Finite Group Databasebeta

← C107×#25390 #41051354

Subgroups — C107×#25390 #41051354

Order 27392.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C107C211yesmaximal, characteristic, complemented
2C2×#468×C107C211yesmaximal, characteristic, complemented
3C2×#463×C107C211yesmaximal, characteristic, complemented
4C2×#436×C107C211yesmaximal, characteristic, complemented
5C107×#2540C211yesmaximal, characteristic, complemented
6C107×#2535C211yesmaximal, characteristic, complemented
7C107×#2035C211yesmaximal, characteristic, complemented
8C107×#2033C211yesmaximal, characteristic, complemented
9C107×#2000C211yesmaximal, characteristic, complemented
10C107×#1999C211yesmaximal, characteristic, complemented
11C107×#1958C211yesmaximal, characteristic, complemented
12C107×#1949C211yesmaximal, characteristic, complemented
13C107×#1895C211yesmaximal, characteristic, complemented
14C107×#1894C211yesmaximal, characteristic, complemented
15C4×#102×C107C211yesmaximal, characteristic, complemented
16C22×SD16×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×M16×C107C2211yescharacteristic
19C22×M16×C107C2211yescharacteristic
20C2×#124×C107C2211yescharacteristic
21C2×C22⋊Q8×C107C2211yescharacteristic
22C2×C22⋊Q8×C107C2211yescharacteristic
23C2×#121×C107C2211yescharacteristic
24C2×#121×C107C2211yescharacteristic
25C2×#121×C107C2211yescharacteristic
26C2×#121×C107C2211yescharacteristic
27C2×C4×D4×C107C2211yescharacteristic
28C2×C4×D4×C107C2211yescharacteristic
29#469×C107—24no—
30#468×C107—24no—
31#463×C107—24no—
32#436×C107—24no—
33C2×#107×C107C2211yescharacteristic
34C2×#106×C107C2211yescharacteristic
35C2×C4⋊C8×C107C2211yescharacteristic
36C2×#103×C107C2211yescharacteristic
37C2×#103×C107C2211yescharacteristic
38C2×#103×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×C22⋊C8×C107C2211yescharacteristic
45C2×C22⋊C8×C107C2211yescharacteristic
46C2×C4×C8×C107C2211yescharacteristic
47#399×C107—21no—
48#397×C107—21no—
49#392×C107—21no—
50#392×C107—21no—
51#390×C107—21no—
52#390×C107—21no—
53#386×C107—21no—
54#386×C107—21no—
55#382×C107C2211yescharacteristic
56#380×C107C2211yescharacteristic
57#380×C107C2211yescharacteristic
58C4×C4⋊C4×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#340×C107C2211yescharacteristic
61#340×C107C2211yescharacteristic
62#340×C107C2211yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—21no—
68C22×D4×C107D411yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C23×C4×C107—21no—
72C23×C4×C107C2311yescharacteristic
73C23×C4×C107C2311yescharacteristic
74C2×SD16×C107—22no—
75C2×SD16×C107—22no—
76C2×SD16×C107—41no—
77C2×D8×C107—22no—
78C2×D8×C107—22no—
79C2×D8×C107—41no—
80C2×M16×C107—22no—
81C2×M16×C107—22no—
82C2×M16×C107—22no—
83C2×M16×C107—22no—
84C2×M16×C107—41no—
85C2×M16×C107—41no—
86C22×C8×C107C2311yescharacteristic
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90#124×C107—22no—
91#124×C107—22no—
92C22⋊Q8×C107—22no—
93C22⋊Q8×C107—22no—
94C22⋊Q8×C107—41no—
95C22⋊Q8×C107—41no—
96#121×C107—22no—
97#121×C107—22no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—41no—
101#121×C107—41no—
102#121×C107—41no—
103#121×C107—41no—
104C4×D4×C107—22no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
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—22no—
133C4⋊C8×C107D414yescomplemented
134#103×C107—22no—
135#103×C107—22no—
136#103×C107—41no—
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—41no—
141#102×C107D414yescomplemented
142C22⋊C8×C107—22no—
143C22⋊C8×C107—22no—
144C4×C8×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
154C2×Q8×C107—21no—
155C2×Q8×C107—21no—
156C2×Q8×C107—21no—
157C2×Q8×C107—21no—
158C2×Q8×C107—21no—
159C2×Q8×C107—21no—
160C2×D4×C107—22no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
