Finite Group Databasebeta

← #25153129

Subgroups — #25153129

Order 11008.

1260 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D43C211yesmaximal, characteristic
2C2×#14583266C211yesmaximal, characteristic, complemented
3C2×#14583204C211yesmaximal, characteristic, complemented
4#19139760C211yesmaximal, characteristic
5#19135798C211yesmaximal, characteristic, complemented
6#19135796C211yesmaximal, characteristic, complemented
7#19135792C211yesmaximal, characteristic, complemented
8#19135790C211yesmaximal, characteristic, complemented
9#19135516C211yesmaximal, characteristic, complemented
10#19135391C211yesmaximal, characteristic
11#19134530C211yesmaximal, characteristic, complemented
12#19134528C211yesmaximal, characteristic, complemented
13#19134528C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1787C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17Q8×C22⋊D43—24no—
18Q8×C22⋊D43—24no—
19C2×#13063323—21no—
20C2×#13063323C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063301—21no—
25C2×#13063301C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29#14583266—24no—
30#14583204—24no—
31C2×#13063258C2211yescharacteristic
32C2×#13063257C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582841—21no—
47#14582815—21no—
48#14582788—21no—
49#14582787—21no—
50#14582759C2211yescharacteristic
51#14582756C2211yescharacteristic
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56C23×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C2×Q8×D43—22no—
66C2×Q8×D43—22no—
67C2×Q8×D43—22no—
68C2×Q8×D43—22no—
69C2×Q8×D43—41no—
70C2×Q8×D43—41no—
71C22×C22⋊D43D411yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063323—28no—
77#13063323—22no—
78#13063323D414yes—
79#13063316—22no—
80#13063316—22no—
81#13063304—28no—
82#13063304—22no—
83#13063304—22no—
84#13063301—28no—
85#13063301—22no—
86#13063301—22no—
87Q8×Dic43—22no—
88Q8×Dic43D414yes—
89C4×C22⋊D43—28no—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063258—22no—
114#13063257—22no—
115Dic43⋊C8—22no—
116#13063250—22no—
117#13063250—41no—
118#13063249—22no—
119#13063249—22no—
120#13063249—22no—
121#13063249—41no—
122#13063248—22no—
123#13063248—41no—
124C22⋊(C43⋊C8)—41no—
125(C2×D43)⋊C8—41no—
126(C2×D43)⋊C8—41no—
127#13063235—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C22×Q8×C43—22no—
133C22×Q8×C43—22no—
134C22×Q8×C43—21no—
135C22×Q8×C43—22no—
136C22×Q8×C43—22no—
137C22×Q8×C43—41no—
138C22×Q8×C43—41no—
139C22×Q8×C43C2311yescharacteristic
140C22×Q8×C43C2311yescharacteristic
141C23×C4×C43—21no—
142C23×C4×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148#103×C43—22no—
149#103×C43—22no—
150#103×C43—22no—
151#103×C43—41no—
152C22⋊C8×C43—41no—
153#95×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—24no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—42no—
166C2×Q8×C43—42no—
167C2×Q8×C43—44no—
168C2×Q8×C43—44no—
169C2×Q8×C43—44no—
170C2×Q8×C43—44no—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43C2×D412yes—
173C2×Q8×C43#4112yes—
174C2×Q8×C43#4112yes—
175C22×C4×C43—24no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200Q8×D43—44no—
201Q8×D43—44no—
202Q8×D43—44no—
203Q8×D43—44no—
204C2×C4×D43—24no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86—24no—
218C2×Dic86—21no—
219C2×Dic86—42no—
220C2×Dic86—42no—
221C2×Dic86C2×D412yes—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—21no—
227C2×C8×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C22⋊C4×C43—81no—
233C22⋊Dic43—24no—
234C22⋊Dic43—22no—
235C22⋊Dic43—42no—
236(C2×D43)⋊C4—24no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—42no—
239(C2×D43)⋊C4—81no—
240C4⋊Dic43—21no—
241C4⋊Dic43—24no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—42no—
247C4⋊Dic43C2×D412yes—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—22no—
253Dic43⋊C4—42no—
254C4×Dic43—24no—
255C4×Dic43—81no—
256C4×Dic43C2×D412yes—
