Finite Group Databasebeta

← C107×#14722 #41040686

Subgroups — C107×#14722 #41040686

Order 27392.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C107C211yesmaximal, characteristic, complemented
2C22×C4×D4×C107C211yesmaximal, characteristic, complemented
3C2×#394×C107C211yesmaximal, characteristic, complemented
4C2×#392×C107C211yesmaximal, characteristic, complemented
5C2×#392×C107C212yesmaximal, complemented
6C2×#386×C107C212yesmaximal, complemented
7C107×#1441C211yesmaximal, characteristic, complemented
8C107×#1439C211yesmaximal, characteristic, complemented
9C107×#1438C212yesmaximal, complemented
10C107×#1437C212yesmaximal, complemented
11C107×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C107C2211yescharacteristic
13C23×D4×C107C2212yes—
14C23×D4×C107C2211yescharacteristic
15C23×D4×C107C2212yes—
16C24×C4×C107C2211yescharacteristic
17C24×C4×C107C2211yescharacteristic
18C2×#121×C107—24no—
19C2×#121×C107—28no—
20C2×C4×D4×C107—24no—
21C2×C4×D4×C107—24no—
22C2×C4×D4×C107—24no—
23C22×C4⋊C4×C107C2211yescharacteristic
24C22×C4⋊C4×C107C2211yescharacteristic
25C22×C22⋊C4×C107C2212yes—
26C22×C22⋊C4×C107C2211yescharacteristic
27C22×C22⋊C4×C107C2212yes—
28C22×C22⋊C4×C107C2212yes—
29C22×C22⋊C4×C107C2212yes—
30C22×C22⋊C4×C107C2212yes—
31C22×C22⋊C4×C107C2211yescharacteristic
32C22×C22⋊C4×C107C2212yes—
33C22×C42×C107C2211yescharacteristic
34#394×C107—24no—
35#392×C107—28no—
36#392×C107—24no—
37#386×C107—28no—
38C2×#95×C107C2211yescharacteristic
39C2×#95×C107C2212yes—
40C2×#95×C107C2211yescharacteristic
41C2×#95×C107C2212yes—
42C2×#95×C107C2212yes—
43C2×#95×C107C2212yes—
44C25×C107C2312yes—
45C25×C107C2311yescharacteristic
46C25×C107C2311yescharacteristic
47C22×D4×C107—22no—
48C22×D4×C107—22no—
49C22×D4×C107—22no—
50C22×D4×C107—22no—
51C22×D4×C107—24no—
52C22×D4×C107—24no—
53C22×D4×C107—24no—
54C22×D4×C107—24no—
55C22×D4×C107—24no—
56C22×D4×C107—24no—
57C22×D4×C107—24no—
58C22×D4×C107—24no—
59C22×D4×C107—24no—
60C22×D4×C107—22no—
61C22×D4×C107—24no—
62C22×D4×C107—22no—
63C22×D4×C107—22no—
64C22×D4×C107—22no—
65C22×D4×C107—22no—
66C22×D4×C107—24no—
67C22×D4×C107—42no—
68C22×D4×C107—42no—
69C22×D4×C107—42no—
70C22×D4×C107—42no—
71C22×D4×C107—42no—
72C22×D4×C107D414yescomplemented
73C23×C4×C107—22no—
74C23×C4×C107—22no—
75C23×C4×C107—22no—
76C23×C4×C107—22no—
77C23×C4×C107—22no—
78C23×C4×C107—24no—
79C23×C4×C107—24no—
80C23×C4×C107—42no—
81C23×C4×C107—42no—
82C23×C4×C107D414yescomplemented
83C23×C4×C107C2312yes—
84C23×C4×C107C2312yes—
85C23×C4×C107C2311yescharacteristic
86C23×C4×C107C2311yescharacteristic
87C23×C4×C107C2312yes—
88C23×C4×C107C2311yescharacteristic
89C23×C4×C107C2311yescharacteristic
90C23×C4×C107C2311yescharacteristic
91#121×C107—232no—
92C4×D4×C107—232no—
93C2×C4⋊C4×C107—22no—
94C2×C4⋊C4×C107—22no—
95C2×C4⋊C4×C107—24no—