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—41no—
173C2×D4×C107—41no—
174C2×D4×C107—42no—
175C2×D4×C107—42no—
176C2×D4×C107—42no—
177C2×D4×C107—42no—
178C2×D4×C107—42no—
179C2×D4×C107—42no—
180C2×D4×C107—42no—
181C2×D4×C107—42no—
182C2×D4×C107—81no—
183C2×D4×C107—81no—
184C2×D4×C107—81no—
185C2×D4×C107—81no—
186C2×D4×C107C2×D412yes—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
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—42no—
206C22×C4×C107—81no—
207C22×C4×C107—81no—
208C22×C4×C107C2×D411yescharacteristic
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212C22×C4×C107C2411yescharacteristic
213SD16×C107—44no—
214D8×C107—44no—
215M16×C107—44no—
216M16×C107—44no—
217C2×C8×C107—21no—
218C2×C8×C107—21no—
219C2×C8×C107—21no—
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×C107C2×D412yes—
227C2×C8×C107C2×D412yes—
228C2×C8×C107C2×D412yes—
229C4⋊C4×C107—22no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—42no—
239C4⋊C4×C107—42no—
240C4⋊C4×C107C2×D412yes—
241C4⋊C4×C107#4112yes—
242C22⋊C4×C107—22no—
243C22⋊C4×C107—22no—
244C22⋊C4×C107—42no—
245C22⋊C4×C107—42no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—42no—
248C22⋊C4×C107—42no—
249C22⋊C4×C107—42no—
250C22⋊C4×C107—42no—
251C22⋊C4×C107—42no—
252C22⋊C4×C107—42no—
253C22⋊C4×C107—81no—
254C22⋊C4×C107—81no—
255C42×C107—81no—
256C42×C107C2×D412yes—
257C42×C107#4112yes—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—22no—
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—21no—
271C23×C107—21no—
272C23×C107—21no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
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×C107C22×D411yescharacteristic
287Q8×C107—41no—
288Q8×C107—41no—
289Q8×C107—41no—
290Q8×C107—41no—
291D4×C107—22no—
292D4×C107—22no—
293D4×C107—44no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—41no—
297D4×C107—41no—
298D4×C107—41no—
299D4×C107—41no—
300D4×C107—84no—
301D4×C107—84no—
302D4×C107—84no—
303D4×C107—84no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—22no—
312C2×C4×C107—21no—
313C2×C4×C107—22no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
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—84no—
341C2×C4×C107#12112yes—
342C2×C4×C107#12112yes—
343C2×C4×C107C22×D411yescharacteristic
344C2×C4×C107C22×D411yescharacteristic
345C2×C4×C107C2×#4111yescharacteristic
346C2×C4×C107C2×#4111yescharacteristic
347C2×C4×C107H(5,𝔽2)11yescharacteristic
348C2×C4×C107H(5,𝔽2)11yescharacteristic
349C8×C107—22no—
350C8×C107—22no—
351C8×C107—22no—
352C8×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—42no—
356C22×C107—41no—
357C22×C107—41no—
358C22×C107—42no—
359C22×C107—41no—
360C22×C107—42no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—41no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—41no—
368C22×C107—41no—
369C22×C107—41no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—81no—
377C22×C107—81no—
378C22×C107—81no—
379C22×C107—81no—
380C22×C107—81no—
381C22×C107C2×#12111yescharacteristic
382C22×C107D4211yescharacteristic
383C22×C107#54611yescharacteristic
384C22×C107#57511yescharacteristic
385C22×C107#57511yescharacteristic
386C22×C107#57611yescharacteristic
387C22×C107#57711yescharacteristic
388C4×C107—22no—
389C4×C107—22no—
390C4×C107—41no—
391C4×C107—41no—
392C4×C107—42no—
393C4×C107—42no—
394C4×C107—81no—
395C4×C107—81no—
396C4×C107—81no—
397C4×C107—81no—
398C4×C107#53211yescharacteristic
399C4×C107#54011yescharacteristic
400C4×C107D4211yescharacteristic
401C4×C107#55011yescharacteristic
402#25390C10711yesmaximal, characteristic, direct product factor, Sylow
403C2×C107—81no—
404C2×C107—81no—
405C2×C107—82no—
406C2×C107—161no—
407C2×C107#242811yescharacteristic
408C2×C107#305411yescharacteristic
409C2×C107#306211yescharacteristic
