Finite Group Databasebeta

← #25113606

Subgroups — #25113606

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582861C211yesmaximal, characteristic
2#19136974C211yesmaximal, characteristic
3#19135208C211yesmaximal, characteristic, complemented
4#19135207C211yesmaximal, characteristic, complemented
5#19135201C211yesmaximal, characteristic, complemented
6#19135200C211yesmaximal, characteristic, complemented
7#19134776C211yesmaximal, characteristic, complemented
8#19134776C211yesmaximal, characteristic, complemented
9#19134666C211yesmaximal, characteristic, complemented
10#19134577C211yesmaximal, characteristic, complemented
11#19134504C211yesmaximal, characteristic
12#19134380C211yesmaximal, characteristic, complemented
13#19134378C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic, complemented
21C2×Dic43⋊C8C2211yescharacteristic, complemented
22#14582861—24no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×#13063235C2211yescharacteristic, complemented
32C2×C8×Dic43C2211yescharacteristic, complemented
33#14582760C411yescharacteristic
34#14582760C411yescharacteristic
35#14582756C411yescharacteristic
36#14582756C411yescharacteristic
37#14582756C411yescharacteristic
38#14582756C411yescharacteristic
39#14582754C411yescharacteristic
40#14582754C411yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42C4×(C2×D43)⋊C4C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582654C2211yescharacteristic, complemented
46#14582654C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582654C2211yescharacteristic, complemented
49#14582653C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C43×#433—24no—
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C2×C4⋊C8×C43C2211yescharacteristic, complemented
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic, complemented
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C24×D43C2×C411yescharacteristic
62C23×Dic43C2×C411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—41no—
68C22×C4×D43—41no—
69C22×C4×D43C2×C411yescharacteristic
70C22×C4×D43C2×C411yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—41no—
78C2×#10621872—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063284—41no—
84#13063284—41no—
85C2×C4⋊Dic43C2×C411yescharacteristic
86C2×C4⋊Dic43C2×C411yescharacteristic
87C2×C22⋊Dic43C2×C411yescharacteristic
88C2×C22⋊Dic43C2×C411yescharacteristic
89C2×(C2×D43)⋊C4C2×C411yescharacteristic
90C2×(C2×D43)⋊C4C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C411yescharacteristic
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×(C2×D43)⋊C4C2×C411yescharacteristic
94C2×(C2×D43)⋊C4C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99Dic43⋊C8—41no—
100Dic43⋊C8—41no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—22no—
105(C2×D43)⋊C8—22no—
106(C2×D43)⋊C8—22no—
107(C2×D43)⋊C8—41no—
108(C2×D43)⋊C8—41no—
109#13063235—41no—
110C8×Dic43—41no—
111C43⋊#95C2×C411yescharacteristic
112C43⋊#95C2×C411yescharacteristic
113C43⋊#95C2×C411yescharacteristic
114C43⋊#95C2×C411yescharacteristic
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#117×C43—22no—
125#117×C43—22no—
126C2×C4⋊C4×C43C2×C411yescharacteristic
127C2×C4⋊C4×C43C2×C411yescharacteristic
128C2×C22⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43C2×C411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43—22no—
133C4⋊C8×C43—22no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43D414yes—
136#97×C43—22no—
137C4×C8×C43—22no—
138C24×C43C22×C411yescharacteristic
139C23×D43—22no—
140C23×D43—22no—
141C23×D43—22no—
142C23×D43—41no—
143C23×D43—41no—
144C23×D43—41no—
145C23×D43—41no—
146C23×D43C22×C411yescharacteristic
147C23×D43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C2×D412yes—
158C22×C4×C43#4112yes—
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—41no—
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—44no—
186C2×C4×D43—44no—
187C2×C4×D43—44no—
188C2×C4×D43—44no—
189C2×C4×D43#4112yes—
190C2×C4×D43#4112yes—
191C2×C8×C43—21no—
192C2×C8×C43—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×C43C2×D412yes—
202C2×C8×C43C2×D412yes—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—22no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—41no—
216(C2×D43)⋊C4—41no—
217(C2×D43)⋊C4—41no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—41no—
221C4⋊Dic43—41no—
222C4⋊Dic43—41no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
