Finite Group Databasebeta

← C101×#13996 #38796147

Subgroups — C101×#13996 #38796147

Order 25856.

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×C101C211yesmaximal, characteristic
2C2×#386×C101C211yesmaximal, characteristic
3C2×#386×C101C211yesmaximal, characteristic
4C2×#385×C101C211yesmaximal, characteristic, complemented
5C2×#381×C101C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
7C22×#95×C101C211yesmaximal, characteristic, complemented
8C101×#1445C212yesmaximal, complemented
9C101×#1439C212yesmaximal, complemented
10C101×#1437C212yesmaximal, complemented
11C101×C4⋊#95C212yesmaximal, complemented
12C23×D4×C101C2211yescharacteristic
13C24×C4×C101C2211yescharacteristic
14C24×C4×C101C2211yescharacteristic
15C24×C4×C101C2211yescharacteristic
16C2×#123×C101—24no—
17C2×#123×C101—24no—
18C2×#123×C101C418yescomplemented
19C22×C4⋊C4×C101C2212yes—
20C22×C4⋊C4×C101C2212yes—
21C22×C22⋊C4×C101C2211yescharacteristic
22C22×C22⋊C4×C101C2211yescharacteristic
23C22×C22⋊C4×C101C2212yes—
24C22×C22⋊C4×C101C2212yes—
25C22×C22⋊C4×C101C2211yescharacteristic
26C22×C22⋊C4×C101C2211yescharacteristic
27C22×C22⋊C4×C101C2211yescharacteristic
28C22×C42×C101C2212yes—
29#386×C101—24no—
30#386×C101—24no—
31#385×C101—24no—
32#381×C101—24no—
33C4×C22⋊C4×C101—24no—
34C2×#95×C101—24no—
35C2×#95×C101C2211yescharacteristic
36C2×#95×C101C2212yes—
37C2×#95×C101C2212yes—
38C2×#95×C101C2212yes—
39C2×#95×C101C2212yes—
40C2×#95×C101C2212yes—
41C2×#95×C101C2212yes—
42C2×#95×C101C2212yes—
43C2×#95×C101C2211yescharacteristic
44C25×C101C2311yescharacteristic
45C25×C101C2311yescharacteristic
46C22×D4×C101—22no—
47C22×D4×C101—22no—
48C22×D4×C101—22no—
49C22×D4×C101—22no—
50C22×D4×C101—22no—
51C22×D4×C101—22no—
52C22×D4×C101C2×C414yes—
53C23×C4×C101—22no—
54C23×C4×C101—22no—
55C23×C4×C101—22no—
56C23×C4×C101—22no—
57C23×C4×C101—22no—
58C23×C4×C101—22no—
59C23×C4×C101—22no—
60C23×C4×C101—22no—
61C23×C4×C101—22no—
62C23×C4×C101—24no—
63C23×C4×C101—24no—
64C23×C4×C101—22no—
65C23×C4×C101—22no—
66C23×C4×C101—42no—
67C23×C4×C101—42no—
68C23×C4×C101C2×C414yes—
69C23×C4×C101D414yes—
70C23×C4×C101C2311yescharacteristic
71C23×C4×C101C2311yescharacteristic
72C23×C4×C101C2312yes—
73C23×C4×C101C2311yescharacteristic
74C23×C4×C101C2312yes—
75C23×C4×C101C2311yescharacteristic
76C23×C4×C101C2312yes—
77C23×C4×C101C2312yes—
78C23×C4×C101C2311yescharacteristic
79#123×C101—232no—
80C2×C4⋊C4×C101—24no—
81C2×C4⋊C4×C101—24no—
82C2×C4⋊C4×C101—24no—
83C2×C4⋊C4×C101—24no—
84C2×C4⋊C4×C101—42no—
85C2×C4⋊C4×C101C2×C418yescomplemented
86C2×C22⋊C4×C101—22no—
87C2×C22⋊C4×C101—22no—
88C2×C22⋊C4×C101—24no—
89C2×C22⋊C4×C101—24no—
90C2×C22⋊C4×C101—22no—
91C2×C22⋊C4×C101—22no—
92C2×C22⋊C4×C101—22no—
93C2×C22⋊C4×C101—24no—
94C2×C22⋊C4×C101—22no—
95C2×C22⋊C4×C101—22no—
96C2×C22⋊C4×C101—24no—
97C2×C22⋊C4×C101—24no—
98C2×C22⋊C4×C101—42no—
99C2×C22⋊C4×C101—42no—
100C2×C22⋊C4×C101C2×C414yes—
101C2×C22⋊C4×C101C2×C418yescomplemented
102C2×C22⋊C4×C101D414yes—
103C2×C22⋊C4×C101D414yes—
104C2×C22⋊C4×C101D414yes—
105C2×C42×C101—24no—
106C2×C42×C101—24no—
107C2×C42×C101—42no—
108#95×C101—24no—
109#95×C101—24no—
110#95×C101—24no—
111#95×C101—24no—
112#95×C101—24no—
