Finite Group Databasebeta

← C107×#13996 #41039960

Subgroups — C107×#13996 #41039960

Order 27392.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C107C211yesmaximal, characteristic
2C2×#386×C107C211yesmaximal, characteristic
3C2×#386×C107C211yesmaximal, characteristic
4C2×#385×C107C211yesmaximal, characteristic, complemented
5C2×#381×C107C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C107C211yesmaximal, characteristic, complemented
7C22×#95×C107C211yesmaximal, characteristic, complemented
8C107×#1445C212yesmaximal, complemented
9C107×#1439C212yesmaximal, complemented
10C107×#1437C212yesmaximal, complemented
11C107×C4⋊#95C212yesmaximal, complemented
12C23×D4×C107C2211yescharacteristic
13C24×C4×C107C2211yescharacteristic
14C24×C4×C107C2211yescharacteristic
15C24×C4×C107C2211yescharacteristic
16C2×#123×C107—24no—
17C2×#123×C107—24no—
18C2×#123×C107C418yescomplemented
19C22×C4⋊C4×C107C2212yes—
20C22×C4⋊C4×C107C2212yes—
21C22×C22⋊C4×C107C2211yescharacteristic
22C22×C22⋊C4×C107C2211yescharacteristic
23C22×C22⋊C4×C107C2212yes—
24C22×C22⋊C4×C107C2212yes—
25C22×C22⋊C4×C107C2211yescharacteristic
26C22×C22⋊C4×C107C2211yescharacteristic
27C22×C22⋊C4×C107C2211yescharacteristic
28C22×C42×C107C2212yes—
29#386×C107—24no—
30#386×C107—24no—
31#385×C107—24no—
32#381×C107—24no—
33C4×C22⋊C4×C107—24no—
34C2×#95×C107—24no—
35C2×#95×C107C2211yescharacteristic
36C2×#95×C107C2212yes—
37C2×#95×C107C2212yes—
38C2×#95×C107C2212yes—
39C2×#95×C107C2212yes—
40C2×#95×C107C2212yes—
41C2×#95×C107C2212yes—
42C2×#95×C107C2212yes—
43C2×#95×C107C2211yescharacteristic
44C25×C107C2311yescharacteristic
45C25×C107C2311yescharacteristic
46C22×D4×C107—22no—
47C22×D4×C107—22no—
48C22×D4×C107—22no—
49C22×D4×C107—22no—
50C22×D4×C107—22no—
51C22×D4×C107—22no—
52C22×D4×C107C2×C414yes—
53C23×C4×C107—22no—
54C23×C4×C107—22no—
55C23×C4×C107—22no—
56C23×C4×C107—22no—
57C23×C4×C107—22no—
58C23×C4×C107—22no—
59C23×C4×C107—22no—
60C23×C4×C107—22no—
61C23×C4×C107—22no—
62C23×C4×C107—24no—
63C23×C4×C107—24no—
64C23×C4×C107—22no—
65C23×C4×C107—22no—
66C23×C4×C107—42no—
67C23×C4×C107—42no—
68C23×C4×C107C2×C414yes—
69C23×C4×C107D414yes—
70C23×C4×C107C2311yescharacteristic
71C23×C4×C107C2311yescharacteristic
72C23×C4×C107C2312yes—
73C23×C4×C107C2311yescharacteristic
74C23×C4×C107C2311yescharacteristic
75C23×C4×C107C2312yes—
76C23×C4×C107C2312yes—
77C23×C4×C107C2312yes—
78C23×C4×C107C2311yescharacteristic
79#123×C107—232no—
80C2×C4⋊C4×C107—24no—
81C2×C4⋊C4×C107—24no—
82C2×C4⋊C4×C107—24no—
83C2×C4⋊C4×C107—24no—
84C2×C4⋊C4×C107—42no—
85C2×C4⋊C4×C107C2×C418yescomplemented
86C2×C22⋊C4×C107—22no—
87C2×C22⋊C4×C107—22no—
88C2×C22⋊C4×C107—24no—
89C2×C22⋊C4×C107—24no—
90C2×C22⋊C4×C107—22no—
91C2×C22⋊C4×C107—22no—
92C2×C22⋊C4×C107—22no—
93C2×C22⋊C4×C107—24no—
94C2×C22⋊C4×C107—22no—
95C2×C22⋊C4×C107—22no—
96C2×C22⋊C4×C107—24no—
97C2×C22⋊C4×C107—24no—
98C2×C22⋊C4×C107—42no—
99C2×C22⋊C4×C107—42no—
100C2×C22⋊C4×C107C2×C414yes—
101C2×C22⋊C4×C107C2×C418yescomplemented
102C2×C22⋊C4×C107D414yes—
103C2×C22⋊C4×C107D414yes—
104C2×C22⋊C4×C107D414yes—
105C2×C42×C107—24no—
106C2×C42×C107—24no—
107C2×C42×C107—42no—
108#95×C107—24no—
109#95×C107—24no—
110#95×C107—24no—