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⋊C8—21no—
239#10621872—44no—
240#10621872—44no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43C4×D412yes—
248C23×C43C23×C411yescharacteristic
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—44no—
262C22×D43—44no—
263C22×D43—44no—
264C22×D43—44no—
265C22×D43—44no—
266C22×D43—44no—
267C22×D43—44no—
268C22×D43#11712yes—
269C22×D43#13112yes—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×Dic43—21no—
296C2×Dic43—21no—
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—44no—
313C2×Dic43#11712yes—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—44no—
319C4×D43—44no—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324C8×C43—22no—
325C8×C43—22no—
326C8×C43—41no—
327C8×C43—41no—
328C43⋊C8—41no—
329C43⋊C8—41no—
330C43⋊C8—41no—
331C43⋊C8—41no—
332#22559—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×#11711yescharacteristic
341C22×C43C2×C4×D411yescharacteristic
342C22×C43#51811yescharacteristic
343C22×C43C2×#13111yescharacteristic
344C22×C43#56811yescharacteristic
345C22×C43#56811yescharacteristic
346C22×C43#56811yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—416no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43—41no—
362C4×C43—22no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43#54611yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370C4×C43#55111yescharacteristic
371Dic43—22no—
372Dic43—41no—
373Dic43—41no—
374Dic43—41no—
375Dic43—41no—
376Dic43—41no—
377C2×#433D4311yescharacteristic, complemented
378C2×#407—431no—
379#2280—431no—
380#1924—431no—
381#1924—431no—
382#1923—431no—
383#1923—431no—
384#1851—431no—
385#1851—431no—
386#1818—431no—
387#1798—431no—
388#1779—431no—
389#1753—431no—
390#1753—431no—
391#1750—431no—
392C2×C43—42no—
393C2×C43#234211yescharacteristic
394C2×C43#292111yescharacteristic
395C2×C43#292411yescharacteristic
396C2×C43#293011yescharacteristic
397C2×C43#293311yescharacteristic
398C2×C43#297611yescharacteristic
399C2×C43#297811yescharacteristic
400D43—42no—
401D43—42no—
402C24×C4—431no—
403C22×M16—431no—
404C22×M16—431no—
405C2×#117—431no—
406C2×#117C2×D4311yescharacteristic
407#433—24no—
408C2×C4⋊C8—431no—
409C2×C4⋊C8—431no—
410C2×C4⋊C8C2×D4311yescharacteristic, complemented
411C2×C4⋊C8C2×D4311yescharacteristic, complemented
412#407—864no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8C2×D4311yescharacteristic
422C2×C22⋊C8C2×D4311yescharacteristic
423C2×#97—431no—
424C2×#97C2×D4311yescharacteristic, complemented
425C2×C4×C8—431no—
426C2×C4×C8C2×D4311yescharacteristic, complemented
427#381—431no—
428#381—431no—
429#380—431no—
430#380—431no—
431#380—431no—
432#380—431no—
433#379—431no—
434#379—431no—
435C4×C22⋊C4—431no—
436C4×C22⋊C4—431no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—431no—
439#336—431no—
440#336—431no—
441#336—431no—
442#336—431no—
443#336—431no—
444#336—431no—
445#336—431no—
446#336—431no—
447C43#2255911yescharacteristic, complemented, Sylow
448C25—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—862no—
455C23×C4—862no—
456C23×C4—862no—
457C23×C4—862no—
458C23×C4—1721no—
459C23×C4—1721no—
460C23×C4C22×D4311yescharacteristic
461C2×M16—862no—
462C2×M16—862no—
463C2×M16—862no—
464C2×M16—862no—
465C2×M16—1721no—
466C2×M16—1721no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8C22×D4311yescharacteristic
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475#117—22no—
476#117—22no—
477#117—1721no—
478#117—1721no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4C4×D4311yescharacteristic
482C2×C4⋊C4C4×D4311yescharacteristic
483C2×C22⋊C4—431no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4C4×D4311yescharacteristic
494C2×C22⋊C4C4×D4311yescharacteristic
495C2×C42—431no—
496C2×C42—431no—
497C2×C42C22×D4311yescharacteristic
498C2×C42C22×D4311yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—22no—
501C4⋊C8—1721no—
502C4⋊C8—1721no—
503C22⋊C8—22no—
504C22⋊C8—862no—
505C22⋊C8—862no—
506C22⋊C8—862no—
507C22⋊C8—862no—
508C22⋊C8—862no—
509C22⋊C8—862no—
510C22⋊C8—1721no—
511C22⋊C8—1721no—
512C22⋊C8C22⋊D4314yes—
513#97—22no—
514#97—1721no—
515C4×C8—22no—
516C4×C8—1721no—
517#95—431no—
518#95—431no—
519#95—431no—
520#95—431no—
521#95—431no—
522#95—431no—
523#95—431no—
524#95—431no—
525C24—431no—
526C24—431no—
527C24—862no—
528C24—862no—
529C24—862no—
530C24—1721no—
531C24—1721no—
532C24—1721no—
