Finite Group Databasebeta

← #34026974

Subgroups — #34026974

Order 18688.

1042 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989598C211yesmaximal, characteristic, complemented
2C22×#14556660C211yesmaximal, characteristic, complemented
3#22626447C211yesmaximal, characteristic
4D4×C4⋊#64408C211yesmaximal, characteristic
5#22626044C211yesmaximal, characteristic, complemented
6#22626042C211yesmaximal, characteristic, complemented
7#22625882C211yesmaximal, characteristic, complemented
8#22625881C211yesmaximal, characteristic, complemented
9#22625880C211yesmaximal, characteristic, complemented
10#22625880C211yesmaximal, characteristic, complemented
11#22625869C211yesmaximal, characteristic, complemented
12#22625809C211yesmaximal, characteristic, complemented
13#22625807C211yesmaximal, characteristic, complemented
14#22625745C211yesmaximal, characteristic, complemented
15#435×D73C211yesmaximal, characteristic
16C2×D4×#64408—21no—
17C2×#14556670C2211yescharacteristic
18C22×C4⋊#64408C2211yescharacteristic
19C22×C4⋊#64408C2211yescharacteristic
20C22×C4⋊#64408C2211yescharacteristic
21#17989598—24no—
22C2×#14556660—24no—
23C2×#14556660C2211yescharacteristic
24C2×#14556660C2211yescharacteristic
25C2×#14556660C2211yescharacteristic
26C2×#14556660C2211yescharacteristic
27C2×#14556660C2211yescharacteristic
28C2×#14556660C2211yescharacteristic
29C2×#14556659C2211yescharacteristic
30C2×#14556659C2211yescharacteristic
31C2×#14556659C2211yescharacteristic
32C2×#14556659C2211yescharacteristic
33#17989538—21no—
34#17989537—21no—
35#17989536—21no—
36#17989535—21no—
37#17989534—21no—
38#17989534—21no—
39#17989533C2211yescharacteristic
40#17989531C2211yescharacteristic
41#17989529C2211yescharacteristic
42#17989529C2211yescharacteristic
43#17989529C2211yescharacteristic
44#17989529C2211yescharacteristic
45C4×C4⋊#64408C2211yescharacteristic
46C4×C4⋊#64408C2211yescharacteristic
47C22⋊C4×#64408—21no—
48#17989461C2211yescharacteristic
49#17989461C2211yescharacteristic
50#17989461C2211yescharacteristic
51#17989461C2211yescharacteristic
52#17989461C2211yescharacteristic
53#17989461C2211yescharacteristic
54C2×M16×D73C2211yescharacteristic
55C22×C8×D73C2211yescharacteristic
56C4×D4×D73C2211yescharacteristic
57#17988661C411yescharacteristic, complemented
58#17988660C411yescharacteristic, complemented
59#17988659C411yescharacteristic, complemented
60#17988658C411yescharacteristic, complemented
61#17988657C411yescharacteristic, complemented
62#17988656C411yescharacteristic, complemented
63#17988655C411yescharacteristic, complemented
64C4⋊C8×D73C2211yescharacteristic
65C22⋊C8×D73C2211yescharacteristic
66C22⋊C8×D73C2211yescharacteristic
67#97×D73C2211yescharacteristic
68#435×C73C411yescharacteristic, complemented
69C23×#64408—21no—
70C23×#64408—21no—
71C23×#64408—21no—