111#95×C107—24no—
112#95×C107—24no—
113#95×C107—24no—
114#95×C107—24no—
115#95×C107—22no—
116#95×C107—22no—
117C24×C107—22no—
118C24×C107—22no—
119C24×C107—22no—
120C24×C107—22no—
121C24×C107—21no—
122C24×C107—21no—
123C24×C107—21no—
124C24×C107—21no—
125C24×C107—22no—
126C24×C107—22no—
127C24×C107—21no—
128C24×C107—21no—
129C24×C107—22no—
130C24×C107—22no—
131C24×C107C22×C412yes—
132C24×C107C22×C412yes—
133C24×C107C2×D412yes—
134C24×C107C2×D412yes—
135C24×C107C2×D412yes—
136C24×C107C2×D412yes—
137C24×C107#4112yes—
138C24×C107#4112yes—
139C24×C107C2411yescharacteristic
140C2×D4×C107—28no—
141C2×D4×C107—28no—
142C2×D4×C107—28no—
143C2×D4×C107—44no—
144C2×D4×C107—44no—
145C2×D4×C107—44no—
146C2×D4×C107—44no—
147C22×C4×C107—21no—
148C22×C4×C107—22no—
149C22×C4×C107—22no—
150C22×C4×C107—21no—
151C22×C4×C107—22no—
152C22×C4×C107—22no—
153C22×C4×C107—22no—
154C22×C4×C107—28no—
155C22×C4×C107—28no—
156C22×C4×C107—28no—
157C22×C4×C107—28no—
158C22×C4×C107—28no—
159C22×C4×C107—22no—
160C22×C4×C107—22no—
161C22×C4×C107—21no—
162C22×C4×C107—22no—
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—22no—
166C22×C4×C107—22no—
167C22×C4×C107—22no—
168C22×C4×C107—22no—
169C22×C4×C107—22no—
170C22×C4×C107—21no—
171C22×C4×C107—21no—
172C22×C4×C107—22no—
173C22×C4×C107—22no—
174C22×C4×C107—22no—
175C22×C4×C107—22no—
176C22×C4×C107—22no—
177C22×C4×C107—21no—
178C22×C4×C107—22no—
179C22×C4×C107—22no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—22no—
183C22×C4×C107—22no—
184C22×C4×C107—22no—
185C22×C4×C107—22no—
186C22×C4×C107—22no—
187C22×C4×C107—28no—
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—22no—
195C22×C4×C107—22no—
196C22×C4×C107—22no—
197C22×C4×C107—22no—
198C22×C4×C107—44no—
199C22×C4×C107—48no—
200C22×C4×C107—48no—
201C22×C4×C107—48no—
202C22×C4×C107—48no—
203C22×C4×C107—44no—
204C22×C4×C107—44no—
205C22×C4×C107—44no—
206C22×C4×C107—44no—
207C22×C4×C107—44no—
208C22×C4×C107—44no—
209C22×C4×C107C22×C414yes—
210C22×C4×C107C22×C412yes—
211C22×C4×C107C22×C414yes—
212C22×C4×C107C2×D414yes—
213C22×C4×C107C2×D412yes—
214C22×C4×C107C2×D414yes—
215C22×C4×C107C2×D414yes—
216C22×C4×C107C2×D412yes—
217C22×C4×C107#4114yes—
218C22×C4×C107#4114yes—
219C4⋊C4×C107—216no—
220C4⋊C4×C107—48no—
221C22⋊C4×C107—28no—
222C22⋊C4×C107—216no—
223C22⋊C4×C107—48no—
224C22⋊C4×C107—44no—
225C22⋊C4×C107—44no—
226C22⋊C4×C107—44no—
227C22⋊C4×C107C22⋊C4116yescomplemented
228C42×C107—48no—
229C23×C107—24no—
230C23×C107—24no—
231C23×C107—22no—
232C23×C107—22no—
233C23×C107—24no—
234C23×C107—22no—
235C23×C107—22no—
236C23×C107—24no—
237C23×C107—24no—
238C23×C107—24no—
239C23×C107—24no—
240C23×C107—24no—
241C23×C107—24no—
242C23×C107—24no—
243C23×C107—24no—
244C23×C107—24no—
245C23×C107—22no—
246C23×C107—22no—
247C23×C107—22no—
248C23×C107—24no—
249C23×C107—24no—
250C23×C107—41no—
251C23×C107—41no—
252C23×C107—41no—
253C23×C107—41no—
254C23×C107—41no—
255C23×C107—42no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—42no—
260C23×C107—42no—
261C23×C107—42no—
262C23×C107—42no—
263C23×C107—42no—
264C23×C107—42no—
265C23×C107—42no—
266C23×C107—42no—
267C23×C107—42no—
268C23×C107C2×C22⋊C414yes—
269C23×C107C4×D414yes—
