Finite Group Databasebeta

← #25102677

Subgroups — #25102677

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582974C211yesmaximal, characteristic, complemented
2C2×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582969C211yesmaximal, characteristic, complemented
4C2×C4×#10621877C211yesmaximal, characteristic, complemented
5C4×#13063299C211yesmaximal, characteristic
6#19135392C211yesmaximal, characteristic, complemented
7#19135316C211yesmaximal, characteristic, complemented
8#19135199C211yesmaximal, characteristic, complemented
9#19135199C211yesmaximal, characteristic, complemented
10#19134890C211yesmaximal, characteristic, complemented
11#19134890C211yesmaximal, characteristic, complemented
12#19134472C211yesmaximal, characteristic, complemented
13#19134375C211yesmaximal, characteristic, complemented
14#19134365C211yesmaximal, characteristic, complemented
15C43×#1797C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063299C411yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×C22⋊D43C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24#14582974—24no—
25#14582973—24no—
26#14582969—24no—
27C2×Dic43⋊C8C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C4×#10621877—24no—
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40C2×C4×C43⋊C8C2211yescharacteristic
41C2×C8×Dic43C2211yescharacteristic
42#14582801C411yescharacteristic
43#14582797C411yescharacteristic
44#14582790C411yescharacteristic
45#14582790C411yescharacteristic
46#14582778C411yescharacteristic
47#14582778C411yescharacteristic
48#14582759C411yescharacteristic
49C4×C4⋊Dic43C2211yescharacteristic
50C4×(C2×D43)⋊C4C2211yescharacteristic
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×D172C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621877—22no—
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877D414yescomplemented
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C8×D43—22no—
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84#13063299—24no—
85C4×D172—22no—
86C4×D172—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×C22⋊Dic43C2×C411yescharacteristic
97C2×C22⋊Dic43C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109Dic43⋊C8—22no—
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115(C2×D43)⋊C8—22no—
116#13063236—22no—
117#13063236D414yescomplemented
118#13063235—22no—
119C4×C43⋊C8—22no—
120C4×C43⋊C8—22no—
121C8×Dic43—22no—
122C43⋊#95C2×C411yescharacteristic
123C43⋊#95C2×C411yescharacteristic
124C43⋊#95C2×C411yescharacteristic
125C43⋊#95C2×C411yescharacteristic
126C43⋊#95C2×C411yescharacteristic
127C43⋊#95C2×C411yescharacteristic
128C23×C4×C43C2×C411yescharacteristic
129C23×C4×C43C2×C411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C42×C43—22no—
136C2×C42×C43—22no—
137C2×C42×C43C2×C411yescharacteristic
138C2×C42×C43C2×C411yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C4⋊C8×C43—22no—
142C4⋊C8×C43—22no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145C24×C43C22×C411yescharacteristic
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C2×D412yes—
164C22×C4×C43#4112yes—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—41no—
171C2×C22⋊D43—41no—
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C411yescharacteristic
174C22×Dic43C22×C411yescharacteristic
175C22×Dic43C22×C411yescharacteristic
176C22×Dic43C22×C411yescharacteristic
177C22×Dic43C22×C411yescharacteristic
178C2×D172—22no—
179C2×D172—22no—
180C2×D172—41no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C42×C43—22no—
206C42×C43—22no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43C2×D412yes—
210C42×C43#4112yes—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—22no—
218(C2×D43)⋊C4—22no—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4M1614yescomplemented
221C4⋊Dic43—22no—
222C4⋊Dic43—22no—
223C4⋊Dic43—41no—
224Dic43⋊C4—22no—
225Dic43⋊C4—22no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230#10621877—28no—
231#10621877—28no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C2×D412yes—
