Finite Group Databasebeta

← #30621752

Subgroups — #30621752

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840752C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic, complemented
4#21462324C211yesmaximal, characteristic, complemented
5#21461966C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461833C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461783C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#103×#6923C211yesmaximal, characteristic, complemented
14#21461554C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840752—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33#16840714—21no—
34#16840714—21no—
35#16840714—21no—
36#16840714C2211yescharacteristic
37#16840714C2211yescharacteristic
38#16840714C2211yescharacteristic
39#16840713C2211yescharacteristic
40#16840712—21no—
41#16840710—21no—
42#16840704—21no—
43#16840704C2211yescharacteristic
44C4⋊C4×#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46C4×C22⋊#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839910C411yescharacteristic, complemented
59#16839909C411yescharacteristic, complemented
60#16839908C411yescharacteristic, complemented
61#16839907C411yescharacteristic, complemented
62#16839906C411yescharacteristic, complemented
63#16839905C411yescharacteristic, complemented
64#16839904C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#449C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×D61⋊C8—22no—
71C2×D61⋊C8—21no—
72C2×D61⋊C8—41no—
73C2×D61⋊C8C2311yescharacteristic
74C2×D61⋊C8C2311yescharacteristic
75C22×#92420—21no—
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923—41no—
79Q8×#6923—41no—
80D4×#6923—22no—
81D4×#6923—41no—
82#14519856—22no—
83#14519856—41no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923D411yescharacteristic
101C2×C22⋊#6923D411yescharacteristic
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104C2×C4×#6923—21no—
105C2×C4×#6923—21no—
106C2×C4×#6923C2311yescharacteristic
107C2×C4×#6923C2311yescharacteristic
108#14519846—41no—
109#14519845—22no—
110#14519840—22no—
111#14519840D414yescomplemented
112#14519839—22no—
113#14519839—22no—
114#14519839—22no—
115#14519839—41no—
116C8×#6923—22no—
117C8×#6923—41no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C2×#11758226C2×C411yescharacteristic, complemented
124C2×#11758222—21no—
125C2×#11758222C2×C411yescharacteristic, complemented
126C2×#11758224—21no—
127C2×#11758224C2×C411yescharacteristic, complemented
128#41×D61—22no—
129#41×D61—22no—
130#41×D61—41no—
131#41×D61—41no—
132C2×Q8×D61C2311yescharacteristic
133C2×D4×D61—21no—
134C2×D4×D61—21no—
135C2×D4×D61C2311yescharacteristic
136C2×D4×D61C2311yescharacteristic
137C22×C4×D61—21no—
138C22×C4×D61C2311yescharacteristic
139C2×#11758190C2×C411yescharacteristic
140C2×#11758200C2×C411yescharacteristic
141C2×#11758201C2×C411yescharacteristic
142SD16×D61—22no—
143SD16×D61—22no—
144C2×D488C2×C411yescharacteristic
145C2×#11758199C2×C411yescharacteristic
146C2×#11758199C2×C411yescharacteristic
147D8×D61—41no—
148D8×D61—41no—
149C2×C8×D61C2311yescharacteristic
150C2×C8×D61C2311yescharacteristic
151#14519752C2×C411yescharacteristic
152#14519751C2×C411yescharacteristic
153#14519750—21no—
154#14519749—21no—
155#14519748C2×C411yescharacteristic
156C4⋊C4×D61C2311yescharacteristic
157C22⋊C4×D61—21no—
158#14519702C2×C411yescharacteristic, complemented
159#14519701C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161#14519699C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic, complemented
164C22⋊#92418C2×C411yescharacteristic, complemented
165#14519689C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167C2×#41×C61C2×C411yescharacteristic, complemented
168C2×SD16×C61C2×C411yescharacteristic
169C2×D8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171#103×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173C22⋊C8×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61—21no—
176C23×D61C2×D411yescharacteristic