96C2×C4⋊C4×C107—22no—
97C2×C4⋊C4×C107D414yescomplemented
98C2×C22⋊C4×C107—22no—
99C2×C22⋊C4×C107—22no—
100C2×C22⋊C4×C107—22no—
101C2×C22⋊C4×C107—22no—
102C2×C22⋊C4×C107—22no—
103C2×C22⋊C4×C107—24no—
104C2×C22⋊C4×C107—24no—
105C2×C22⋊C4×C107—24no—
106C2×C22⋊C4×C107—24no—
107C2×C22⋊C4×C107—24no—
108C2×C22⋊C4×C107—24no—
109C2×C22⋊C4×C107—24no—
110C2×C22⋊C4×C107—24no—
111C2×C22⋊C4×C107—24no—
112C2×C22⋊C4×C107—24no—
113C2×C22⋊C4×C107—24no—
114C2×C22⋊C4×C107—24no—
115C2×C22⋊C4×C107—24no—
116C2×C22⋊C4×C107—42no—
117C2×C22⋊C4×C107—42no—
118C2×C22⋊C4×C107—42no—
119C2×C22⋊C4×C107—42no—
120C2×C22⋊C4×C107D418yescomplemented
121C2×C22⋊C4×C107D414yescomplemented
122C2×C42×C107—22no—
123C2×C42×C107—22no—
124C2×C42×C107—22no—
125#95×C107—24no—
126#95×C107—24no—
127#95×C107—22no—
128#95×C107—24no—
129#95×C107—22no—
130#95×C107—42no—
131C24×C107—21no—
132C24×C107—21no—
133C24×C107—21no—
134C24×C107—21no—
135C24×C107—22no—
136C24×C107—22no—
137C24×C107—22no—
138C24×C107—21no—
139C24×C107—21no—
140C24×C107—21no—
141C24×C107—21no—
142C24×C107—22no—
143C24×C107—22no—
144C24×C107—22no—
145C24×C107—22no—
146C24×C107—22no—
147C24×C107—22no—
148C24×C107—22no—
149C24×C107—22no—
150C24×C107—22no—
151C24×C107—22no—
152C24×C107—22no—
153C24×C107—22no—
154C24×C107—22no—
155C24×C107—22no—
156C24×C107—22no—
157C24×C107—22no—
158C24×C107—22no—
159C24×C107—22no—
160C24×C107—22no—
161C24×C107C2×D414yes—
162C24×C107C2×D412yes—
163C24×C107C2×D412yes—
164C24×C107C2×D412yes—
165C24×C107C2×D412yes—
166C24×C107#4112yes—
167C24×C107#4112yes—
168C24×C107C2411yescharacteristic
169C2×D4×C107—28no—
170C2×D4×C107—28no—
171C2×D4×C107—28no—
172C2×D4×C107—28no—
173C2×D4×C107—28no—
174C2×D4×C107—28no—
175C2×D4×C107—28no—
176C2×D4×C107—216no—
177C2×D4×C107—216no—
178C2×D4×C107—28no—
179C2×D4×C107—48no—
180C2×D4×C107—48no—
181C2×D4×C107—48no—
182C2×D4×C107—48no—
183C2×D4×C107—48no—
184C2×D4×C107—48no—
185C2×D4×C107—44no—
186C2×D4×C107—48no—
187C2×D4×C107—48no—
188C2×D4×C107—48no—
189C2×D4×C107—48no—
190C2×D4×C107—48no—
191C2×D4×C107—48no—
192C2×D4×C107—48no—
193C2×D4×C107—48no—
194C2×D4×C107—44no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—22no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—22no—
203C22×C4×C107—22no—
204C22×C4×C107—28no—
205C22×C4×C107—22no—
206C22×C4×C107—22no—
207C22×C4×C107—22no—
208C22×C4×C107—22no—
209C22×C4×C107—22no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—22no—
215C22×C4×C107—22no—
216C22×C4×C107—22no—
217C22×C4×C107—22no—
218C22×C4×C107—22no—
219C22×C4×C107—22no—
220C22×C4×C107—22no—
221C22×C4×C107—22no—
222C22×C4×C107—22no—
223C22×C4×C107—22no—
224C22×C4×C107—22no—
225C22×C4×C107—28no—
226C22×C4×C107—28no—
227C22×C4×C107—22no—
228C22×C4×C107—22no—
229C22×C4×C107—22no—
230C22×C4×C107—22no—
231C22×C4×C107—22no—
232C22×C4×C107—22no—