72D4×#64408—44no—
73#14556670—22no—
74#14556670—41no—
75C2×C4⋊#64408—22no—
76C2×C4⋊#64408—22no—
77C2×C4⋊#64408—22no—
78C2×C4⋊#64408—21no—
79C2×C4⋊#64408—21no—
80C2×C4⋊#64408—21no—
81C2×C4⋊#64408—21no—
82C2×C4⋊#64408—21no—
83C2×C4⋊#64408—41no—
84C2×C4⋊#64408—41no—
85C2×C4⋊#64408—41no—
86C2×C4⋊#64408C2311yescharacteristic
87C2×C4⋊#64408C2311yescharacteristic
88C2×C4⋊#64408C2311yescharacteristic
89C2×C4⋊#64408C2311yescharacteristic
90C2×C4⋊#64408C2311yescharacteristic
91C2×C4⋊#64408C2311yescharacteristic
92C2×C4⋊#64408C2311yescharacteristic
93C2×C4⋊#64408C2311yescharacteristic
94C2×C22⋊#64408—21no—
95C2×C22⋊#64408—21no—
96C2×C22⋊#64408—21no—
97C2×C22⋊#64408—21no—
98C2×C22⋊#64408—21no—
99C2×C4×#64408—21no—
100C2×C4×#64408—21no—
101C2×C4×#64408—21no—
102#14556660—22no—
103#14556660—22no—
104#14556660—22no—
105#14556660—22no—
106#14556660—41no—
107#14556660D414yescomplemented
108#14556659—22no—
109#14556659—22no—
110#14556659—22no—
111#14556659—41no—
112(C2×#64408)⋊C4—21no—
113(C2×#64408)⋊C4—21no—
114(C2×#64408)⋊C4—21no—
115(C2×#64408)⋊C4—21no—
116(C2×#64408)⋊C4—21no—
117(C2×#64408)⋊C4—21no—
118(C2×#64408)⋊C4—21no—
119(C2×#64408)⋊C4—21no—
120C2×D4×D73D411yescharacteristic
121C22×C4×D73C2311yescharacteristic
122C22×C4×D73C2311yescharacteristic
123C2×#11924012C2×C411yescharacteristic, complemented
124C2×#11924011C2×C411yescharacteristic, complemented
125C2×#11924011C2×C411yescharacteristic, complemented
126M16×D73—22no—
127M16×D73—22no—
128C22×#10596831C2×C411yescharacteristic, complemented
129C2×C8×D73—22no—
130C2×C8×D73—22no—
131C2×C8×D73C2×C411yescharacteristic, complemented
132C2×C8×D73C2×C411yescharacteristic, complemented
133C2×C8×D73C2311yescharacteristic
134C2×C8×D73C2311yescharacteristic
135C2×C8×D73C2311yescharacteristic
136C2×C8×D73C2311yescharacteristic
137C4×D292C2×C411yescharacteristic
138D4×Dic73Q811yescharacteristic
139#14556553Q811yescharacteristic
140C4×C22⋊D73C2×C411yescharacteristic
141C4×C22⋊D73C2×C411yescharacteristic
142#14556551Q811yescharacteristic
143#14556551Q811yescharacteristic
144C4⋊C4×D73D411yescharacteristic
145C22⋊C4×D73D411yescharacteristic
146C22⋊C4×D73D411yescharacteristic
147C42×D73C2311yescharacteristic
148C4⋊#10596831C2×C411yescharacteristic, complemented
149#14556520C2×C411yescharacteristic, complemented
150#14556520C2×C411yescharacteristic, complemented
151C22⋊#10596831C2×C411yescharacteristic, complemented
152C22⋊#10596831C2×C411yescharacteristic, complemented
153#14556503C2×C411yescharacteristic, complemented
154#14556503C2×C411yescharacteristic, complemented
155#14556503C2×C411yescharacteristic, complemented
156#14556503C2×C411yescharacteristic, complemented
157#14556502C2×C411yescharacteristic, complemented
158#14556501C2×C411yescharacteristic, complemented
159#14556501C2×C411yescharacteristic, complemented