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—81no—
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C22×#6923C2×D411yescharacteristic
188#41×C61—22no—
189#41×C61—41no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61C22×C411yescharacteristic
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61—21no—
196C22×C4×C61C22×C411yescharacteristic
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C22×Dic61—21no—
204C22×Dic61#4111yescharacteristic
205#11758226—22no—
206#11758226—41no—
207Q8×D61—21no—
208Q8×D61—21no—
209Q8×D61C2×D412yes—
210Q8×D61#4112yes—
211#11758224—22no—
212#11758224—41no—
213#11758224—42no—
214#11758224—42no—
215D4×D61—21no—
216D4×D61—21no—
217D4×D61—21no—
218D4×D61—21no—
219D4×D61—21no—
220D4×D61—21no—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—42no—
224D4×D61—42no—
225D4×D61—81no—
226D4×D61—81no—
227#11758222—22no—
228#11758222—42no—
229#11758222—42no—
230#11758222—41no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244C22×C411yescharacteristic
234C2×D244C22×C411yescharacteristic
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—42no—
244C2×C4×D61—42no—
245C2×C4×D61C22×C411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61#4111yescharacteristic
248C2×C4×D61C2411yescharacteristic
249C2×Dic122—21no—
250C2×Dic122C22×C411yescharacteristic
251C22⋊#6923—22no—
252C22⋊#6923—22no—
253C22⋊#6923—42no—
254C22⋊#6923—42no—
255C22⋊#6923—42no—
256C22⋊#6923—42no—
257C22⋊#6923—42no—
258C22⋊#6923—81no—
259C22⋊#6923—81no—
260C22⋊#6923—81no—
261C22⋊#6923—81no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—42no—
265C4⋊#6923—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—42no—
273C4⋊#6923—42no—
274C4⋊#6923—81no—
275C4⋊#6923C2×D412yes—
276C4×#6923—21no—
277C4×#6923—21no—
278C4×#6923—21no—
279C4×#6923—21no—
280C4×#6923—42no—
281C4×#6923—42no—
282C4×#6923—42no—
283C4×#6923—81no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8—42no—
288D61⋊C8C2×D412yes—
289SD16×C61—22no—
290D8×C61—41no—
291C2×C8×C61C22×C411yescharacteristic
292C2×C8×C61C22×C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊Dic61—21no—
296#11758201—22no—
297#11758200—22no—
298#11758199—41no—
299#11758199—41no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304C2×#92418C22×C411yescharacteristic
305C2×#92418C22×C411yescharacteristic
306D488—41no—
307#11758190—22no—
308C8×D61—21no—
309C8×D61—21no—
310C8×D61—21no—
311C8×D61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61C4×D411yescharacteristic
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61C4×D411yescharacteristic
336C22×D61C22×D411yescharacteristic
337C2×#6923—21no—
338C2×#6923—21no—
339C2×#6923—21no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—22no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—21no—
347C2×#6923—21no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—84no—
360C2×#6923#13512yes—
361C2×#6923#13512yes—
362Q8×C61—21no—
363Q8×C61C4×D412yes—
364D4×C61—21no—
365D4×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—42no—
369D4×C61—81no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—42no—
375C2×C4×C61C4×D411yescharacteristic
376C2×C4×C61C23×C411yescharacteristic
377C22⋊D61—42no—
378C22⋊D61—42no—
379C22⋊D61—41no—
380C22⋊D61—41no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—81no—
384C22⋊D61—81no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—42no—
390C2×Dic61C4×D411yescharacteristic
391C2×Dic61C2×#4111yescharacteristic
392D244—21no—
393D244—21no—
394D244—21no—
395D244—21no—
396D244—42no—
397D244—81no—
398C4×D61—21no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—42no—
407C4×D61—42no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61C22×D411yescharacteristic
411C4×D61C2×#4111yescharacteristic
412C4×D61H(5,𝔽2)11yescharacteristic
413C4×D61H(5,𝔽2)11yescharacteristic
414Dic122—21no—
415Dic122—22no—
416Dic122—22no—
417Dic122C4×D412yes—
418#92420—22no—
419#92420—41no—
420C8×C61—21no—
421C8×C61—21no—