257C4×Dic43C2×D412yes—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43#13712yes—
271C23×C43C22×D411yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43#13712yes—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—48no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43#12414yes—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—48no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43C2×#4111yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×C4×C43H(5,𝔽2)11yescharacteristic
314C22⋊D43—28no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—22no—
320C2×Dic43—21no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43#12012yes—
335C2×Dic43#12012yes—
336C4×D43—48no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C4×D43—41no—
341Dic86—22no—
342Dic86—22no—
343Dic86—48no—
344Dic86—41no—
345Dic86—41no—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350#25894—431nomaximal, Sylow
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43C2×#12011yescharacteristic
359C22×C43#54611yescharacteristic
360C22×C43#54611yescharacteristic
361C22×C43C2×#13711yescharacteristic
362C22×C43C2×#13711yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57811yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C4×C43—24no—
373C4×C43—41no—
374C4×C43—42no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43C2×#12411yescharacteristic
378C4×C43#53511yescharacteristic
379C4×C43#54611yescharacteristic
380C4×C43#54611yescharacteristic
381Dic43—22no—
382Dic43—22no—
383Dic43—42no—
384Dic43—41no—
385Dic43—42no—
386Dic43—81no—
387Dic43—81no—
388C2×D4×Q8—431no—
389C2×#491—431no—
390C2×#479—431no—
391#2562—431no—
392#2036—431no—
393#2036—431no—
394#2035—431no—
395#2035—431no—
396#1981—431no—
397#1955—431no—
398#1787—431no—
399#1787—431no—
400#1787—431no—
401#1787D4311yescharacteristic, complemented
402#1763—431no—
403C2×C43—42no—
404C2×C43#243511yescharacteristic
405C2×C43#300411yescharacteristic
406C2×C43#301311yescharacteristic
407C2×C43#331211yescharacteristic
408C2×C43#331211yescharacteristic
409C2×C43#332011yescharacteristic
410C2×C43#332011yescharacteristic
411D43—42no—
412C23×Q8—431no—
413C23×Q8C2×D4311yescharacteristic
414D4×Q8—864no—
415D4×Q8—864no—
416C2×C4⋊Q8—431no—
417C2×C4⋊Q8—861no—
418C2×#125—431no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8—861no—
422C2×C22⋊Q8—861no—
423C2×C4×Q8—431no—
424C2×C4×D4—431no—
425C2×C4×D4—861no—
426#491—864no—
427#479—864no—
428C2×#107—431no—
429C2×#106—431no—
430C2×C4⋊C8—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103C2×D4311yescharacteristic
440C2×#103C2×D4311yescharacteristic
441C2×#103C2×D4311yescharacteristic
442C2×#103C2×D4311yescharacteristic
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8C2×D4311yescharacteristic
447C2×#97—431no—
448#400—861no—
449#394—861no—
450#388—861no—
451#388—861no—
452#380—431no—
453#380—431no—
454#380—431no—
455#380C2×D4311yescharacteristic
456C4×C4⋊C4—431no—
457#340—431no—
458#340—431no—
459C43#2589411yescharacteristic, complemented, Sylow
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—21no—
463C22×Q8—22no—
464C22×Q8—22no—
465C22×Q8—41no—
466C22×Q8—41no—
467C22×Q8—431no—
468C22×Q8—861no—
469C22×Q8—862no—
470C22×Q8—862no—
471C22×Q8—862no—
472C22×Q8—862no—
473C22×Q8—1721no—
474C22×Q8—1721no—
475C22×Q8C22×D4311yescharacteristic
476C22×Q8C22×D4311yescharacteristic
477C22×D4—431no—
478C23×C4—21no—
479C23×C4—431no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486C4⋊Q8—434no—
487C4⋊Q8—862no—
488C4⋊Q8—868no—
489#125—862no—
490#125—862no—
491C22⋊Q8—862no—
492C22⋊Q8—862no—
493C22⋊Q8—862no—
494C22⋊Q8—868no—
495C22⋊Q8—868no—
496C22⋊Q8—862no—
497C4×Q8—434no—
498C4×Q8—862no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—868no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C42—431no—
524C2×C42—861no—
525C2×C42—861no—
526#107—862no—
527#106—862no—
528C4⋊C8—862no—
529#103—22no—