233C22×C4×C107—22no—
234C22×C4×C107—44no—
235C22×C4×C107—48no—
236C22×C4×C107—48no—
237C22×C4×C107—48no—
238C22×C4×C107—48no—
239C22×C4×C107—44no—
240C22×C4×C107—44no—
241C22×C4×C107C2×D414yes—
242C22×C4×C107C2×D412yes—
243C22×C4×C107C2×D412yes—
244C22×C4×C107C2×D414yes—
245C22×C4×C107C2×D412yes—
246C22×C4×C107C2×D412yes—
247C22×C4×C107C2×D412yes—
248C22×C4×C107C2×D412yes—
249C22×C4×C107C2×D412yes—
250C22×C4×C107C2×D412yes—
251C22×C4×C107#4114yes—
252C22×C4×C107#4112yes—
253C4⋊C4×C107—28no—
254C4⋊C4×C107—28no—
255C22⋊C4×C107—28no—
256C22⋊C4×C107—28no—
257C22⋊C4×C107—216no—
258C22⋊C4×C107—48no—
259C22⋊C4×C107—48no—
260C22⋊C4×C107—48no—
261C22⋊C4×C107—48no—
262C22⋊C4×C107—48no—
263C42×C107—28no—
264C23×C107—22no—
265C23×C107—22no—
266C23×C107—22no—
267C23×C107—22no—
268C23×C107—22no—
269C23×C107—22no—
270C23×C107—22no—
271C23×C107—22no—
272C23×C107—22no—
273C23×C107—22no—
274C23×C107—22no—
275C23×C107—22no—
276C23×C107—22no—
277C23×C107—24no—
278C23×C107—22no—
279C23×C107—22no—
280C23×C107—22no—
281C23×C107—24no—
282C23×C107—24no—
283C23×C107—24no—
284C23×C107—24no—
285C23×C107—24no—
286C23×C107—24no—
287C23×C107—24no—
288C23×C107—24no—
289C23×C107—24no—
290C23×C107—24no—
291C23×C107—24no—
292C23×C107—24no—
293C23×C107—24no—
294C23×C107—24no—
295C23×C107—24no—
296C23×C107—24no—
297C23×C107—41no—
298C23×C107—42no—
299C23×C107—42no—
300C23×C107—42no—
301C23×C107—41no—
302C23×C107—41no—
303C23×C107—41no—
304C23×C107—42no—
305C23×C107—42no—
306C23×C107—42no—
307C23×C107—42no—
308C23×C107—42no—
309C23×C107—42no—
310C23×C107—42no—
311C23×C107—42no—
312C23×C107—42no—
313C23×C107—42no—
314C23×C107—42no—
315C23×C107—42no—
316C23×C107—42no—
317C23×C107—42no—
318C23×C107—42no—
319C23×C107—42no—
320C23×C107—42no—
321C23×C107—42no—
322C23×C107—42no—
323C23×C107—42no—
324C23×C107—42no—
325C23×C107—42no—
326C23×C107—42no—
327C23×C107—42no—
328C23×C107—42no—
329C23×C107—42no—
330C23×C107—42no—
331C23×C107—42no—
332C23×C107—42no—
333C23×C107—42no—
334C23×C107—42no—
335C23×C107—42no—
336C23×C107—42no—
337C23×C107—42no—
338C23×C107—42no—
339C23×C107—42no—
340C23×C107—42no—
341C23×C107—42no—
342C23×C107—42no—
343C23×C107#12114yes—
344C23×C107#12114yescomplemented
345C23×C107C22×D411yescharacteristic
346C23×C107C22×D411yescharacteristic
347C23×C107C22×D411yescharacteristic
348C23×C107C22×D412yes—
349C23×C107C22×D411yescharacteristic
350C23×C107C2×#4111yescharacteristic
351C23×C107C2×#4111yescharacteristic
352C23×C107C2×#4111yescharacteristic
353C23×C107C2×#4112yes—
354C23×C107H(5,𝔽2)12yes—
355C23×C107H(5,𝔽2)12yes—
356D4×C107—232no—
357D4×C107—416no—
358D4×C107—432no—
359D4×C107—432no—
360C2×C4×C107—22no—
361C2×C4×C107—22no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—22no—
369C2×C4×C107—22no—
370C2×C4×C107—24no—
371C2×C4×C107—24no—
372C2×C4×C107—24no—