160C2×M16×C73C2×C411yescharacteristic, complemented
161C22×C8×C73C2×C411yescharacteristic, complemented
162C4×D4×C73C2×C411yescharacteristic
163C4⋊C8×C73C2×C411yescharacteristic, complemented
164C22⋊C8×C73C2×C411yescharacteristic, complemented
165C22⋊C8×C73C2×C411yescharacteristic, complemented
166#97×C73C2×C411yescharacteristic, complemented
167C22×#64408—21no—
168C22×#64408—21no—
169C22×#64408—21no—
170C22×#64408—21no—
171C22×#64408—21no—
172C22×#64408—21no—
173C22×#64408—21no—
174C22×#64408—21no—
175C22×#64408—42no—
176C22×#64408—42no—
177C22×#64408—42no—
178C22×#64408—42no—
179C22×#64408—42no—
180C22×#64408—42no—
181C22×#64408—81no—
182C22×#64408—81no—
183C22×#64408—81no—
184C4⋊#64408—21no—
185C4⋊#64408—21no—
186C4⋊#64408—21no—
187C4⋊#64408—21no—
188C4⋊#64408—21no—
189C4⋊#64408—21no—
190C4⋊#64408—21no—
191C4⋊#64408—21no—
192C4⋊#64408—21no—
193C4⋊#64408—21no—
194C4⋊#64408—21no—
195C4⋊#64408—21no—
196C4⋊#64408—21no—
197C4⋊#64408—21no—
198C4⋊#64408—42no—
199C4⋊#64408—42no—
200C4⋊#64408—42no—
201C4⋊#64408—42no—
202C4⋊#64408—81no—
203C4⋊#64408C2×D412yes—
204C4⋊#64408C2×D412yes—
205C22⋊#64408—42no—
206C22⋊#64408—42no—
207C22⋊#64408—42no—
208C22⋊#64408—42no—
209C22⋊#64408—81no—
210C4×#64408—42no—
211C4×#64408—42no—
212C4×#64408—81no—
213C23×D73C2×D411yescharacteristic
214C23×D73C2×D411yescharacteristic
215C2×D292C4⋊C411yescharacteristic
216C2×C22⋊D73C4⋊C411yescharacteristic
217C2×C22⋊D73C4⋊C411yescharacteristic
218D4×D73—22no—
219D4×D73—22no—
220C22×Dic73C2×Q811yescharacteristic
221C22×Dic73C2×Q811yescharacteristic
222C2×C4×D73—21no—
223C2×C4×D73—21no—
224C2×C4×D73—21no—
225C2×C4×D73—21no—
226C2×C4×D73—21no—
227C2×C4×D73—21no—
228C2×C4×D73—21no—
229C2×C4×D73—21no—
230C2×C4×D73C22×C411yescharacteristic
231C2×C4×D73C22×C411yescharacteristic
232C2×C4×D73C2×D411yescharacteristic
233C2×C4×D73C2×D411yescharacteristic
234C2×C4×D73C2×D411yescharacteristic
235C2×C4×D73C2×D411yescharacteristic
236C2×C4×D73C2×Q811yescharacteristic
237C2×C4×D73C2×Q811yescharacteristic
238C2×C4×D73C2411yescharacteristic
239#11924012—22no—
240#11924011—22no—
241#11924011—22no—
242C2×#10596831—22no—
243C2×#10596831C22×C411yescharacteristic
244C2×#10596831C22×C411yescharacteristic
245C2×#10596831C22×C411yescharacteristic
246C2×#10596831C22×C411yescharacteristic
247C8×D73—21no—
248C8×D73—21no—
249C8×D73—21no—
250C8×D73—21no—
251C8×D73—21no—
252C8×D73—21no—
253C8×D73—22no—
254C8×D73—22no—
255C8×D73C2×D412yes—
256C8×D73#4112yes—
257C4⋊Dic73C4⋊C411yescharacteristic
258#11924007C4⋊C411yescharacteristic
259#11924007C4⋊C411yescharacteristic
260C22⋊Dic73C4⋊C411yescharacteristic
261C22⋊Dic73C4⋊C411yescharacteristic
262#11924005C4⋊C411yescharacteristic
263#11924005C4⋊C411yescharacteristic
264#11924005C4⋊C411yescharacteristic
265#11924005C4⋊C411yescharacteristic
266C4×Dic73C22×C411yescharacteristic
