Finite Group Databasebeta

← #25112804

Subgroups — #25112804

Order 11008.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583550C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3#19137491C211yesmaximal, characteristic, complemented
4#19135554C211yesmaximal, characteristic, complemented
5#19135545C211yesmaximal, characteristic, complemented
6#19135022C211yesmaximal, characteristic, complemented
7#19135021C211yesmaximal, characteristic, complemented
8#19134911C211yesmaximal, characteristic, complemented
9#19134910C211yesmaximal, characteristic, complemented
10#19134680C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134409C211yesmaximal, characteristic, complemented
13C2×#14582661C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1823C211yesmaximal, characteristic, complemented
16C22×#10621898—21no—
17C23×C43⋊C8C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583550—24no—
20#14583550C418yescomplemented
21C2×#13063324C2211yescharacteristic
22C2×#13063310—21no—
23C2×#13063308—21no—
24C2×#13063303—21no—
25C2×#13063300C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33(C22⋊D43)⋊C8—24no—
34C2×Dic43⋊C8C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×C8×Dic43C2211yescharacteristic
41#14582796—21no—
42#14582773—21no—
43#14582771—21no—
44#14582768C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—28no—
63C2×#10621898—44no—
64C2×#10621898—44no—
65C22×Dic86—21no—
66C22×D172—21no—
67C22×D172C2311yescharacteristic
68C22×C22⋊D43—21no—
69C22×C22⋊D43D411yescharacteristic
70C23×Dic43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—41no—
83#13063324—22no—
84#13063324C2×C414yescomplemented
85#13063310—28no—
86#13063308—28no—
87#13063303—28no—
88#13063300—22no—
89#13063300C2×C414yescomplemented
90#13063299—22no—
91#13063299C2×C414yescomplemented
92#13063287—22no—
93#13063287C2×C414yescomplemented
94C4×C22⋊D43C2×C414yes—
95C4×C22⋊D43D414yes—
96(C22⋊D43)⋊C4—44no—
97C2×C4⋊Dic43—22no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—41no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C4⋊C4×D43—22no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—41no—
112C4⋊C4×D43C2×C414yescomplemented
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122#13063247—22no—
123#13063247—41no—
124#13063245—22no—
125#13063245—41no—
126(C2×D43)⋊C8—22no—
127C8×Dic43—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C23×C4×C43—21no—
131C23×C4×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43C2×C414yescomplemented
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C22⋊C8×C43—22no—
143#95×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43—21no—
146C23×D43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—24no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43C22⋊C414yes—
166C2×C22⋊D43D814yes—
167C2×C22⋊D43SD1614yes—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—81no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177#10621898—432no—
178C2×D172—21no—
179C2×D172—24no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—42no—
185C2×D172—42no—
186C2×D172C22×C412yes—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—24no—
192C2×C4×D43—24no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—81no—
200C2×C4×D43C22×C412yes—
201C2×C4×D43C2×D412yes—
202C2×Dic86—24no—
203C2×Dic86—42no—
204C2×Dic86—42no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C4⋊C4×C43—24no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C22×C412yes—
219C4⋊C4×C43C22×C412yes—
220C22⋊C4×C43—42no—
221C22⋊Dic43C22⋊C414yes—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4C22⋊C414yes—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—42no—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43#4112yescomplemented
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238Dic43⋊C4—81no—
239Dic43⋊C4C22⋊C414yes—
240C4×Dic43—42no—
241C4×Dic43C22×C412yes—
242C4×Dic43C2×D412yes—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—44no—
249C2×C43⋊C8#4112yescomplemented
250C8×D43—44no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43C2×C22⋊C412yes—
256C23×C43C2×D812yes—
257C23×C43C2×SD1612yes—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43C2×C22⋊C412yes—
271C22×D43C2×D812yes—