373C2×C4×C107—24no—
374C2×C4×C107—22no—
375C2×C4×C107—22no—
376C2×C4×C107—24no—
377C2×C4×C107—24no—
378C2×C4×C107—24no—
379C2×C4×C107—24no—
380C2×C4×C107—24no—
381C2×C4×C107—24no—
382C2×C4×C107—24no—
383C2×C4×C107—24no—
384C2×C4×C107—416no—
385C2×C4×C107—416no—
386C2×C4×C107—41no—
387C2×C4×C107—42no—
388C2×C4×C107—42no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—42no—
393C2×C4×C107—42no—
394C2×C4×C107—42no—
395C2×C4×C107—42no—
396C2×C4×C107—42no—
397C2×C4×C107—42no—
398C2×C4×C107—42no—
399C2×C4×C107—42no—
400C2×C4×C107—42no—
401C2×C4×C107—42no—
402C2×C4×C107—42no—
403C2×C4×C107—42no—
404C2×C4×C107—42no—
405C2×C4×C107—42no—
406C2×C4×C107—42no—
407C2×C4×C107#12014yes—
408C2×C4×C107#12014yes—
409C2×C4×C107#12114yescomplemented
410C22×C107—24no—
411C22×C107—24no—
412C22×C107—24no—
413C22×C107—28no—
414C22×C107—24no—
415C22×C107—42no—
416C22×C107—42no—
417C22×C107—42no—
418C22×C107—42no—
419C22×C107—42no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—44no—
423C22×C107—44no—
424C22×C107—44no—
425C22×C107—42no—
426C22×C107—42no—
427C22×C107—44no—
428C22×C107—44no—
429C22×C107—44no—
430C22×C107—44no—
431C22×C107—42no—
432C22×C107—44no—
433C22×C107—44no—
434C22×C107—44no—
435C22×C107—44no—
436C22×C107—44no—
437C22×C107—44no—
438C22×C107—44no—
439C22×C107—82no—
440C22×C107—82no—
441C22×C107—82no—
442C22×C107—82no—
443C22×C107—82no—
444C22×C107—82no—
445C22×C107—82no—
446C22×C107—82no—
447C22×C107C2×#12011yescharacteristic
448C22×C107C2×#12011yescharacteristic
449C22×C107C2×#12111yescharacteristic
450C22×C107C2×#12111yescharacteristic
451C22×C107C2×#12111yescharacteristic
452C22×C107#52511yescharacteristic
453C22×C107#52511yescharacteristic
454C22×C107#52511yescharacteristic
455C22×C107#52512yes—
456C22×C107#53212yes—
457C22×C107#53211yescharacteristic
458C22×C107#53411yescharacteristic
459C22×C107#53511yescharacteristic
460C22×C107#53812yes—
461C22×C107#54012yes—
462C22×C107D4212yes—
463C22×C107D4212yes—
464C22×C107D4212yes—
465C22×C107#54612yes—
466C22×C107#54612yes—
467C22×C107#54612yes—
468C22×C107#55012yes—
469C22×C107#55312yes—
470C4×C107—24no—
471C4×C107—24no—
472C4×C107—24no—
473C4×C107—42no—
474C4×C107—44no—
475C4×C107—44no—
476C4×C107—42no—
477C4×C107—82no—
478#14722C10711yesmaximal, characteristic, direct product factor, Sylow
479C2×C107—44no—
480C2×C107—44no—
481C2×C107—84no—
482C2×C107#238811yescharacteristic
483C2×C107#240311yescharacteristic
484C2×C107#240811yescharacteristic
485C2×C107#242412yes—
486C2×C107#242812yes—
487C2×C107#243111yescharacteristic
488C2×C107#245612yes—
489C2×C107#246412yes—
490C2×C107#254311yescharacteristic
491C2×C107#263511yescharacteristic
492C2×C107#284711yescharacteristic
493C22×#121C2×C10711yescharacteristic, complemented
494C22×C4×D4C2×C10711yescharacteristic, complemented