267C4×Dic73C2×Q811yescharacteristic
268C4×Dic73C2×Q811yescharacteristic
269C2×D4×C73C4⋊C411yescharacteristic
270C22×C4×C73C22×C411yescharacteristic
271C22×C4×C73C22×C411yescharacteristic
272M16×C73—22no—
273C2×C8×C73—22no—
274C2×C8×C73C22×C411yescharacteristic
275C2×C8×C73C22×C411yescharacteristic
276C2×C8×C73C22×C411yescharacteristic
277C2×C8×C73C22×C411yescharacteristic
278C4⋊C4×C73C4⋊C411yescharacteristic
279C22⋊C4×C73C4⋊C411yescharacteristic
280C22⋊C4×C73C4⋊C411yescharacteristic
281C42×C73C22×C411yescharacteristic
282C23×C73C2×C4⋊C411yescharacteristic
283C23×C73C2×C4⋊C411yescharacteristic
284C22×D73—21no—
285C22×D73—21no—
286C22×D73—21no—
287C22×D73—21no—
288C22×D73—21no—
289C22×D73—21no—
290C22×D73—21no—
291C22×D73—21no—
292C22×D73—21no—
293C22×D73—21no—
294C22×D73C2×C4⋊C411yescharacteristic
295C22×D73C2×C4⋊C411yescharacteristic
296C22×D73AGL(1,ℤ/8)12yes—
297C22×D73#13712yes—
298C22×D73C22×D411yescharacteristic
299C2×#64408—22no—
300C2×#64408—22no—
301C2×#64408—41no—
302C2×#64408—41no—
303C2×#64408—41no—
304C2×#64408—41no—
305C2×#64408—41no—
306C2×#64408—41no—
307C2×#64408—41no—
308C2×#64408—41no—
309C2×#64408—41no—
310C2×#64408—41no—
311C2×#64408—41no—
312C2×#64408—41no—
313C2×#64408—41no—
314C2×#64408—41no—
315C2×#64408—41no—
316C2×#64408—41no—
317C2×#64408—41no—
318C2×#64408—41no—
319C2×#64408—41no—
320C2×#64408—41no—
321C2×#64408—41no—
322C2×#64408—41no—
323C2×#64408—84no—
324C2×#64408—84no—
325C2×#64408—84no—
326D4×C73—22no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73C2×C4⋊C411yescharacteristic
332C2×C4×C73C2×C4⋊C411yescharacteristic
333C2×C4×C73C2×C4⋊C411yescharacteristic
334C2×C4×C73C2×C4⋊C411yescharacteristic
335C2×C4×C73C23×C411yescharacteristic
336C22⋊D73—22no—
337C22⋊D73—22no—
338C2×Dic73—21no—
339C2×Dic73—21no—
340C2×Dic73—21no—
341C2×Dic73—21no—
342C2×Dic73C2×C4⋊C411yescharacteristic
343C2×Dic73C2×C4⋊C411yescharacteristic
344C2×Dic73C2×C4⋊C411yescharacteristic
345C2×Dic73C2×C4⋊C411yescharacteristic
346C2×Dic73C22×Q811yescharacteristic
347D292—22no—
348C4×D73—21no—
349C4×D73—21no—
350C4×D73—21no—
351C4×D73—21no—
352C4×D73—21no—
353C4×D73—21no—
354C4×D73—21no—
355C4×D73—21no—
356C4×D73—21no—
357C4×D73—21no—
358C4×D73—21no—
359C4×D73—21no—
360C4×D73—21no—
361C4×D73—21no—
362C4×D73—21no—
363C4×D73—21no—
364C4×D73C22×D411yescharacteristic
365C4×D73C2×#4111yescharacteristic
366C4×D73H(5,𝔽2)11yescharacteristic
367C4×D732−1+411yescharacteristic
368C8×C73—21no—
369C8×C73—21no—
370C8×C73—21no—
371C8×C73C4×D412yescomplemented
372#10596831—21no—
373#10596831—21no—
374#10596831—21no—
375#10596831C4×D412yescomplemented
376C22×C73—21no—
377C22×C73—21no—
378C22×C73—21no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73#42812yescomplemented
382C22×C73C22×C4⋊C411yescharacteristic
383C2×D73—21no—
384C2×D73—21no—
385C2×D73—22no—