270C23×C107C4×D414yes—
271C23×C107#12114yes—
272C23×C107#12114yes—
273C23×C107#12414yes—
274C23×C107#12714yes—
275C23×C107C23×C411yescharacteristic
276C23×C107C22×D411yescharacteristic
277C23×C107C22×D411yescharacteristic
278C23×C107C22×D411yescharacteristic
279C23×C107C22×D411yescharacteristic
280C23×C107C2×#4111yescharacteristic
281C23×C107C2×#4111yescharacteristic
282C23×C107C2×#4112yes—
283C23×C107C2×#4112yes—
284C23×C107H(5,𝔽2)12yes—
285C23×C1072−1+412yes—
286D4×C107—416no—
287C2×C4×C107—24no—
288C2×C4×C107—24no—
289C2×C4×C107—22no—
290C2×C4×C107—22no—
291C2×C4×C107—24no—
292C2×C4×C107—24no—
293C2×C4×C107—24no—
294C2×C4×C107—24no—
295C2×C4×C107—24no—
296C2×C4×C107—24no—
297C2×C4×C107—24no—
298C2×C4×C107—22no—
299C2×C4×C107—24no—
300C2×C4×C107—24no—
301C2×C4×C107—22no—
302C2×C4×C107—22no—
303C2×C4×C107—24no—
304C2×C4×C107—22no—
305C2×C4×C107—22no—
306C2×C4×C107—24no—
307C2×C4×C107—22no—
308C2×C4×C107—24no—
309C2×C4×C107—24no—
310C2×C4×C107—24no—
311C2×C4×C107—24no—
312C2×C4×C107—416no—
313C2×C4×C107—416no—
314C2×C4×C107—42no—
315C2×C4×C107—42no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—42no—
319C2×C4×C107—41no—
320C2×C4×C107—42no—
321C2×C4×C107—42no—
322C2×C4×C107—42no—
323C2×C4×C107—41no—
324C2×C4×C107—42no—
325C2×C4×C107—42no—
326C2×C4×C107—42no—
327C2×C4×C107—42no—
328C2×C4×C107—42no—
329C2×C4×C107—42no—
330C2×C4×C107—42no—
331C2×C4×C107—42no—
332C2×C4×C107—416no—
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—42no—
340C2×C4×C107—42no—
341C2×C4×C107—42no—
342C2×C4×C107—42no—
343C2×C4×C107C2×C22⋊C418yes—
344C2×C4×C107#12314yescomplemented
345C22×C107—24no—
346C22×C107—28no—
347C22×C107—28no—
348C22×C107—24no—
349C22×C107—24no—
350C22×C107—28no—
351C22×C107—28no—
352C22×C107—24no—
353C22×C107—24no—
354C22×C107—24no—
355C22×C107—42no—
356C22×C107—44no—
357C22×C107—44no—
358C22×C107—42no—
359C22×C107—42no—
360C22×C107—81no—
361C22×C107—81no—
362C22×C107—82no—
363C22×C107—82no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107#39018yes—
367C22×C107C22×C22⋊C411yescharacteristic
368C22×C107C2×C4×D411yescharacteristic
369C22×C107C2×C4×D411yescharacteristic
370C22×C107C4×#4112yes—
371C22×C107#52012yes—
372C22×C107C2×#12111yescharacteristic
373C22×C107C2×#12111yescharacteristic
374C22×C107C2×#12311yescharacteristic
375C22×C107#52511yescharacteristic
376C22×C107C2×#12411yescharacteristic
377C22×C107#52912yes—
378C22×C107C2×#12711yescharacteristic
379C22×C107#53411yescharacteristic
380C22×C107#53611yescharacteristic
381C22×C107#53912yes—
382C22×C107#54612yes—
383C22×C107#54612yes—
384C22×C107#54612yes—
385C22×C107#54712yes—
386C22×C107#54712yes—
387C22×C107#54712yes—
388C22×C107#55112yes—
389C22×C107#55212yes—
390C4×C107—28no—
391C4×C107—24no—
392C4×C107—42no—
393C4×C107—44no—
394C4×C107—44no—
395C4×C107—44no—
396C4×C107—42no—
397C4×C107—81no—
398C4×C107—81no—
399#13996C10711yesmaximal, characteristic, direct product factor, Sylow
400C2×C107—28no—
401C2×C107—82no—
402C2×C107C2×#39011yescharacteristic
403C2×C107C4×#12311yescharacteristic
404C2×C107#232211yescharacteristic
405C2×C107#233912yes—
406C2×C107#235912yes—
407C2×C107#241211yescharacteristic
408C2×C107#241311yescharacteristic