495C2×#394C2×C10711yescharacteristic, complemented
496C2×#392C2×C10712yescomplemented
497C2×#392C2×C10711yescharacteristic, complemented
498C2×#386C2×C10712yescomplemented
499#1441C2×C10711yescharacteristic, complemented
500#1439C2×C10711yescharacteristic, complemented
501#1438C2×C10712yescomplemented
502#1437C2×C10712yescomplemented
503C22⋊#95C2×C10711yescharacteristic, complemented
504C107#1472211yescharacteristic, direct product factor, Sylow
505C23×D4C22×C10711yescharacteristic
506C23×D4C22×C10712yes—
507C23×D4C22×C10711yescharacteristic
508C23×D4C22×C10712yes—
509C24×C4C22×C10711yescharacteristic
510C24×C4C22×C10711yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C10711yescharacteristic
517C22×C4⋊C4C22×C10711yescharacteristic
518C22×C22⋊C4C22×C10712yes—
519C22×C22⋊C4C22×C10711yescharacteristic
520C22×C22⋊C4C22×C10712yes—
521C22×C22⋊C4C22×C10712yes—
522C22×C22⋊C4C22×C10712yes—
523C22×C22⋊C4C22×C10712yes—
524C22×C22⋊C4C22×C10711yescharacteristic
525C22×C22⋊C4C22×C10712yes—
526C22×C42C22×C10711yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C10711yescharacteristic
532C2×#95C22×C10712yes—
533C2×#95C22×C10711yescharacteristic
534C2×#95C22×C10712yes—
535C2×#95C22×C10712yes—
536C2×#95C22×C10712yes—
537C25C23×C10712yes—
538C25C23×C10711yescharacteristic
539C25C23×C10711yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C10714yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C10714yescomplemented
576C23×C4C23×C10712yes—
577C23×C4C23×C10711yescharacteristic
578C23×C4C23×C10711yescharacteristic
579C23×C4C23×C10712yes—
580C23×C4C23×C10712yes—
581C23×C4C23×C10711yescharacteristic
582C23×C4C23×C10711yescharacteristic
583C23×C4C23×C10711yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C10714yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C10714yescomplemented
614C2×C22⋊C4D4×C10718yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C10714yes—
655C24C2×D4×C10712yes—
656C24C2×D4×C10712yes—
657C24C2×D4×C10712yes—
658C24C2×D4×C10712yes—
659C24#41×C10712yes—
660C24#41×C10712yes—
661C24C24×C10711yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C10714yes—
735C22×C4C2×D4×C10712yes—
736C22×C4C2×D4×C10712yes—
737C22×C4C2×D4×C10714yes—
738C22×C4C2×D4×C10712yes—
739C22×C4C2×D4×C10712yes—
740C22×C4C2×D4×C10712yes—
741C22×C4C2×D4×C10712yes—
742C22×C4C2×D4×C10712yes—
743C22×C4C2×D4×C10712yes—
744C22×C4#41×C10714yes—
745C22×C4#41×C10712yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C10714yes—
837C23#121×C10714yescomplemented
838C23C22×D4×C10711yescharacteristic
839C23C22×D4×C10711yescharacteristic
840C23C22×D4×C10711yescharacteristic
841C23C22×D4×C10712yes—
842C23C22×D4×C10711yescharacteristic
843C23C2×#41×C10711yescharacteristic
844C23C2×#41×C10711yescharacteristic
845C23C2×#41×C10711yescharacteristic