386C2×D73—22no—
387C2×D73—22no—
388C2×D73—22no—
389C2×D73—21no—
390C2×D73—21no—
391C2×D73—21no—
392C2×D73—41no—
393C2×D73—41no—
394C2×D73—41no—
395C2×D73—41no—
396C2×D73#42812yescomplemented
397C2×D73D4211yescharacteristic
398C2×D73#54711yescharacteristic
399C2×D73C2×AGL(1,ℤ/8)11yescharacteristic
400C2×D73C2×#13711yescharacteristic
401C2×D73#57611yescharacteristic
402C2×D73#57811yescharacteristic
403#64408—42no—
404#64408—42no—
405#64408—81no—
406#64408—81no—
407#64408—81no—
408#64408—81no—
409#64408—81no—
410#64408—81no—
411C4×C73—21no—
412C4×C73—21no—
413C4×C73—21no—
414C4×C73—21no—
415C4×C73C2×C4×D411yescharacteristic
416C4×C73#52011yescharacteristic
417Dic73—21no—
418Dic73—21no—
419Dic73—21no—
420Dic73—21no—
421Dic73D4×Q811yescharacteristic
422Dic73#55411yescharacteristic
423#22661—731nomaximal, Sylow
424C2×C73—22no—
425C2×C73—41no—
426C2×C73D4×C4⋊C411yescharacteristic
427C2×C73C2×#42811yescharacteristic
428C2×C73#291311yescharacteristic
429D73—22no—
430D73—41no—
431D73#326411yescharacteristic
432D73#327011yescharacteristic
433D73#334311yescharacteristic
434D73#334611yescharacteristic
435C2×#435—731no—
436C2×#428—731no—
437C22×#107—731no—
438#2352—731no—
439D4×C4⋊C4—731no—
440#1949—731no—
441#1947—731no—
442#1854—731no—
443#1853—731no—
444#1852—731no—
445#1852—731no—
446#1847—731no—
447#1809—731no—
448#1807—731no—
449#1776—731no—
450C73#2266111yescharacteristic, complemented, Sylow
451C22×M16—731no—
452C23×C8—731no—
453C2×C4×D4—731no—
454C2×C4×D4—1461no—
455C2×#117—731no—
456C22×C4⋊C4—731no—
457C22×C4⋊C4—731no—
458C22×C4⋊C4—731no—
459#435—731no—
460#435—731no—
461#435—731no—
462#435—731no—
463#435—731no—
464#435—731no—
465#435—731no—
466#435#6440811yescharacteristic, complemented
467#428—1464no—
468C2×#107—731no—
469C2×#107—731no—
470C2×#107—731no—
471C2×#107—731no—
472C2×#107—731no—
473C2×#107—731no—
474C2×#107—1464no—
475C2×#106—731no—
476C2×#106—731no—
477C2×#106—731no—
478C2×#106—731no—
479C2×C4⋊C8—731no—
480C2×C22⋊C8—731no—
481C2×C22⋊C8—731no—
482C2×#97—731no—
483#389—1461no—
484#388—1461no—
485#387—1461no—
486#386—1461no—
487#385—1461no—
488#385—1461no—
489#384—731no—
490#382—731no—
491#380—731no—
492#380—731no—
493#380—731no—
494#380—731no—
495C4×C4⋊C4—731no—
496C4×C4⋊C4—731no—
497C4×C22⋊C4—1461no—
498#340—731no—
499#340—731no—
500#340—731no—
501#340—731no—
502#340—731no—
503#340—731no—
504C22×D4—731no—
505C23×C4—731no—
506C23×C4—731no—
507C23×C4—1461no—
508C23×C4—1461no—
509C23×C4—1461no—
510C2×M16—731no—
511C2×M16—731no—
512C2×M16—731no—
513C2×M16—1462no—
514C2×M16—1462no—
515C2×M16C2×#6440811yescharacteristic, complemented
516C22×C8—731no—
517C22×C8—731no—
518C22×C8—731no—
519C22×C8—731no—
520C22×C8—731no—
521C22×C8—731no—
522C22×C8—731no—
523C22×C8—1462no—
524C22×C8—1462no—
525C22×C8C2×#6440811yescharacteristic, complemented