272C22×D43C2×SD1612yes—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—48no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43C2×C22⋊C412yes—
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C432−1+411yescharacteristic
299C22⋊D43—48no—
300C22⋊D43#102116yescomplemented
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—84no—
315C2×Dic43C2×C22⋊C412yes—
316C2×Dic43C2×C22⋊C412yes—
317C2×Dic43C2×C22⋊C412yes—
318C2×Dic43C2×D812yes—
319C2×Dic43C2×SD1612yes—
320D172—22no—
321D172—22no—
322D172—48no—
323D172—41no—
324D172—41no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—48no—
330C4×D43—48no—
331C4×D43—84no—
332Dic86—48no—
333C8×C43—41no—
334C8×C43—41no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337#22485—431nomaximal, Sylow
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43C2×#10214yes—
345C22×C43C22×C22⋊C411yescharacteristic
346C22×C43#54611yescharacteristic
347C22×C43#54711yescharacteristic
348C22×C43C22×D811yescharacteristic
349C22×C43C22×SD1611yescharacteristic
350C22×C43#57711yescharacteristic
351C22×C43#57811yescharacteristic
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C2×D43—81no—
365C2×D43C2×#10214yes—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—81no—
370C4×C43—81no—
371C4×C43C4×#4111yescharacteristic
372C4×C43#52011yescharacteristic
373C4×C43#54611yescharacteristic
374C4×C43#54711yescharacteristic
375Dic43—22no—
376Dic43—22no—
377Dic43—42no—
378Dic43—42no—
379Dic43—81no—
380Dic43C2×#10214yes—
381C2×#547—431no—
382C2×C8×D4—431no—
383D4×C4⋊C4—431no—
384#1990—431no—
385#1988—431no—
386#1893—431no—
387#1893—431no—
388#1874—431no—
389#1874—431no—
390#1823—431no—
391#1823D4311yescharacteristic, complemented
392#1802—431no—
393C4×#102—431no—
394C2×#340—431no—
395C2×#340—431no—
396C2×C43—24no—
397C2×C43#233911yescharacteristic
398C2×C43C22×#10211yescharacteristic
399C2×C43#289811yescharacteristic
400C2×C43#329411yescharacteristic
401C2×C43#329811yescharacteristic
402C2×C43#333411yescharacteristic
403C2×C43#333511yescharacteristic
404D43—24no—
405D43—82no—
406C22×#41—861no—
407C23×C8—431no—
408C23×C8—431no—
409#547—438no—
410#547—864no—
411C2×C4⋊Q8—431no—
412C2×#123—861no—
413C2×#123—861no—
414C2×C22⋊Q8—861no—
415C2×#121—431no—
416C2×#121—431no—
417C2×C4×D4—431no—
418C2×C4×D4—431no—
419C2×C4×D4—861no—
420C22×C4⋊C4—431no—
421C22×C4⋊C4—431no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4C2×D4311yescharacteristic
424C8×D4—864no—
425C2×C4⋊C8—431no—
426C2×#102—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×C22⋊C8—431no—
431C2×C22⋊C8C2×D4311yescharacteristic
432C2×C4×C8—431no—
433#389—861no—
434#385—861no—
435#385—861no—
436#384—431no—
437#380—431no—
438#380C2×D4311yescharacteristic
439C4×C4⋊C4—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#340C2×D4311yescharacteristic
449#340C2×D4311yescharacteristic
450#340C2×D4311yescharacteristic
451#340C2×D4311yescharacteristic
452C43#2248511yescharacteristic, complemented, Sylow
453C2×#41—868no—
454C2×#41—1724no—
455C2×#41—1724no—
456C22×Q8—861no—
457C22×D4—431no—
458C22×D4—431no—
459C22×D4—861no—
460C22×D4—861no—
461C23×C4—21no—
462C23×C4—431no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4C22×D4311yescharacteristic
468C22×C8—431no—
469C22×C8—431no—
470C22×C8—862no—
471C22×C8—862no—
472C22×C8—862no—
473C22×C8—862no—
474C22×C8—1721no—
475C22×C8—1721no—
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478C4⋊Q8—434no—
479C4⋊Q8—862no—
480#123—868no—
481#123—868no—
482C22⋊Q8—868no—
483#121—434no—
484#121—434no—
485#121—862no—
486#121—862no—
487C4×D4—434no—
488C4×D4—434no—
489C4×D4—434no—
490C4×D4—862no—
491C4×D4—1724no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—434no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—862no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—1721no—
509C2×C4⋊C4—1721no—
510C2×C4⋊C4C4×D4314yescomplemented
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
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×C42—431no—
523C2×C42—861no—
524C4⋊C8—862no—
525#102—862no—
526#102—862no—
527#102—1721no—
528#102—1721no—
529C22⋊C8—22no—
530C22⋊C8—862no—
531C4×C8—862no—
532#95—21no—
533#95—861no—
534#95—861no—
535C24—431no—
536C24—861no—
537C24D4×D4311yescharacteristic
538#41—17232no—
