Finite Group Databasebeta

← #25149830

Subgroups — #25149830

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2C2×#14583248C211yesmaximal, characteristic, complemented
3C2×#14583107C211yesmaximal, characteristic, complemented
4#19139545C211yesmaximal, characteristic
5#19135604C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135602C211yesmaximal, characteristic, complemented
8#19135541C211yesmaximal, characteristic, complemented
9#19135387C211yesmaximal, characteristic
10#19134903C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134900C211yesmaximal, characteristic, complemented
13#19134899C211yesmaximal, characteristic, complemented
14#103×Dic43C211yesmaximal, characteristic, complemented
15C43×#2001C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17#14583607—24no—
18#14583607—24no—
19C2×#13063324C2211yescharacteristic
20C2×#13063323C2211yescharacteristic
21C2×#13063315—21no—
22C2×#13063305—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063301C2211yescharacteristic
27C2×#13063301C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×(C22⋊D43)⋊C4—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14583248—24no—
34#14583107—24no—
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063249C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C8×Dic43C2211yescharacteristic
46#14582835—21no—
47#14582834—21no—
48#14582799—21no—
49#14582768—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621885—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—22no—
75#13063324D414yes—
76#13063323—22no—
77#13063323—22no—
78#13063315—28no—
79#13063305—28no—
80#13063305—22no—
81#13063305—41no—
82#13063304—22no—
83#13063304—41no—
84#13063302—28no—
85#13063301—22no—
86#13063301—22no—
87#13063301—22no—
88#13063301—41no—
89Q8×Dic43—22no—
90Q8×Dic43D414yes—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93(C22⋊D43)⋊C4—28no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—22no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4D411yescharacteristic
110C4⋊C4×D43—22no—
111C4⋊C4×D43—22no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122#13063250—22no—
123#13063250—22no—
124#13063249—22no—
125#13063249—22no—
126#13063249—22no—
127#13063248—22no—
128C22⋊(C43⋊C8)—41no—
129(C2×D43)⋊C8—41no—
130(C2×D43)⋊C8—41no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C22×Q8×C43C2311yescharacteristic
134C22×Q8×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×Q16×C43—22no—
137C2×Q16×C43—41no—
138C2×Q16×C43—41no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22⋊Q8×C43—22no—
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—22no—
144C22⋊Q8×C43—41no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151#103×C43—22no—
152#103×C43—22no—
153C22⋊C8×C43—41no—
154C24×C43C2×D411yescharacteristic
155C23×D43C2×D411yescharacteristic
156C2×Q8×C43—21no—
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—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C2×D412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—22no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43Q1614yescomplemented
183C22×Dic43—24no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—81no—
189C22×Dic43—81no—
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—24no—
200C2×C4×D43—81no—
201C2×C4×D43—81no—
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—24no—
209C2×Dic86—81no—
210C2×Dic86—81no—
211Q16×C43—44no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C4⋊C4×C43—24no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—42no—
222C4⋊C4×C43C2×D412yes—
223C4⋊C4×C43#4112yes—
224C22⋊C4×C43—24no—
225C22⋊C4×C43—42no—
226C22⋊Dic43—22no—
227C22⋊Dic43—42no—
228#10621885—44no—
229(C2×D43)⋊C4—24no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—42no—
232(C2×D43)⋊C4—42no—
233C4⋊Dic43—24no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—24no—
238C4⋊Dic43—42no—
239C4⋊Dic43C2×D412yes—
240C4⋊Dic43C2×D412yes—