409C2×C107#242512yes—
410C2×C107#248812yes—
411C2×C107#250111yescharacteristic
412C2×C107#253911yescharacteristic
413C22×#123C2×C10711yescharacteristic
414C2×#386C2×C10711yescharacteristic
415C2×#386C2×C10711yescharacteristic
416C2×#385C2×C10711yescharacteristic, complemented
417C2×#381C2×C10711yescharacteristic, complemented
418C2×C4×C22⋊C4C2×C10711yescharacteristic, complemented
419C22×#95C2×C10711yescharacteristic, complemented
420#1445C2×C10712yescomplemented
421#1439C2×C10712yescomplemented
422#1437C2×C10712yescomplemented
423C4⋊#95C2×C10712yescomplemented
424C107#1399611yescharacteristic, direct product factor, Sylow
425C23×D4C22×C10711yescharacteristic
426C24×C4C22×C10711yescharacteristic
427C24×C4C22×C10711yescharacteristic
428C24×C4C22×C10711yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C10718yescomplemented
432C22×C4⋊C4C22×C10712yes—
433C22×C4⋊C4C22×C10712yes—
434C22×C22⋊C4C22×C10711yescharacteristic
435C22×C22⋊C4C22×C10711yescharacteristic
436C22×C22⋊C4C22×C10712yes—
437C22×C22⋊C4C22×C10712yes—
438C22×C22⋊C4C22×C10711yescharacteristic
439C22×C22⋊C4C22×C10711yescharacteristic
440C22×C22⋊C4C22×C10711yescharacteristic
441C22×C42C22×C10712yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C10711yescharacteristic
449C2×#95C22×C10712yes—
450C2×#95C22×C10712yes—
451C2×#95C22×C10712yes—
452C2×#95C22×C10712yes—
453C2×#95C22×C10712yes—
454C2×#95C22×C10712yes—
455C2×#95C22×C10712yes—
456C2×#95C22×C10711yescharacteristic
457C25C23×C10711yescharacteristic
458C25C23×C10711yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C10714yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4C2×C4×C10714yes—
482C23×C4D4×C10714yes—
483C23×C4C23×C10711yescharacteristic
484C23×C4C23×C10711yescharacteristic
485C23×C4C23×C10712yes—
486C23×C4C23×C10711yescharacteristic
487C23×C4C23×C10712yes—
488C23×C4C23×C10711yescharacteristic
489C23×C4C23×C10712yes—
490C23×C4C23×C10712yes—
491C23×C4C23×C10711yescharacteristic
492#123—232no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4C2×C4×C10718yescomplemented
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4C2×C4×C10714yes—
514C2×C22⋊C4C2×C4×C10718yescomplemented
515C2×C22⋊C4D4×C10714yes—
516C2×C22⋊C4D4×C10714yes—
517C2×C22⋊C4D4×C10714yes—
518C2×C42—24no—
519C2×C42—24no—
520C2×C42—42no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—22no—
529#95—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—21no—
541C24—21no—
542C24—22no—
543C24—22no—
544C24C22×C4×C10712yes—
545C24C22×C4×C10712yes—
546C24C2×D4×C10712yes—
547C24C2×D4×C10712yes—
548C24C2×D4×C10712yes—
549C24C2×D4×C10712yes—
550C24#41×C10712yes—
551C24#41×C10712yes—
552C24C24×C10711yescharacteristic
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—28no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C10714yes—
623C22×C4C22×C4×C10712yes—
624C22×C4C22×C4×C10714yes—
625C22×C4C2×D4×C10714yes—
626C22×C4C2×D4×C10712yes—
627C22×C4C2×D4×C10714yes—
628C22×C4C2×D4×C10714yes—
629C22×C4C2×D4×C10712yes—
630C22×C4#41×C10714yes—
631C22×C4#41×C10714yes—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4C22⋊C4×C107116yescomplemented
641C42—48no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23C2×C22⋊C4×C10714yes—