539C2×Q8—864no—
540C2×Q8—1722no—
541C2×Q8—1722no—
542C2×D4—434no—
543C2×D4—434no—
544C2×D4—434no—
545C2×D4—432no—
546C2×D4—864no—
547C2×D4—864no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—1722no—
554C2×D4—1722no—
555C2×D4—1722no—
556C2×D4—1722no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—1722no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4—1722no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4C2×C4×D4312yes—
593C22×C4D4×D4311yescharacteristic
594C22×C4D4×D4312yes—
595C22×C4C23×D4311yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—432no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—1724no—
609C2×C8—1724no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—434no—
618C4⋊C4—432no—
619C4⋊C4—432no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—3441no—
627C4⋊C4—1722no—
628C4⋊C4—1722no—
629C4⋊C4—1722no—
630C4⋊C4C2×C4×D4312yes—
631C4⋊C4C2×C4×D4312yes—
632C22⋊C4—42no—
633C22⋊C4—434no—
634C22⋊C4—434no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—1722no—
639C42—432no—
640C42—432no—
641C42—1722no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—432no—
647C23—432no—
648C23—432no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—862no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23—1721no—
660C23C22⋊C4×D4312yes—
661C23D8×D4312yes—
662C23SD16×D4312yes—
663C23C2×D4×D4311yescharacteristic
664Q8—1728no—
665D4—4316no—
666D4—862no—
667D4—862no—
668D4—1728no—
669D4—1728no—
670D4—1721no—
671D4—1721no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—432no—
692C2×C4—432no—
693C2×C4—432no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—3444no—
707C2×C4—3444no—
708C2×C4—1728no—
709C2×C4—1728no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4C22⋊C4×D4312yes—
718C2×C4C22×C4×D4311yescharacteristic
719C2×C4C2×D4×D4311yescharacteristic
720C2×C4#41×D4311yescharacteristic
721C2×C4#41×D4311yescharacteristic
722C2×C4#1306337111yescharacteristic
723C2×C4#1306337211yescharacteristic
724C8—41no—
725C8—41no—
726C8—862no—
727C8—1721no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—434no—
735C22—862no—
736C22—862no—
737C22—862no—
738C22—862no—
739C22—862no—
740C22—862no—
741C22—3441no—
742C22—3441no—
743C22—3441no—
744C22—3441no—
745C22—1722no—
746C22—1722no—
747C22—1722no—
748C22#102×D4314yes—
749C22C2×C22⋊C4×D4311yescharacteristic
750C22#1458354111yescharacteristic
751C22#1458354711yescharacteristic
752C22C2×D8×D4311yescharacteristic
753C22C2×SD16×D4311yescharacteristic
754C22#1458370811yescharacteristic
755C22#1458371511yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4—434no—
762C4—862no—
763C4—862no—
764C4—3441no—
765C4—1722no—
766C4—1722no—
767C4#1458336711yescharacteristic
768C4#1458337911yescharacteristic
769C4#1458354111yescharacteristic
770C4#1458354711yescharacteristic
771C2—24no—
772C2—864no—
773C2—3442no—
774C2#1913741911yescharacteristic
775C2C2×#102×D4311yescharacteristic
776C2#1914312711yescharacteristic
777C2#1914640611yescharacteristic
778C2#1914645811yescharacteristic
779C2#1914693711yescharacteristic
780C2#1914694511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1823C2
socleC23×C43C22×D4
prime radicalC2×#14583550C2
cosocleC22×C4×C43C24
hypercenter#1823D43
hypocenterC43#22485
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C8C2semidirect
3. #19137491C2semidirect
4. #19135554C2semidirect
5. #19135545C2semidirect
6. #19135022C2semidirect
7. #19135021C2semidirect
8. #19134911C2semidirect
9. #19134910C2semidirect
10. #19134680C2semidirect
11. #19134594C2semidirect
12. #19134409C2semidirect
13. C2×#14582661C2semidirect
14. #340×D43C2semidirect
15. C43×#1823C2semidirect
20. #14583550C4semidirect
84. #13063324C2×C4semidirect
89. #13063300C2×C4semidirect
91. #13063299C2×C4semidirect
93. #13063287C2×C4semidirect
112. C4⋊C4×D43C2×C4semidirect
136. C2×C4⋊C4×C43C2×C4semidirect
233. C4⋊Dic43#41semidirect
249. C2×C43⋊C8#41semidirect
300. C22⋊D43#102semidirect
391. #1823D43semidirect
452. C43#22485semidirect
510. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835502
C2×(C22⋊D43)⋊C82
#191374912
#191355542
#191355452
#191350222
#191350212
#191349112
#191349102
#191346802
#191345942
#191344092
C2×#145826612
#340×D432
C43×#18232
#2248543