241C4⋊Dic43#4112yes—
242Dic43⋊C4—24no—
243Dic43⋊C4—24no—
244Dic43⋊C4—24no—
245Dic43⋊C4—22no—
246Dic43⋊C4—42no—
247Dic43⋊C4—42no—
248Dic43⋊C4—42no—
249Dic43⋊C4—42no—
250C4×Dic43—24no—
251C4×Dic43—42no—
252C4×Dic43C2×D412yes—
253C4×Dic43C2×D412yes—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43C2×Q1612yes—
267C23×C43C22×D411yescharacteristic
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43C2×Q1612yes—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280Q8×C43—41no—
281Q8×C43—41no—
282Q8×C43—41no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
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×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C22⋊D43—28no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327C2×Dic43#12012yes—
328C2×Dic43#12012yes—
329C2×Dic43C2×Q1612yes—
330C2×Dic43#13712yes—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—41no—
335C4×D43—84no—
336Dic86—41no—
337Dic86—41no—
338Dic86—41no—
339Dic86—41no—
340Dic86—84no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#25573—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43C2×#12011yescharacteristic
354C22×C43#54611yescharacteristic
355C22×C43#54611yescharacteristic
356C22×C43C22×Q1611yescharacteristic
357C22×C43C2×#13711yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57711yescharacteristic
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—41no—
364C2×D43—41no—
365C2×D43—41no—
366C2×D43—41no—
367C4×C43—42no—
368C4×C43—41no—
369C4×C43—42no—
370C4×C43—42no—
371C4×C43—81no—
372C4×C43#53211yescharacteristic
373C4×C43#53511yescharacteristic
374C4×C43#55011yescharacteristic
375C4×C43#55011yescharacteristic
376Dic43—22no—
377Dic43—42no—
378Dic43—41no—
379Dic43—42no—
380Dic43—42no—
381Dic43—81no—
382Dic43#45114yes—
383C2×#554—431no—
384C2×#487—431no—
385C2×#462—431no—
386#2542—431no—
387#2001—431no—
388#2001—431no—
389#2001—431no—
390#2001D4311yescharacteristic, complemented
391#1987—431no—
392#1954—431no—
393#1872—431no—
394#1872—431no—
395#1872—431no—
396#1872—431no—
397C4×#103—431no—
398C2×C43—42no—
399C2×C43#243111yescharacteristic
400C2×C43C2×#45111yescharacteristic
401C2×C43#300911yescharacteristic
402C2×C43#329911yescharacteristic
403C2×C43#329911yescharacteristic
404C2×C43#333111yescharacteristic
405C2×C43#333111yescharacteristic
406D43—42no—
407C22×Q16—431no—
408C22×Q16C2×D4311yescharacteristic
409#554—864no—
410#554—864no—
411C2×C4⋊Q8—431no—
412C2×C4⋊Q8—431no—
413C2×#125—861no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—431no—
416C2×C22⋊Q8—431no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—861no—
419C2×C22⋊Q8—861no—
420C2×C22⋊Q8C2×D4311yescharacteristic
421C2×C22⋊Q8C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×D4—431no—
424C2×C4×D4—861no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427#487—864no—
428#462—864no—
429C2×C4⋊C8—431no—
430C2×#103—431no—
431C2×#103—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103C2×D4311yescharacteristic
437C2×#103C2×D4311yescharacteristic
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8C2×D4311yescharacteristic
442C2×C4×C8—431no—
443#399—861no—
444#399—861no—
445#390—861no—
446#384—861no—
447C4×C4⋊C4—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340C2×D4311yescharacteristic
454C43#2557311yescharacteristic, complemented, Sylow
455C22×Q8—431no—
456C22×Q8—861no—
457C22×Q8C22×D4311yescharacteristic
458C22×Q8C22×D4311yescharacteristic
459C22×D4—431no—
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C2×Q16—22no—
465C2×Q16—41no—
466C2×Q16—41no—
467C2×Q16—862no—
468C2×Q16—1721no—
469C2×Q16—1721no—
470C22×C8—431no—
471C22×C8—431no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474C4⋊Q8—434no—
475C4⋊Q8—862no—
476C4⋊Q8—862no—
477C4⋊Q8—862no—
478#125—868no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—41no—
483C22⋊Q8—868no—
484C22⋊Q8—868no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489C22⋊Q8—862no—