239C2×C43⋊C8C2×D412yes—
240C2×C43⋊C8C2×D412yes—
241C2×C43⋊C8C2×D412yes—
242C2×C43⋊C8#4112yes—
243C2×C43⋊C8#4112yes—
244#10621872—44no—
245C8×D43—44no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43C4×D412yes—
253C23×C43C23×C411yescharacteristic
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43C2×M1612yes—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—44no—
283C2×C4×C43—44no—
284C2×C4×C43C4×D412yes—
285C2×C4×C43C4×D412yes—
286C2×C4×C43C4×D412yes—
287C2×C4×C43C2×M1612yes—
288C2×C4×C43#13112yes—
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C22⋊D43—44no—
296C22⋊D43—44no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43C2×M1612yes—
315D172—44no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324C8×C43—41no—
325C8×C43—41no—
326C8×C43—41no—
327C8×C43—41no—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C43⋊C8—22no—
331C43⋊C8#12114yescomplemented
332#21490—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43C2×C4×D411yescharacteristic
341C22×C43C2×C4×D411yescharacteristic
342C22×C43C4×#4111yescharacteristic
343C22×C43C22×M1611yescharacteristic
344C22×C43C2×#13111yescharacteristic
345C22×C43#56811yescharacteristic
346C22×C43#56811yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43C2×#12111yescharacteristic
367C4×C43#52511yescharacteristic
368C4×C43#52911yescharacteristic
369C4×C43#53211yescharacteristic
370Dic43—22no—
371Dic43—41no—
372Dic43—41no—
373Dic43—41no—
374Dic43—41no—
375Dic43—41no—
376C2×#436—431no—
377C2×#435—431no—
378C2×#435—431no—
379C2×C4×M16—431no—
380C4×#121—431no—
381#1955—431no—
382#1940—431no—
383#1923—431no—
384#1923—431no—
385#1870—431no—
386#1870—431no—
387#1797D4311yescharacteristic, complemented
388#1771—431no—
389#1753—431no—
390C8×C22⋊C4—431no—
391C2×C43—42no—
392C2×C43C4×#12111yescharacteristic
393C2×C43#293311yescharacteristic
394C2×C43D4×M1611yescharacteristic
395C2×C43D4×M1611yescharacteristic
396C2×C43#293511yescharacteristic
397C2×C43#296511yescharacteristic
398C2×C43#296711yescharacteristic
399D43—42no—
400D43—81no—
401C22×M16—431no—
402C22×M16—431no—
403C22×M16—431no—
404C23×C8—431no—
405C2×#121—431no—
406C2×C4×D4—431no—
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C22×C42C2×D4311yescharacteristic
410#436—864no—
411#435—864no—
412#435—864no—
413C2×C4⋊C8—431no—
414C2×C4⋊C8—431no—
415C2×C4⋊C8C2×D4311yescharacteristic
416C2×C4⋊C8C2×D4311yescharacteristic
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8C2×D4311yescharacteristic
424C2×C22⋊C8C2×D4311yescharacteristic
425C4×M16—864no—
426C2×#97—431no—
427C2×#97—431no—
428C2×#97—431no—
429C2×C4×C8—431no—
430C2×C4×C8—431no—
431C2×C4×C8—431no—
432#390—431no—
433#389—431no—
434#388—431no—
435#388—431no—
436#386—431no—
437#386—431no—
438#380—431no—
439C4×C4⋊C4—431no—
440C4×C22⋊C4—431no—
441C4×C22⋊C4—431no—
442#336—431no—
443#336—431no—
444#336—431no—
445#336—431no—
446#336C2×D4311yescharacteristic
447#336C2×D4311yescharacteristic
448C43#2149011yescharacteristic, complemented, Sylow
449C22×D4—431no—
450C22×D4—431no—
451C22×D4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4C4×D4311yescharacteristic
455C23×C4C4×D4311yescharacteristic
456C23×C4C22×D4311yescharacteristic
457C2×M16—434no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—862no—
464C2×M16—862no—
465C2×M16—862no—
466C22×C8—431no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—862no—
471C22×C8—862no—
472C22×C8—862no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C22×C8C22×D4311yescharacteristic
476C22×C8C22×D4311yescharacteristic
477#121—864no—
478C4×D4—862no—
479C4×D4—862no—
480C4×D4—862no—
481C4×D4—862no—
482C4×D4—862no—
483C4×D4—862no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—431no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—431no—
502C2×C42—431no—
503C2×C42C4×D4311yescharacteristic
504C2×C42C4×D4311yescharacteristic
505C2×C42C22×D4311yescharacteristic
506C2×C42C22×D4311yescharacteristic
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8—862no—
510C4⋊C8—862no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—862no—