410C2×C107#327311yescharacteristic
411C2×C107#327511yescharacteristic
412C2×C107#332211yescharacteristic
413C2×C107#332611yescharacteristic
414C2×#469C2×C10711yescharacteristic, complemented
415C2×#468C2×C10711yescharacteristic, complemented
416C2×#463C2×C10711yescharacteristic, complemented
417C2×#436C2×C10711yescharacteristic, complemented
418#2540C2×C10711yescharacteristic, complemented
419#2535C2×C10711yescharacteristic, complemented
420#2035C2×C10711yescharacteristic, complemented
421#2033C2×C10711yescharacteristic, complemented
422#2000C2×C10711yescharacteristic, complemented
423#1999C2×C10711yescharacteristic, complemented
424#1958C2×C10711yescharacteristic, complemented
425#1949C2×C10711yescharacteristic, complemented
426#1895C2×C10711yescharacteristic, complemented
427#1894C2×C10711yescharacteristic, complemented
428C4×#102C2×C10711yescharacteristic, complemented
429C107#2539011yescharacteristic, direct product factor, Sylow
430C22×SD16C22×C10711yescharacteristic
431C22×D8C22×C10711yescharacteristic
432C22×M16C22×C10711yescharacteristic
433C22×M16C22×C10711yescharacteristic
434C2×#124C22×C10711yescharacteristic
435C2×C22⋊Q8C22×C10711yescharacteristic
436C2×C22⋊Q8C22×C10711yescharacteristic
437C2×#121C22×C10711yescharacteristic
438C2×#121C22×C10711yescharacteristic
439C2×#121C22×C10711yescharacteristic
440C2×#121C22×C10711yescharacteristic
441C2×C4×D4C22×C10711yescharacteristic
442C2×C4×D4C22×C10711yescharacteristic
443#469—24no—
444#468—24no—
445#463—24no—
446#436—24no—
447C2×#107C22×C10711yescharacteristic
448C2×#106C22×C10711yescharacteristic
449C2×C4⋊C8C22×C10711yescharacteristic
450C2×#103C22×C10711yescharacteristic
451C2×#103C22×C10711yescharacteristic
452C2×#103C22×C10711yescharacteristic
453C2×#102C22×C10711yescharacteristic
454C2×#102C22×C10711yescharacteristic
455C2×#102C22×C10711yescharacteristic
456C2×#102C22×C10711yescharacteristic
457C2×#102C22×C10711yescharacteristic
458C2×C22⋊C8C22×C10711yescharacteristic
459C2×C22⋊C8C22×C10711yescharacteristic
460C2×C4×C8C22×C10711yescharacteristic
461#399—21no—
462#397—21no—
463#392—21no—
464#392—21no—
465#390—21no—
466#390—21no—
467#386—21no—
468#386—21no—
469#382C22×C10711yescharacteristic
470#380C22×C10711yescharacteristic
471#380C22×C10711yescharacteristic
472C4×C4⋊C4C22×C10711yescharacteristic
473#340C22×C10711yescharacteristic
474#340C22×C10711yescharacteristic
475#340C22×C10711yescharacteristic
476#340C22×C10711yescharacteristic
477C22×Q8C23×C10711yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4D4×C10711yescharacteristic
483C22×D4C23×C10711yescharacteristic
484C22×D4C23×C10711yescharacteristic
485C23×C4—21no—
486C23×C4C23×C10711yescharacteristic
487C23×C4C23×C10711yescharacteristic
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—41no—
494C2×M16—22no—
495C2×M16—22no—
496C2×M16—22no—
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C22×C8C23×C10711yescharacteristic
501C22×C8C23×C10711yescharacteristic
502C22×C8C23×C10711yescharacteristic
503C22×C8C23×C10711yescharacteristic
504#124—22no—
505#124—22no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—41no—
515#121—41no—
516#121—41no—
517#121—41no—
518C4×D4—22no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4D4×C10711yescharacteristic
525C2×C4⋊C4C23×C10711yescharacteristic
526C2×C4⋊C4C23×C10711yescharacteristic
527C2×C4⋊C4C23×C10711yescharacteristic
528C2×C4⋊C4C23×C10711yescharacteristic
529C2×C4⋊C4C23×C10711yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
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⋊C4D4×C10711yescharacteristic
542C2×C22⋊C4D4×C10711yescharacteristic
543C2×C42—21no—
544C2×C42C23×C10711yescharacteristic
545#107—22no—
546#106—22no—
547C4⋊C8D4×C10714yescomplemented
548#103—22no—
549#103—22no—