113#95×C101—24no—
114#95×C101—24no—
115#95×C101—22no—
116#95×C101—22no—
117C24×C101—22no—
118C24×C101—22no—
119C24×C101—22no—
120C24×C101—22no—
121C24×C101—21no—
122C24×C101—21no—
123C24×C101—21no—
124C24×C101—21no—
125C24×C101—22no—
126C24×C101—22no—
127C24×C101—21no—
128C24×C101—21no—
129C24×C101—22no—
130C24×C101—22no—
131C24×C101C22×C412yes—
132C24×C101C22×C412yes—
133C24×C101C2×D412yes—
134C24×C101C2×D412yes—
135C24×C101C2×D412yes—
136C24×C101C2×D412yes—
137C24×C101#4112yes—
138C24×C101#4112yes—
139C24×C101C2411yescharacteristic
140C2×D4×C101—28no—
141C2×D4×C101—28no—
142C2×D4×C101—28no—
143C2×D4×C101—44no—
144C2×D4×C101—44no—
145C2×D4×C101—44no—
146C2×D4×C101—44no—
147C22×C4×C101—21no—
148C22×C4×C101—22no—
149C22×C4×C101—22no—
150C22×C4×C101—21no—
151C22×C4×C101—22no—
152C22×C4×C101—22no—
153C22×C4×C101—22no—
154C22×C4×C101—28no—
155C22×C4×C101—28no—
156C22×C4×C101—28no—
157C22×C4×C101—28no—
158C22×C4×C101—28no—
159C22×C4×C101—22no—
160C22×C4×C101—22no—
161C22×C4×C101—21no—
162C22×C4×C101—22no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—22no—
166C22×C4×C101—22no—
167C22×C4×C101—22no—
168C22×C4×C101—22no—
169C22×C4×C101—22no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—22no—
173C22×C4×C101—22no—
174C22×C4×C101—22no—
175C22×C4×C101—22no—
176C22×C4×C101—22no—
177C22×C4×C101—21no—
178C22×C4×C101—22no—
179C22×C4×C101—22no—
180C22×C4×C101—21no—
181C22×C4×C101—21no—
182C22×C4×C101—22no—
183C22×C4×C101—22no—
184C22×C4×C101—22no—
185C22×C4×C101—22no—
186C22×C4×C101—22no—
187C22×C4×C101—28no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—21no—
191C22×C4×C101—21no—
192C22×C4×C101—21no—
193C22×C4×C101—21no—
194C22×C4×C101—22no—
195C22×C4×C101—22no—
196C22×C4×C101—22no—
197C22×C4×C101—22no—
198C22×C4×C101—44no—
199C22×C4×C101—48no—
200C22×C4×C101—48no—
201C22×C4×C101—48no—
202C22×C4×C101—48no—
203C22×C4×C101—44no—
204C22×C4×C101—44no—
205C22×C4×C101—44no—
206C22×C4×C101—44no—
207C22×C4×C101—44no—
208C22×C4×C101—44no—
209C22×C4×C101C22×C414yes—
210C22×C4×C101C22×C412yes—
211C22×C4×C101C22×C414yes—
212C22×C4×C101C2×D414yes—
213C22×C4×C101C2×D412yes—
214C22×C4×C101C2×D414yes—
215C22×C4×C101C2×D414yes—
216C22×C4×C101C2×D412yes—
217C22×C4×C101#4114yes—
218C22×C4×C101#4114yes—
219C4⋊C4×C101—216no—
220C4⋊C4×C101—48no—
221C22⋊C4×C101—28no—
222C22⋊C4×C101—216no—
223C22⋊C4×C101—48no—
224C22⋊C4×C101—44no—
225C22⋊C4×C101—44no—
226C22⋊C4×C101—44no—
227C22⋊C4×C101C22⋊C4116yescomplemented
228C42×C101—48no—
229C23×C101—24no—
230C23×C101—24no—
231C23×C101—22no—
232C23×C101—22no—
233C23×C101—24no—
234C23×C101—22no—
235C23×C101—22no—
236C23×C101—24no—
237C23×C101—24no—
238C23×C101—24no—
239C23×C101—24no—
240C23×C101—24no—
241C23×C101—24no—
242C23×C101—24no—
243C23×C101—24no—
244C23×C101—24no—
245C23×C101—22no—
246C23×C101—22no—
247C23×C101—22no—
248C23×C101—24no—
249C23×C101—24no—
250C23×C101—41no—
251C23×C101—41no—
252C23×C101—41no—
253C23×C101—41no—
254C23×C101—41no—
255C23×C101—42no—
256C23×C101—41no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—42no—
260C23×C101—42no—
261C23×C101—42no—
262C23×C101—42no—
263C23×C101—42no—
264C23×C101—42no—
265C23×C101—42no—
266C23×C101—42no—