530#103—22no—
531#103—22no—
532#103—41no—
533#103—862no—
534#103—862no—
535#103—862no—
536#103—862no—
537#103—862no—
538#103—1721no—
539#103—1721no—
540#103—1721no—
541C22⋊C8—41no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544C22⋊C8—1721no—
545#97—862no—
546#95—21no—
547#95—861no—
548#95—861no—
549#95—861no—
550#95—861no—
551C24—431no—
552C24D4×D4311yescharacteristic
553C2×Q8—24no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—432no—
569C2×Q8—864no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—1722no—
576C2×Q8—1722no—
577C2×Q8—1724no—
578C2×Q8—1724no—
579C2×Q8—1724no—
580C2×Q8—1724no—
581C2×Q8#1062189812yes—
582C2×Q8D4×D4312yes—
583C2×Q8D4×D4312yes—
584C2×Q8#1062190012yes—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—864no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4D4×D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—432no—
636C4⋊C4—862no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—864no—
641C4⋊C4—864no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—1722no—
648C4⋊C4—1722no—
649C22⋊C4—81no—
650C22⋊C4—862no—
651C22⋊C4—864no—
652C22⋊C4—862no—
653C22⋊C4—864no—
654C22⋊C4—3441no—
655C22⋊C4—1722no—
656C22⋊C4—1722no—
657C42—432no—
658C42—432no—
659C42—864no—
660C42—3441no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—432no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23#1306335712yes—
675C23C2×D4×D4311yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—48no—
682Q8—41no—
683Q8—41no—
684Q8—862no—
685Q8—862no—
686Q8—1728no—
687Q8—1721no—
688Q8—1721no—
689Q8#1306331114yes—
690D4—868no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—48no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—432no—
712C2×C4—432no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—862no—
718C2×C4—861no—
719C2×C4—862no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—1728no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4C2×D4×D4311yescharacteristic
738C2×C4C2×D4×D4311yescharacteristic
739C2×C4C2×#1062190011yescharacteristic
740C2×C4C2×#1062189811yescharacteristic
741C2×C4#1306337011yescharacteristic
742C2×C4#1306337011yescharacteristic
743C8—41no—
744C8—41no—
745C8—1721no—
746C8—1721no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—1721no—
758C22—1721no—
759C22—1721no—
760C22—1721no—
761C22#120×D4311yescharacteristic
762C22#1458353611yescharacteristic
763C22#1458353911yescharacteristic
764C22#137×D4311yescharacteristic
765C22C2×#1306335711yescharacteristic
766C22#1458370511yescharacteristic
767C22#1458371511yescharacteristic
768C4—24no—
769C4—41no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—862no—
774C4—862no—
775C4—3441no—
776C4—3441no—
777C4—1721no—
778C4—1722no—
779C4—1722no—
780C4C2×#1306331111yescharacteristic
781C4#1458346411yescharacteristic
782C4#1458353611yescharacteristic
783C4#1458353911yescharacteristic
784C2—42no—
785C2—1722no—
786C2#1913824411yescharacteristic
787C2#1914383011yescharacteristic
788C2#1914390511yescharacteristic
789C2#1914664711yescharacteristic
790C2#1914665011yescharacteristic
791C2#1914675911yescharacteristic
792C2#1914676211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1787C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#1787D43
hypocenterC43#25894
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#14583266C2semidirect
3. C2×#14583204C2semidirect
5. #19135798C2semidirect
6. #19135796C2semidirect
7. #19135792C2semidirect
8. #19135790C2semidirect
9. #19135516C2semidirect
11. #19134530C2semidirect
12. #19134528C2semidirect
13. #19134528C2semidirect
14. #19134427C2semidirect
15. C43×#1787C2semidirect
401. #1787D43semidirect
459. C43#25894semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D432
C2×#145832662
C2×#145832042
#191397602
#191357982
#191357962
#191357922
#191357902
#191355162
#191353912
#191345302
#191345282
#191344272
C43×#17872
#2589443