550#103—41no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—41no—
555#102D4×C10714yescomplemented
556C22⋊C8—22no—
557C22⋊C8—22no—
558C4×C8—22no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564C24—21no—
565C24—21no—
566C24C2×D4×C10711yescharacteristic
567C24C2×D4×C10711yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4C2×D4×C10712yes—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
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—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C10711yescharacteristic
623C22×C4C2×D4×C10711yescharacteristic
624C22×C4C2×D4×C10711yescharacteristic
625C22×C4C2×D4×C10711yescharacteristic
626C22×C4C24×C10711yescharacteristic
627SD16—44no—
628D8—44no—
629M16—44no—
630M16—44no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C2×D4×C10712yes—
641C2×C8C2×D4×C10712yes—
642C2×C8C2×D4×C10712yes—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4C2×D4×C10712yes—
655C4⋊C4#41×C10712yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—81no—
670C42C2×D4×C10712yes—
671C42#41×C10712yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23C22×D4×C10711yescharacteristic
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705D4—22no—
706D4—22no—
707D4—44no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—84no—
715D4—84no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
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—84no—
755C2×C4#121×C10712yes—
756C2×C4#121×C10712yes—
757C2×C4C22×D4×C10711yescharacteristic
758C2×C4C22×D4×C10711yescharacteristic
759C2×C4C2×#41×C10711yescharacteristic
760C2×C4C2×#41×C10711yescharacteristic
761C2×C4H(5,𝔽2)×C10711yescharacteristic
762C2×C4H(5,𝔽2)×C10711yescharacteristic
763C8—22no—
764C8—22no—
765C8—22no—
766C8—41no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×#121×C10711yescharacteristic
796C22D42×C10711yescharacteristic
797C22#546×C10711yescharacteristic
798C22#575×C10711yescharacteristic
799C22#575×C10711yescharacteristic
800C22#576×C10711yescharacteristic
801C22#577×C10711yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4#532×C10711yescharacteristic
813C4#540×C10711yescharacteristic
814C4D42×C10711yescharacteristic
815C4#550×C10711yescharacteristic
816C2—81no—
817C2—81no—
818C2—82no—
819C2—161no—
820C2C107×#242811yescharacteristic
821C2C107×#305411yescharacteristic
822C2C107×#306211yescharacteristic
823C2C107×#327311yescharacteristic
824C2C107×#327511yescharacteristic
825C2C107×#332211yescharacteristic
826C2C107×#332611yescharacteristic
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×#469×C107C2semidirect
2. C2×#468×C107C2semidirect
3. C2×#463×C107C2semidirect
4. C2×#436×C107C2semidirect
5. C107×#2540C2semidirect
6. C107×#2535C2semidirect
7. C107×#2035C2semidirect
8. C107×#2033C2semidirect
9. C107×#2000C2semidirect
10. C107×#1999C2semidirect
11. C107×#1958C2semidirect
12. C107×#1949C2semidirect
13. C107×#1895C2semidirect
14. C107×#1894C2semidirect
15. C4×#102×C107C2semidirect
133. C4⋊C8×C107D4semidirect
141. #102×C107D4semidirect
402. #25390C107direct (N × H)
414. C2×#469C2×C107semidirect
415. C2×#468C2×C107semidirect
416. C2×#463C2×C107semidirect
417. C2×#436C2×C107semidirect
418. #2540C2×C107semidirect
419. #2535C2×C107semidirect
420. #2035C2×C107semidirect
421. #2033C2×C107semidirect
422. #2000C2×C107semidirect
423. #1999C2×C107semidirect
424. #1958C2×C107semidirect
425. #1949C2×C107semidirect
426. #1895C2×C107semidirect
427. #1894C2×C107semidirect
428. C4×#102C2×C107semidirect
429. C107#25390direct (N × H)
547. C4⋊C8D4×C107semidirect
555. #102D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1072
C2×#468×C1072
C2×#463×C1072
C2×#436×C1072
C107×#25402
C107×#25352
C107×#20352
C107×#20332
C107×#20002
C107×#19992
C107×#19582
C107×#19492
C107×#18952
C107×#18942
C4×#102×C1072
#25390107