682C23C4×D4×C10714yes—
683C23C4×D4×C10714yes—
684C23#121×C10714yes—
685C23#121×C10714yes—
686C23#124×C10714yes—
687C23#127×C10714yes—
688C23C23×C4×C10711yescharacteristic
689C23C22×D4×C10711yescharacteristic
690C23C22×D4×C10711yescharacteristic
691C23C22×D4×C10711yescharacteristic
692C23C22×D4×C10711yescharacteristic
693C23C2×#41×C10711yescharacteristic
694C23C2×#41×C10711yescharacteristic
695C23C2×#41×C10712yes—
696C23C2×#41×C10712yes—
697C23H(5,𝔽2)×C10712yes—
698C232−1+4×C10712yes—
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—416no—
726C2×C4—416no—
727C2×C4—416no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4C2×C22⋊C4×C10718yes—
757C2×C4#123×C10714yescomplemented
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—81no—
774C22—81no—
775C22—82no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22#390×C10718yes—
780C22C22×C22⋊C4×C10711yescharacteristic
781C22C2×C4×D4×C10711yescharacteristic
782C22C2×C4×D4×C10711yescharacteristic
783C22C4×#41×C10712yes—
784C22#520×C10712yes—
785C22C2×#121×C10711yescharacteristic
786C22C2×#121×C10711yescharacteristic
787C22C2×#123×C10711yescharacteristic
788C22#525×C10711yescharacteristic
789C22C2×#124×C10711yescharacteristic
790C22#529×C10712yes—
791C22C2×#127×C10711yescharacteristic
792C22#534×C10711yescharacteristic
793C22#536×C10711yescharacteristic
794C22#539×C10712yes—
795C22#546×C10712yes—
796C22#546×C10712yes—
797C22#546×C10712yes—
798C22#547×C10712yes—
799C22#547×C10712yes—
800C22#547×C10712yes—
801C22#551×C10712yes—
802C22#552×C10712yes—
803C4—24no—
804C4—28no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C10711yescharacteristic
815C2C4×#123×C10711yescharacteristic
816C2C107×#232211yescharacteristic
817C2C107×#233912yes—
818C2C107×#235912yes—
819C2C107×#241211yescharacteristic
820C2C107×#241311yescharacteristic
821C2C107×#242512yes—
822C2C107×#248812yes—
823C2C107×#250111yescharacteristic
824C2C107×#253911yescharacteristic
subgroupG/H
center, socleC24×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC24C24×C107
prime radicalC23×D4×C107C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#385×C107C2semidirect
5. C2×#381×C107C2semidirect
6. C2×C4×C22⋊C4×C107C2semidirect
7. C22×#95×C107C2semidirect
8. C107×#1445C2semidirect
9. C107×#1439C2semidirect
10. C107×#1437C2semidirect
11. C107×C4⋊#95C2semidirect
18. C2×#123×C107C4semidirect
85. C2×C4⋊C4×C107C2×C4semidirect
101. C2×C22⋊C4×C107C2×C4semidirect
227. C22⋊C4×C107C22⋊C4semidirect
344. C2×C4×C107#123semidirect
399. #13996C107direct (N × H)
416. C2×#385C2×C107semidirect
417. C2×#381C2×C107semidirect
418. C2×C4×C22⋊C4C2×C107semidirect
419. C22×#95C2×C107semidirect
420. #1445C2×C107semidirect
421. #1439C2×C107semidirect
422. #1437C2×C107semidirect
423. C4⋊#95C2×C107semidirect
424. C107#13996direct (N × H)
431. C2×#123C4×C107semidirect
498. C2×C4⋊C4C2×C4×C107semidirect
514. C2×C22⋊C4C2×C4×C107semidirect
640. C22⋊C4C22⋊C4×C107semidirect
757. C2×C4#123×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1072
C2×#386×C1072
C2×#385×C1072
C2×#381×C1072
C2×C4×C22⋊C4×C1072
C22×#95×C1072
C107×#14452
C107×#14392
C107×#14372
C107×C4⋊#952
#13996107