267C23×C101—42no—
268C23×C101C2×C22⋊C414yes—
269C23×C101C4×D414yes—
270C23×C101C4×D414yes—
271C23×C101#12114yes—
272C23×C101#12114yes—
273C23×C101#12414yes—
274C23×C101#12714yes—
275C23×C101C23×C411yescharacteristic
276C23×C101C22×D411yescharacteristic
277C23×C101C22×D411yescharacteristic
278C23×C101C22×D411yescharacteristic
279C23×C101C22×D411yescharacteristic
280C23×C101C2×#4111yescharacteristic
281C23×C101C2×#4111yescharacteristic
282C23×C101C2×#4112yes—
283C23×C101C2×#4112yes—
284C23×C101H(5,𝔽2)12yes—
285C23×C1012−1+412yes—
286D4×C101—416no—
287C2×C4×C101—24no—
288C2×C4×C101—24no—
289C2×C4×C101—22no—
290C2×C4×C101—22no—
291C2×C4×C101—24no—
292C2×C4×C101—24no—
293C2×C4×C101—24no—
294C2×C4×C101—24no—
295C2×C4×C101—24no—
296C2×C4×C101—24no—
297C2×C4×C101—24no—
298C2×C4×C101—22no—
299C2×C4×C101—24no—
300C2×C4×C101—24no—
301C2×C4×C101—22no—
302C2×C4×C101—22no—
303C2×C4×C101—24no—
304C2×C4×C101—22no—
305C2×C4×C101—22no—
306C2×C4×C101—24no—
307C2×C4×C101—22no—
308C2×C4×C101—24no—
309C2×C4×C101—24no—
310C2×C4×C101—24no—
311C2×C4×C101—24no—
312C2×C4×C101—416no—
313C2×C4×C101—416no—
314C2×C4×C101—42no—
315C2×C4×C101—42no—
316C2×C4×C101—41no—
317C2×C4×C101—41no—
318C2×C4×C101—42no—
319C2×C4×C101—41no—
320C2×C4×C101—42no—
321C2×C4×C101—42no—
322C2×C4×C101—42no—
323C2×C4×C101—41no—
324C2×C4×C101—42no—
325C2×C4×C101—42no—
326C2×C4×C101—42no—
327C2×C4×C101—42no—
328C2×C4×C101—42no—
329C2×C4×C101—42no—
330C2×C4×C101—42no—
331C2×C4×C101—42no—
332C2×C4×C101—416no—
333C2×C4×C101—41no—
334C2×C4×C101—41no—
335C2×C4×C101—41no—
336C2×C4×C101—41no—
337C2×C4×C101—41no—
338C2×C4×C101—41no—
339C2×C4×C101—42no—
340C2×C4×C101—42no—
341C2×C4×C101—42no—
342C2×C4×C101—42no—
343C2×C4×C101C2×C22⋊C418yes—
344C2×C4×C101#12314yescomplemented
345C22×C101—24no—
346C22×C101—28no—
347C22×C101—28no—
348C22×C101—24no—
349C22×C101—24no—
350C22×C101—28no—
351C22×C101—28no—
352C22×C101—24no—
353C22×C101—24no—
354C22×C101—24no—
355C22×C101—42no—
356C22×C101—44no—
357C22×C101—44no—
358C22×C101—42no—
359C22×C101—42no—
360C22×C101—81no—
361C22×C101—81no—
362C22×C101—82no—
363C22×C101—82no—
364C22×C101—81no—
365C22×C101—81no—
366C22×C101#39018yes—
367C22×C101C22×C22⋊C411yescharacteristic
368C22×C101C2×C4×D411yescharacteristic
369C22×C101C2×C4×D411yescharacteristic
370C22×C101C4×#4112yes—
371C22×C101#52012yes—
372C22×C101C2×#12111yescharacteristic
373C22×C101C2×#12111yescharacteristic
374C22×C101C2×#12311yescharacteristic
375C22×C101#52511yescharacteristic
376C22×C101C2×#12411yescharacteristic
377C22×C101#52912yes—
378C22×C101C2×#12711yescharacteristic
379C22×C101#53411yescharacteristic
380C22×C101#53611yescharacteristic
381C22×C101#53912yes—
382C22×C101#54612yes—
383C22×C101#54612yes—
384C22×C101#54612yes—
385C22×C101#54712yes—
386C22×C101#54712yes—
387C22×C101#54712yes—
388C22×C101#55112yes—
389C22×C101#55212yes—
390C4×C101—28no—
391C4×C101—24no—
392C4×C101—42no—
393C4×C101—44no—
394C4×C101—44no—
395C4×C101—44no—
396C4×C101—42no—
397C4×C101—81no—
398C4×C101—81no—
399#13996C10111yesmaximal, characteristic, direct product factor, Sylow
400C2×C101—28no—
401C2×C101—82no—
402C2×C101C2×#39011yescharacteristic
403C2×C101C4×#12311yescharacteristic