533C24—1721no—
534C24C2×C4×D4311yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—431no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—431no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—862no—
548C22×C4—862no—
549C22×C4—862no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—1721no—
564C22×C4—1721no—
565C22×C4—1724no—
566C22×C4—1724no—
567C22×C4—1724no—
568C22×C4—1724no—
569C22×C4—1721no—
570C22×C4C2×C4×D4311yescharacteristic
571C22×C4C2×C4×D4311yescharacteristic
572C22×C4C2×C4×D4311yescharacteristic
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C2×C4×D4311yescharacteristic
575C22×C4#1062189812yes—
576C22×C4C2×C22⋊D4312yes—
577C22×C4C23×D4311yescharacteristic
578M16—1724no—
579M16—1724no—
580C2×C8—21no—
581C2×C8—21no—
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—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8C2×C22⋊D4312yes—
603C2×C8C2×C22⋊D4312yes—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—1721no—
607C4⋊C4—1721no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—1721no—
613C22⋊C4—1721no—
614C22⋊C4—1721no—
615C22⋊C4—1721no—
616C22⋊C4—1721no—
617C22⋊C4—1721no—
618C22⋊C4—1721no—
619C22⋊C4—1721no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—861no—
625C42—861no—
626C42—861no—
627C42—861no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—432no—
635C23—432no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—1724no—
649C23—1724no—
650C23—1724no—
651C23—1724no—
652C23—1724no—
653C23—1724no—
654C23—1724no—
655C23C4×C22⋊D4312yes—
656C23C22×C4×D4311yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—432no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
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—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—1724no—
698C2×C4—1724no—
699C2×C4—1724no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4C4×C22⋊D4312yes—
705C2×C4C22×C22⋊D4311yescharacteristic
706C2×C4#41×D4311yescharacteristic
707C2×C4#41×D4311yescharacteristic
708C2×C4C2×#1062189811yescharacteristic
709C2×C4#1306337111yescharacteristic
710C2×C4#1306337111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C8—1721no—
716C8—1721no—
717C8—1721no—
718C8—1721no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—17216no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22#117×D4311yescharacteristic
742C22C2×C4×C22⋊D4311yescharacteristic
743C22#1458337311yescharacteristic
744C22#131×D4311yescharacteristic
745C22#1458366411yescharacteristic
746C22#1458366411yescharacteristic
747C22#1458366411yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—862no—
754C4—1721no—
755C4—1721no—
756C4—1721no—
757C4—1721no—
758C4—1721no—
759C4#1458353711yescharacteristic
760C4#1458353711yescharacteristic
761C4#1458357311yescharacteristic
762C4#1458357311yescharacteristic
763C2—42no—
764C2—1722no—
765C2—1722no—
766C2#1913744511yescharacteristic
767C2#1914322911yescharacteristic
768C2#1914325111yescharacteristic
769C2#1914329611yescharacteristic
770C2#1914331711yescharacteristic
771C2#1914364111yescharacteristic
772C2#1914365611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#433C2
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#22559
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #19135208C2semidirect
4. #19135207C2semidirect
5. #19135201C2semidirect
6. #19135200C2semidirect
7. #19134776C2semidirect
8. #19134776C2semidirect
9. #19134666C2semidirect
10. #19134577C2semidirect
12. #19134380C2semidirect
13. #19134378C2semidirect
14. #19134363C2semidirect
15. C2×C43×#433C2semidirect
20. C2×Dic43⋊C8C22semidirect
21. C2×Dic43⋊C8C22semidirect
31. C2×#13063235C22semidirect
32. C2×C8×Dic43C22semidirect
45. #14582654C22semidirect
46. #14582654C22semidirect
47. #14582654C22semidirect
48. #14582654C22semidirect
49. #14582653C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
55. C2×C4⋊C8×C43C22semidirect
56. C2×C4⋊C8×C43C22semidirect
59. C2×#97×C43C22semidirect
60. C2×C4×C8×C43C22semidirect
377. C2×#433D43semidirect
410. C2×C4⋊C8C2×D43semidirect
411. C2×C4⋊C8C2×D43semidirect
424. C2×#97C2×D43semidirect
426. C2×C4×C8C2×D43semidirect
447. C43#22559semidirect

Maximal subgroups

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

subgroupindex
C2×#145828612
#191369742
#191352082
#191352072
#191352012
#191352002
#191347762
#191346662
#191345772
#191345042
#191343802
#191343782
#191343632
C2×C43×#4332
#2255943