526C4×D4—2924no—
527C4×D4—731no—
528C4×D4—731no—
529C4×D4—731no—
530C4×D4—731no—
531C4×D4—731no—
532C4×D4—731no—
533C4×D4—731no—
534C4×D4C2×#6440811yescharacteristic
535#117—2921no—
536#117—1462no—
537C2×C4⋊C4—2921no—
538C2×C4⋊C4—2921no—
539C2×C4⋊C4—2921no—
540C2×C4⋊C4—731no—
541C2×C4⋊C4—731no—
542C2×C4⋊C4—731no—
543C2×C4⋊C4—731no—
544C2×C4⋊C4—731no—
545C2×C4⋊C4—731no—
546C2×C4⋊C4—731no—
547C2×C4⋊C4—731no—
548C2×C4⋊C4—731no—
549C2×C4⋊C4—1461no—
550C2×C4⋊C4—1461no—
551C2×C4⋊C4—1461no—
552C2×C4⋊C4—1461no—
553C2×C4⋊C4—1462no—
554C2×C4⋊C4—1462no—
555C2×C4⋊C4—1462no—
556C2×C4⋊C4—1461no—
557C2×C22⋊C4—731no—
558C2×C22⋊C4—731no—
559C2×C22⋊C4—1461no—
560C2×C22⋊C4—1461no—
561C2×C22⋊C4—1461no—
562C2×C22⋊C4—1461no—
563C2×C22⋊C4—1461no—
564C2×C42—731no—
565C2×C42—1461no—
566C2×C42—1461no—
567C2×C42—1461no—
568#107—2921no—
569#107—734no—
570#107—1462no—
571#107—1462no—
572#107—1462no—
573#107—1462no—
574#106—2921no—
575#106—1462no—
576#106—1462no—
577#106—1462no—
578C4⋊C8—731no—
579C4⋊C8—731no—
580C4⋊C8—731no—
581C4⋊C8C2×#6440811yescharacteristic, complemented
582C22⋊C8—731no—
583C22⋊C8—731no—
584C22⋊C8—731no—
585C22⋊C8—731no—
586C22⋊C8—731no—
587C22⋊C8—731no—
588C22⋊C8C2×#6440811yescharacteristic, complemented
589C22⋊C8C2×#6440811yescharacteristic, complemented
590#97—731no—
591#97—731no—
592#97—731no—
593#97C2×#6440811yescharacteristic, complemented
594#95—1461no—
595#95—1461no—
596#95—1461no—
597#95—1461no—
598#95—1461no—
599#95—1461no—
600#95—1461no—
601#95—1461no—
602C24—731no—
603C24—731no—
604C2×D4—731no—
605C2×D4—731no—
606C2×D4—731no—
607C2×D4—1462no—
608C2×D4—1462no—
609C2×D4C4⋊#6440811yescharacteristic
610C22×C4—2922no—
611C22×C4—2922no—
612C22×C4—2922no—
613C22×C4—2922no—
614C22×C4—2922no—
615C22×C4—2922no—
616C22×C4—5841no—
617C22×C4—5841no—
618C22×C4—5841no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—731no—
624C22×C4—731no—
625C22×C4—731no—
626C22×C4—731no—
627C22×C4—731no—
628C22×C4—731no—
629C22×C4—731no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1461no—
633C22×C4—1461no—
634C22×C4—1461no—
635C22×C4—1461no—
636C22×C4—1461no—
637C22×C4—1461no—
638C22×C4—1461no—
639C22×C4—1461no—
640C22×C4—1461no—
641C22×C4—1461no—
642C22×C4—1461no—
643C22×C4—1461no—
644C22×C4—1461no—
645C22×C4—1461no—
646C22×C4C22×#6440811yescharacteristic
647C22×C4C22×#6440811yescharacteristic
648M16—22no—
649M16—1462no—
650M16—1462no—
651M16—1462no—
652C2×C8—22no—
653C2×C8—731no—
654C2×C8—732no—
655C2×C8—732no—
656C2×C8—731no—
657C2×C8—731no—
658C2×C8—731no—
659C2×C8—1462no—
660C2×C8—1461no—
661C2×C8—1461no—
662C2×C8—1461no—
663C2×C8—1461no—
664C2×C8—1461no—
665C2×C8—1461no—
666C2×C8—1462no—
667C2×C8—1462no—
668C2×C8C22×#6440811yescharacteristic
669C2×C8C22×#6440811yescharacteristic
670C2×C8C22×#6440811yescharacteristic
671C2×C8C22×#6440811yescharacteristic