404C2×C101#232211yescharacteristic
405C2×C101#233912yes—
406C2×C101#235912yes—
407C2×C101#241211yescharacteristic
408C2×C101#241311yescharacteristic
409C2×C101#242512yes—
410C2×C101#248812yes—
411C2×C101#250111yescharacteristic
412C2×C101#253911yescharacteristic
413C22×#123C2×C10111yescharacteristic
414C2×#386C2×C10111yescharacteristic
415C2×#386C2×C10111yescharacteristic
416C2×#385C2×C10111yescharacteristic, complemented
417C2×#381C2×C10111yescharacteristic, complemented
418C2×C4×C22⋊C4C2×C10111yescharacteristic, complemented
419C22×#95C2×C10111yescharacteristic, complemented
420#1445C2×C10112yescomplemented
421#1439C2×C10112yescomplemented
422#1437C2×C10112yescomplemented
423C4⋊#95C2×C10112yescomplemented
424C101#1399611yescharacteristic, direct product factor, Sylow
425C23×D4C22×C10111yescharacteristic
426C24×C4C22×C10111yescharacteristic
427C24×C4C22×C10111yescharacteristic
428C24×C4C22×C10111yescharacteristic
429C2×#123—24no—
430C2×#123—24no—
431C2×#123C4×C10118yescomplemented
432C22×C4⋊C4C22×C10112yes—
433C22×C4⋊C4C22×C10112yes—
434C22×C22⋊C4C22×C10111yescharacteristic
435C22×C22⋊C4C22×C10111yescharacteristic
436C22×C22⋊C4C22×C10112yes—
437C22×C22⋊C4C22×C10112yes—
438C22×C22⋊C4C22×C10111yescharacteristic
439C22×C22⋊C4C22×C10111yescharacteristic
440C22×C22⋊C4C22×C10111yescharacteristic
441C22×C42C22×C10112yes—
442#386—24no—
443#386—24no—
444#385—24no—
445#381—24no—
446C4×C22⋊C4—24no—
447C2×#95—24no—
448C2×#95C22×C10111yescharacteristic
449C2×#95C22×C10112yes—
450C2×#95C22×C10112yes—
451C2×#95C22×C10112yes—
452C2×#95C22×C10112yes—
453C2×#95C22×C10112yes—
454C2×#95C22×C10112yes—
455C2×#95C22×C10112yes—
456C2×#95C22×C10111yescharacteristic
457C25C23×C10111yescharacteristic
458C25C23×C10111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4C2×C4×C10114yes—
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×C10114yes—
482C23×C4D4×C10114yes—
483C23×C4C23×C10111yescharacteristic
484C23×C4C23×C10111yescharacteristic
485C23×C4C23×C10112yes—
486C23×C4C23×C10111yescharacteristic
487C23×C4C23×C10112yes—
488C23×C4C23×C10111yescharacteristic
489C23×C4C23×C10112yes—
490C23×C4C23×C10112yes—
491C23×C4C23×C10111yescharacteristic
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×C10118yescomplemented
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×C10114yes—
514C2×C22⋊C4C2×C4×C10118yescomplemented
515C2×C22⋊C4D4×C10114yes—
516C2×C22⋊C4D4×C10114yes—
517C2×C22⋊C4D4×C10114yes—
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×C10112yes—
545C24C22×C4×C10112yes—
546C24C2×D4×C10112yes—
547C24C2×D4×C10112yes—
548C24C2×D4×C10112yes—
549C24C2×D4×C10112yes—
550C24#41×C10112yes—
551C24#41×C10112yes—
552C24C24×C10111yescharacteristic
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×C10114yes—
623C22×C4C22×C4×C10112yes—
624C22×C4C22×C4×C10114yes—
625C22×C4C2×D4×C10114yes—
626C22×C4C2×D4×C10112yes—
627C22×C4C2×D4×C10114yes—
628C22×C4C2×D4×C10114yes—
629C22×C4C2×D4×C10112yes—
630C22×C4#41×C10114yes—
631C22×C4#41×C10114yes—
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×C101116yescomplemented
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×C10114yes—
682C23C4×D4×C10114yes—
