharacteristic
809C22#577×C10711yescharacteristic
810C4—22no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#525×C10711yescharacteristic
821C4#538×C10711yescharacteristic
822C4D42×C10711yescharacteristic
823C4#546×C10711yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C107×#242411yescharacteristic
829C2C107×#305411yescharacteristic
830C2C107×#306211yescharacteristic
831C2C107×#326811yescharacteristic
832C2C107×#327111yescharacteristic
833C2C107×#330711yescharacteristic
834C2C107×#331911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C107C2semidirect
2. C2×#449×C107C2semidirect
3. C2×#435×C107C2semidirect
4. C2×#416×C107C2semidirect
5. C107×#2414C2semidirect
6. C107×#2407C2semidirect
7. C107×#2067C2semidirect
8. C107×#2055C2semidirect
9. C107×#2035C2semidirect
10. C107×#1999C2semidirect
11. C107×#1972C2semidirect
12. C107×#1935C2semidirect
13. C107×#1895C2semidirect
14. C107×#1893C2semidirect
15. C107×#1854C2semidirect
136. #103×C107D4semidirect
143. C22⋊C8×C107D4semidirect
406. #25131C107direct (N × H)
418. C2×#468C2×C107semidirect
419. C2×#449C2×C107semidirect
420. C2×#435C2×C107semidirect
421. C2×#416C2×C107semidirect
422. #2414C2×C107semidirect
423. #2407C2×C107semidirect
424. #2067C2×C107semidirect
425. #2055C2×C107semidirect
426. #2035C2×C107semidirect
427. #1999C2×C107semidirect
428. #1972C2×C107semidirect
429. #1935C2×C107semidirect
430. #1895C2×C107semidirect
431. #1893C2×C107semidirect
432. #1854C2×C107semidirect
433. C107#25131direct (N × H)
554. #103D4×C107semidirect
561. C22⋊C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1072
C2×#449×C1072
C2×#435×C1072
C2×#416×C1072
C107×#24142
C107×#24072
C107×#20672
C107×#20552
C107×#20352
C107×#19992
C107×#19722
C107×#19352
C107×#18952
C107×#18932
C107×#18542
#25131107