672C4⋊C4—2922no—
673C4⋊C4—2922no—
674C4⋊C4—2922no—
675C4⋊C4—2922no—
676C4⋊C4—5841no—
677C4⋊C4—731no—
678C4⋊C4—731no—
679C4⋊C4—731no—
680C4⋊C4—732no—
681C4⋊C4—732no—
682C4⋊C4—1461no—
683C4⋊C4—1461no—
684C4⋊C4—1461no—
685C4⋊C4—1461no—
686C4⋊C4—1461no—
687C4⋊C4—1461no—
688C4⋊C4—1461no—
689C4⋊C4—1461no—
690C4⋊C4—1461no—
691C4⋊C4—1461no—
692C4⋊C4—1461no—
693C4⋊C4—1461no—
694C4⋊C4—1461no—
695C4⋊C4—1461no—
696C4⋊C4C4⋊#6440811yescharacteristic
697C22⋊C4—2922no—
698C22⋊C4—2922no—
699C22⋊C4—2922no—
700C22⋊C4—2922no—
701C22⋊C4—5841no—
702C22⋊C4—731no—
703C22⋊C4—731no—
704C22⋊C4—731no—
705C22⋊C4—731no—
706C22⋊C4—731no—
707C22⋊C4—731no—
708C22⋊C4C4⋊#6440811yescharacteristic
709C22⋊C4C4⋊#6440811yescharacteristic
710C42—2922no—
711C42—2922no—
712C42—5841no—
713C42—731no—
714C42—731no—
715C42—731no—
716C42C22×#6440811yescharacteristic
717C23—731no—
718C23—731no—
719C23—732no—
720C23—732no—
721C23—731no—
722C23—1461no—
723C23—1461no—
724C23—1461no—
725C23—1461no—
726C23—1461no—
727C23—1461no—
728C23—1461no—
729C23—1461no—
730C23—1461no—
731C23—1461no—
732C23C2×C4⋊#6440811yescharacteristic
733C23C2×C4⋊#6440811yescharacteristic
734D4—22no—
735D4—1462no—
736D4—1462no—
737D4—1462no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—2921no—
743C2×C4—2921no—
744C2×C4—2921no—
745C2×C4—2921no—
746C2×C4—2921no—
747C2×C4—2921no—
748C2×C4—2921no—
749C2×C4—2921no—
750C2×C4—2921no—
751C2×C4—2921no—
752C2×C4—2921no—
753C2×C4—2921no—
754C2×C4—2921no—
755C2×C4—2921no—
756C2×C4—2921no—
757C2×C4—2921no—
758C2×C4—2921no—
759C2×C4—2921no—
760C2×C4—2921no—
761C2×C4—2921no—
762C2×C4—2921no—
763C2×C4—2921no—
764C2×C4—5844no—
765C2×C4—5844no—
766C2×C4—5844no—
767C2×C4—731no—
768C2×C4—731no—
769C2×C4—731no—
770C2×C4—731no—
771C2×C4—731no—
772C2×C4—731no—
773C2×C4—731no—
774C2×C4—731no—
775C2×C4—731no—
776C2×C4—1461no—
777C2×C4—1461no—
778C2×C4—1461no—
779C2×C4—1461no—
780C2×C4—1461no—
781C2×C4—1461no—
782C2×C4—1461no—
783C2×C4—1461no—
784C2×C4—1461no—
785C2×C4—1461no—
786C2×C4—1461no—
787C2×C4—1461no—
788C2×C4—1462no—
789C2×C4—1462no—
790C2×C4—1461no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1461no—
795C2×C4—1461no—
796C2×C4—1461no—
797C2×C4—1461no—
798C2×C4C2×C4⋊#6440811yescharacteristic
799C2×C4C2×C4⋊#6440811yescharacteristic
800C2×C4C2×C4⋊#6440811yescharacteristic
801C2×C4C2×C4⋊#6440811yescharacteristic
802C2×C4C23×#6440811yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—732no—
807C8—1461no—
808C8—1461no—
809C8—1461no—
810C8D4×#6440812yescomplemented
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—2921no—
817C22—2921no—
818C22—2921no—
819C22—2921no—
820C22—731no—
821C22—731no—
822C22—731no—
823C22—731no—
824C22—731no—
825C22—731no—
826C22—732no—
827C22—1462no—
828C22—1462no—
829C22—1462no—
830C22—1462no—
831C22—1461no—
832C22—1461no—
833C22—1461no—
834C22—1461no—