683C23C4×D4×C10114yes—
684C23#121×C10114yes—
685C23#121×C10114yes—
686C23#124×C10114yes—
687C23#127×C10114yes—
688C23C23×C4×C10111yescharacteristic
689C23C22×D4×C10111yescharacteristic
690C23C22×D4×C10111yescharacteristic
691C23C22×D4×C10111yescharacteristic
692C23C22×D4×C10111yescharacteristic
693C23C2×#41×C10111yescharacteristic
694C23C2×#41×C10111yescharacteristic
695C23C2×#41×C10112yes—
696C23C2×#41×C10112yes—
697C23H(5,𝔽2)×C10112yes—
698C232−1+4×C10112yes—
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—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—416no—
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×C10118yes—
757C2×C4#123×C10114yescomplemented
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×C10118yes—
780C22C22×C22⋊C4×C10111yescharacteristic
781C22C2×C4×D4×C10111yescharacteristic
782C22C2×C4×D4×C10111yescharacteristic
783C22C4×#41×C10112yes—
784C22#520×C10112yes—
785C22C2×#121×C10111yescharacteristic
786C22C2×#121×C10111yescharacteristic
787C22C2×#123×C10111yescharacteristic
788C22#525×C10111yescharacteristic
789C22C2×#124×C10111yescharacteristic
790C22#529×C10112yes—
791C22C2×#127×C10111yescharacteristic
792C22#534×C10111yescharacteristic
793C22#536×C10111yescharacteristic
794C22#539×C10112yes—
795C22#546×C10112yes—
796C22#546×C10112yes—
797C22#546×C10112yes—
798C22#547×C10112yes—
799C22#547×C10112yes—
800C22#547×C10112yes—
801C22#551×C10112yes—
802C22#552×C10112yes—
803C4—24no—
804C4—28no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—42no—
810C4—81no—
811C4—81no—
812C2—28no—
813C2—82no—
814C2C2×#390×C10111yescharacteristic
815C2C4×#123×C10111yescharacteristic
816C2C101×#232211yescharacteristic
817C2C101×#233912yes—
818C2C101×#235912yes—
819C2C101×#241211yescharacteristic
820C2C101×#241311yescharacteristic
821C2C101×#242512yes—
822C2C101×#248812yes—
823C2C101×#250111yescharacteristic
824C2C101×#253911yescharacteristic
subgroupG/H
center, socleC24×C101C24
commutatorC23C23×C4×C101
Frattini, cosocleC24C24×C101
prime radicalC23×D4×C101C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C101 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#385×C101C2semidirect
5. C2×#381×C101C2semidirect
6. C2×C4×C22⋊C4×C101C2semidirect
7. C22×#95×C101C2semidirect
8. C101×#1445C2semidirect
9. C101×#1439C2semidirect
10. C101×#1437C2semidirect
11. C101×C4⋊#95C2semidirect
18. C2×#123×C101C4semidirect
85. C2×C4⋊C4×C101C2×C4semidirect
101. C2×C22⋊C4×C101C2×C4semidirect
227. C22⋊C4×C101C22⋊C4semidirect
344. C2×C4×C101#123semidirect
399. #13996C101direct (N × H)
416. C2×#385C2×C101semidirect
417. C2×#381C2×C101semidirect
418. C2×C4×C22⋊C4C2×C101semidirect
419. C22×#95C2×C101semidirect
420. #1445C2×C101semidirect
421. #1439C2×C101semidirect
422. #1437C2×C101semidirect
423. C4⋊#95C2×C101semidirect
424. C101#13996direct (N × H)
431. C2×#123C4×C101semidirect
498. C2×C4⋊C4C2×C4×C101semidirect
514. C2×C22⋊C4C2×C4×C101semidirect
640. C22⋊C4C22⋊C4×C101semidirect
757. C2×C4#123×C101semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1012
C2×#386×C1012
C2×#385×C1012
C2×#381×C1012
C2×C4×C22⋊C4×C1012
C22×#95×C1012
C101×#14452
C101×#14392
C101×#14372
C101×C4⋊#952
#13996101