846C23C2×#41×C10712yes—
847C23H(5,𝔽2)×C10712yes—
848C23H(5,𝔽2)×C10712yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C10714yes—
901C2×C4#120×C10714yes—
902C2×C4#121×C10714yescomplemented
903C22—24no—
904C22—28no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—44no—
916C22—44no—
917C22—44no—
918C22—42no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C10711yescharacteristic
941C22C2×#120×C10711yescharacteristic
942C22C2×#121×C10711yescharacteristic
943C22C2×#121×C10711yescharacteristic
944C22C2×#121×C10711yescharacteristic
945C22#525×C10711yescharacteristic
946C22#525×C10712yes—
947C22#525×C10711yescharacteristic
948C22#525×C10711yescharacteristic
949C22#532×C10712yes—
950C22#532×C10711yescharacteristic
951C22#534×C10711yescharacteristic
952C22#535×C10711yescharacteristic
953C22#538×C10712yes—
954C22#540×C10712yes—
955C22D42×C10712yes—
956C22D42×C10712yes—
957C22D42×C10712yes—
958C22#546×C10712yes—
959C22#546×C10712yes—
960C22#546×C10712yes—
961C22#550×C10712yes—
962C22#553×C10712yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C107×#238811yescharacteristic
975C2C107×#240311yescharacteristic
976C2C107×#240811yescharacteristic
977C2C107×#242412yes—
978C2C107×#242812yes—
979C2C107×#243111yescharacteristic
980C2C107×#245612yes—
981C2C107×#246412yes—
982C2C107×#254311yescharacteristic
983C2C107×#263511yescharacteristic
984C2C107×#284711yescharacteristic
subgroupG/H
center, socleC24×C107C24
commutator, Frattini, cosocleC24C24×C107
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C107C2semidirect
2. C22×C4×D4×C107C2semidirect
3. C2×#394×C107C2semidirect
4. C2×#392×C107C2semidirect
5. C2×#392×C107C2semidirect
6. C2×#386×C107C2semidirect
7. C107×#1441C2semidirect
8. C107×#1439C2semidirect
9. C107×#1438C2semidirect
10. C107×#1437C2semidirect
11. C107×C22⋊#95C2semidirect
72. C22×D4×C107D4semidirect
82. C23×C4×C107D4semidirect
97. C2×C4⋊C4×C107D4semidirect
120. C2×C22⋊C4×C107D4semidirect
121. C2×C22⋊C4×C107D4semidirect
344. C23×C107#121semidirect
409. C2×C4×C107#121semidirect
478. #14722C107direct (N × H)
493. C22×#121C2×C107semidirect
494. C22×C4×D4C2×C107semidirect
495. C2×#394C2×C107semidirect
496. C2×#392C2×C107semidirect
497. C2×#392C2×C107semidirect
498. C2×#386C2×C107semidirect
499. #1441C2×C107semidirect
500. #1439C2×C107semidirect
501. #1438C2×C107semidirect
502. #1437C2×C107semidirect
503. C22⋊#95C2×C107semidirect
504. C107#14722direct (N × H)
565. C22×D4D4×C107semidirect
575. C23×C4D4×C107semidirect
590. C2×C4⋊C4D4×C107semidirect
613. C2×C22⋊C4D4×C107semidirect
614. C2×C22⋊C4D4×C107semidirect
837. C23#121×C107semidirect
902. C2×C4#121×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1072
C22×C4×D4×C1072
C2×#394×C1072
C2×#392×C1072
C2×#386×C1072
C107×#14412
C107×#14392
C107×#14382
C107×#14372
C107×C22⋊#952
#14722107