490C22⋊Q8—1721no—
491C22⋊Q8—1721no—
492C22⋊Q8—1721no—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—868no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—861no—
530C2×C42—861no—
531C4⋊C8—862no—
532#103—22no—
533#103—22no—
534#103—862no—
535#103—862no—
536#103—862no—
537#103—862no—
538#103—862no—
539#103—862no—
540C22⋊C8—41no—
541C22⋊C8—1721no—
542C22⋊C8—1721no—
543C22⋊C8—1721no—
544C4×C8—862no—
545#95—861no—
546C24—431no—
547C24D4×D4311yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—864no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—3441no—
567C2×Q8—3441no—
568C2×Q8D4×D4312yes—
569C2×D4—434no—
570C2×D4—862no—
571C2×D4—862no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—864no—
586C22×C4—864no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—3441no—
598C22×C4—3441no—
599C22×C4—3441no—
600C22×C4—3441no—
601C22×C4D4×D4311yescharacteristic
602C22×C4C23×D4311yescharacteristic
603Q16—44no—
604Q16—1724no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—432no—
624C4⋊C4—862no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—1722no—
634C4⋊C4—1722no—
635C4⋊C4—1722no—
636C4⋊C4—1722no—
637C4⋊C4—1722no—
638C4⋊C4D4×D4312yes—
639C4⋊C4#1062190012yes—
640C22⋊C4—24no—
641C22⋊C4—42no—
642C22⋊C4—862no—
643C22⋊C4—864no—
644C22⋊C4—862no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C42—432no—
649C42—432no—
650C42—864no—
651C42—1722no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—432no—
659C23—861no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23Q16×D4312yes—
666C23C2×D4×D4311yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—3444no—
676Q8—1721no—
677Q8—1721no—
678Q8—1721no—
679Q8—1721no—
680D4—868no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—432no—
701C2×C4—432no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—3444no—
713C2×C4—3444no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4C2×D4×D4311yescharacteristic
728C2×C4C2×D4×D4311yescharacteristic
729C2×C4#41×D4311yescharacteristic
730C2×C4C2×#1062190011yescharacteristic
731C2×C4#1306337011yescharacteristic
732C2×C4#1306337011yescharacteristic
733C8—41no—
734C8—41no—
735C8—1721no—
736C8—1721no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—1721no—
748C22—1721no—
749C22—1721no—
750C22—1721no—
751C22#120×D4311yescharacteristic
752C22#1458353611yescharacteristic
753C22#1458353811yescharacteristic
754C22C2×Q16×D4311yescharacteristic
755C22#137×D4311yescharacteristic
756C22#1458370611yescharacteristic
757C22#1458370811yescharacteristic
758C4—42no—
759C4—41no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—434no—
764C4—862no—
765C4—3441no—
766C4—1722no—
767C4—1721no—
768C4—1722no—
769C4—1722no—
770C4#1458344411yescharacteristic
771C4#1458346411yescharacteristic
772C4#1458356711yescharacteristic
773C4#1458356911yescharacteristic
774C2—42no—
775C2—1722no—
776C2#1913820911yescharacteristic
777C2#451×D4311yescharacteristic
778C2#1914386911yescharacteristic
779C2#1914646411yescharacteristic
780C2#1914646611yescharacteristic
781C2#1914690411yescharacteristic
782C2#1914690611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2001C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenter#2001D43
hypocenterC43#25573
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#14583248C2semidirect
3. C2×#14583107C2semidirect
5. #19135604C2semidirect
6. #19135603C2semidirect
7. #19135602C2semidirect
8. #19135541C2semidirect
10. #19134903C2semidirect
11. #19134901C2semidirect
12. #19134900C2semidirect
13. #19134899C2semidirect
14. #103×Dic43C2semidirect
15. C43×#2001C2semidirect
182. C2×C22⋊D43Q16semidirect
390. #2001D43semidirect
454. C43#25573semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145832482
C2×#145831072
#191395452
#191356042
#191356032
#191356022
#191355412
#191353872
#191349032
#191349012
#191349002
#191348992
#103×Dic432
C43×#20012
#2557343