514C22⋊C8—862no—
515C22⋊C8—862no—
516C22⋊C8—862no—
517C22⋊C8—862no—
518C22⋊C8—862no—
519#97—434no—
520#97—862no—
521#97—862no—
522C4×C8—862no—
523C4×C8—862no—
524C4×C8—862no—
525#95—431no—
526#95—431no—
527#95—431no—
528#95—431no—
529#95—431no—
530#95—431no—
531C24—431no—
532C24—431no—
533C24C2×C4×D4311yescharacteristic
534C2×D4—862no—
535C2×D4—862no—
536C2×D4—862no—
537C2×D4—862no—
538C2×D4—862no—
539C2×D4—862no—
540C2×D4—1721no—
541C2×D4—1721no—
542C2×D4—1721no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4C2×C4×D4311yescharacteristic
572C22×C4C2×C4×D4311yescharacteristic
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C2×C4×D4311yescharacteristic
575C22×C4C2×C4×D4311yescharacteristic
576C22×C4D4×D4312yes—
577C22×C4#1062190212yes—
578C22×C4C23×D4311yescharacteristic
579M16—868no—
580M16—868no—
581M16—1724no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—432no—
599C2×C8—432no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—1724no—
607C4⋊C4—862no—
608C4⋊C4—862no—
609C4⋊C4—862no—
610C4⋊C4—862no—
611C4⋊C4—1721no—
612C22⋊C4—434no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—862no—
621C22⋊C4—862no—
622C42—22no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—861no—
627C42—861no—
628C42—861no—
629C42—861no—
630C42D4×D4312yes—
631C42#1062190012yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—432no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23#1306328712yes—
653C23C22×C4×D4311yescharacteristic
654D4—1724no—
655D4—1724no—
656D4—1724no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—432no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4(C22⋊D43)⋊C412yes—
700C2×C4(C22⋊D43)⋊C412yes—
701C2×C4#1306328712yes—
702C2×C4M16×D4312yes—
703C2×C4#1306333112yes—
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4C2×D4×D4311yescharacteristic
706C2×C4#41×D4311yescharacteristic
707C2×C4#41×D4311yescharacteristic
708C2×C4C2×#1062190011yescharacteristic
709C2×C4C2×#1062190211yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—434no—
715C8—862no—
716C8—862no—
717C8—862no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—1721no—
729C22—1721no—
730C22—1721no—
731C22—1721no—
732C22—1721no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22C2×(C22⋊D43)⋊C411yescharacteristic
740C22C2×#1306328711yescharacteristic
741C22#1458336711yescharacteristic
742C22C2×M16×D4311yescharacteristic
743C22C2×#1306333111yescharacteristic
744C22#1458366511yescharacteristic
745C22#1458366511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—862no—
752C4—1721no—
753C4—1721no—
754C4—1721no—
755C4—1721no—
756C4—1721no—
757C4#121×D4311yescharacteristic
758C4#1458341211yescharacteristic
759C4#1458343511yescharacteristic
760C4#1458344411yescharacteristic
761C2—42no—
762C2—3441no—
763C2—1722no—
764C2#1913710111yescharacteristic
765C2#1914331611yescharacteristic
766C2#1914332711yescharacteristic
767C2#1914333011yescharacteristic
768C2#1914333811yescharacteristic
769C2#1914355911yescharacteristic
770C2#1914357511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1797C2
prime radicalC2×#13063299C4
cosocleC22×C4×C43C24
hypercenter#1797D43
hypocenterC43#21490
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
1. C2×#14582974C2semidirect
2. C2×#14582973C2semidirect
3. C2×#14582969C2semidirect
4. C2×C4×#10621877C2semidirect
6. #19135392C2semidirect
7. #19135316C2semidirect
8. #19135199C2semidirect
9. #19135199C2semidirect
10. #19134890C2semidirect
11. #19134890C2semidirect
12. #19134472C2semidirect
13. #19134375C2semidirect
14. #19134365C2semidirect
15. C43×#1797C2semidirect
73. C2×#10621877D4semidirect
117. #13063236D4semidirect
220. (C2×D43)⋊C4M16semidirect
331. C43⋊C8#121semidirect
387. #1797D43semidirect
448. C43#21490semidirect

Maximal subgroups

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

subgroupindex
C2×#145829742
C2×#145829732
C2×#145829692
C2×C4×#106218772
C4×#130632992
#191353922
#191353162
#191351992
#191348902
#191344722
#191343752
#191343652
C43×#17972
#2149043