835C22—1461no—
836C22#1798959812yescomplemented
837C22C22×C4⋊#6440811yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—2922no—
843C4—2922no—
844C4—5841no—
845C4—5841no—
846C4—5841no—
847C4—5841no—
848C4—5841no—
849C4—5841no—
850C4—731no—
851C4—731no—
852C4—1461no—
853C4—1461no—
854C4—1461no—
855C4—1461no—
856C4C2×D4×#6440811yescharacteristic
857C4#1798965611yescharacteristic
858C2—22no—
859C2—41no—
860C2—2921no—
861C2—731no—
862C2—731no—
863C2—731no—
864C2—731no—
865C2—1462no—
866C2D4×C4⋊#6440811yescharacteristic
867C2C2×#1798959811yescharacteristic
868C2#2262658611yescharacteristic
subgroupG/H
centerC22C22×C4⋊#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#435×C73C4
socleC22×C73C22×C4⋊C4
prime radicalC2×D4×D73D4
cosocleC2×C4×D73C24
hypercenter#435#64408
hypocenterC73#22661
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#17989598C2semidirect
2. C22×#14556660C2semidirect
5. #22626044C2semidirect
6. #22626042C2semidirect
7. #22625882C2semidirect
8. #22625881C2semidirect
9. #22625880C2semidirect
10. #22625880C2semidirect
11. #22625869C2semidirect
12. #22625809C2semidirect
13. #22625807C2semidirect
14. #22625745C2semidirect
57. #17988661C4semidirect
58. #17988660C4semidirect
59. #17988659C4semidirect
60. #17988658C4semidirect
61. #17988657C4semidirect
62. #17988656C4semidirect
63. #17988655C4semidirect
68. #435×C73C4semidirect
107. #14556660D4semidirect
123. C2×#11924012C2×C4semidirect
124. C2×#11924011C2×C4semidirect
125. C2×#11924011C2×C4semidirect
128. C22×#10596831C2×C4semidirect
131. C2×C8×D73C2×C4semidirect
132. C2×C8×D73C2×C4semidirect
148. C4⋊#10596831C2×C4semidirect
149. #14556520C2×C4semidirect
150. #14556520C2×C4semidirect
151. C22⋊#10596831C2×C4semidirect
152. C22⋊#10596831C2×C4semidirect
153. #14556503C2×C4semidirect
154. #14556503C2×C4semidirect
155. #14556503C2×C4semidirect
156. #14556503C2×C4semidirect
157. #14556502C2×C4semidirect
158. #14556501C2×C4semidirect
159. #14556501C2×C4semidirect
160. C2×M16×C73C2×C4semidirect
161. C22×C8×C73C2×C4semidirect
163. C4⋊C8×C73C2×C4semidirect
164. C22⋊C8×C73C2×C4semidirect
165. C22⋊C8×C73C2×C4semidirect
166. #97×C73C2×C4semidirect
371. C8×C73C4×D4semidirect
375. #10596831C4×D4semidirect
381. C22×C73#428semidirect
396. C2×D73#428semidirect
450. C73#22661semidirect
466. #435#64408semidirect
515. C2×M16C2×#64408semidirect
525. C22×C8C2×#64408semidirect
581. C4⋊C8C2×#64408semidirect
588. C22⋊C8C2×#64408semidirect
589. C22⋊C8C2×#64408semidirect
593. #97C2×#64408semidirect
810. C8D4×#64408semidirect
836. C22#17989598semidirect

Maximal subgroups

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

subgroupindex
C2×#179895982
C22×#145566602
#226264472
D4×C4⋊#644082
#226260442
#226260422
#226258822
#226258812
#226258802
#226258692
#226258092
#226258072
#226257452
#435×D732
#2266173