422#92418—21no—
423#92418—21no—
424#22877—611nomaximal, Sylow
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61C2×C4×D411yescharacteristic
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—41no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C2×D61—81no—
453C2×D61—81no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61D4211yescharacteristic
457C2×D61#54611yescharacteristic
458C2×D61C2×#13511yescharacteristic
459C2×D61C2×#13511yescharacteristic
460C2×D61#57611yescharacteristic
461C2×D61#57711yescharacteristic
462#6923—22no—
463#6923—22no—
464#6923—42no—
465#6923—41no—
466#6923—41no—
467#6923—81no—
468#6923—81no—
469#6923—81no—
470C4×C61—22no—
471C4×C61—21no—
472C4×C61—41no—
473C4×C61C2×C4×D411yescharacteristic
474C4×C61#51811yescharacteristic
475Dic61—22no—
476Dic61—21no—
477Dic61—41no—
478Dic61#54611yescharacteristic
479Dic61#55111yescharacteristic
480C2×#449—611no—
481C2×C4×SD16—611no—
482C2×#416—611no—
483#2363—611no—
484#2341—611no—
485#1970—611no—
486#1934—611no—
487#1926—611no—
488#1893—611no—
489#1880—611no—
490#1879—611no—
491#1863—611no—
492#1854—611no—
493C4×#103—611no—
494C8×C22⋊C4—611no—
495C2×C61—41no—
496C2×C61—81no—
497C2×C61—81no—
498C2×C61#235811yescharacteristic
499C2×C61C4×#13511yescharacteristic
500C2×C61#294611yescharacteristic
501D61—41no—
502D61—81no—
503D61—81no—
504D61#328211yescharacteristic
505D61#328711yescharacteristic
506D61#330111yescharacteristic
507D61#330511yescharacteristic
508C22×#41—611no—
509C22×SD16—611no—
510C22×D8—611no—
511C23×C8—611no—
512C2×#121—611no—
513C2×C4×Q8—611no—
514C2×C4×Q8—611no—
515C2×C4×D4—611no—
516C2×#117—611no—
517#449—611no—
518#449—611no—
519#449—611no—
520#449—611no—
521#449—611no—
522#449—611no—
523#449—611no—
524#449#692311yescharacteristic, complemented
525C4×SD16—1224no—
526C2×#107—611no—
527C2×#106—611no—
528#416—1224no—
529C2×#103—611no—
530C2×#103—611no—
531C2×#103—611no—
532C2×#102—611no—
533C2×#102—611no—
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—611no—
537C2×C22⋊C8—611no—
538C2×C4×C8—611no—
539C2×C4×C8—611no—
540#390—611no—
541#390—611no—
542#390—611no—
543#390—1221no—
544#390—1221no—
545#390—1221no—
546#389—611no—
547#388—1221no—
548#386—1221no—
549#380—611no—
550#380—1221no—
551C4×C4⋊C4—611no—
552C4×C22⋊C4—611no—
553C4×C22⋊C4—1221no—
554C4×C22⋊C4—1221no—
555#340—611no—
556#340—611no—
557#340—611no—
558#340—611no—
559#336—611no—
560#336—611no—
561C61#2287711yescharacteristic, complemented, Sylow
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—611no—
565C2×#41—1221no—
566C2×#41—1221no—
567C2×#41—1222no—
568C2×#41—1222no—
569C2×#41—2441no—
570C2×#41—2441no—
571C2×#41C2×#692311yescharacteristic, complemented
572C22×Q8—611no—
573C22×D4—611no—
574C22×D4—611no—
575C22×D4—1221no—
576C22×D4—1221no—
577C23×C4—611no—
578C23×C4—1221no—
579C23×C4—1221no—
580C2×SD16—611no—
581C2×SD16—611no—
582C2×SD16—611no—
583C2×SD16—1222no—
584C2×SD16—1222no—
585C2×SD16C2×#692311yescharacteristic
586C2×D8—611no—
587C2×D8—611no—
588C2×D8—611no—
589C2×D8—2441no—
590C2×D8—2441no—
591C2×D8C2×#692311yescharacteristic
592C22×C8—611no—
593C22×C8—611no—
594C22×C8—611no—
595C22×C8—611no—
596C22×C8—1222no—
597C22×C8—1221no—
598C22×C8—1221no—
599C22×C8—2441no—
600#121—611no—
601#121—611no—
602#121—611no—
603#121—1221no—
604#121—1221no—
605#121C2×#692311yescharacteristic
606C4×Q8—1222no—
607C4×Q8—1222no—
608C4×Q8—2441no—
609C4×Q8—2441no—
610C4×D4—1222no—
611C4×D4—2441no—
612#117—1222no—
613#117—2441no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—1221no—
620C2×C4⋊C4—1221no—
621C2×C4⋊C4—1221no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—1221no—
637C2×C42—1221no—
638C2×C42—1221no—
639C2×C42—1221no—
640#107—2441no—
641#106—1222no—
642#103—614no—
643#103—611no—
644#103—611no—
645#103—611no—
646#103—1222no—
647#103C2×#692311yescharacteristic, complemented
648#102—611no—
649#102—611no—
650#102—611no—
651#102—1222no—
652#102—1222no—
653#102—1222no—
654#102—2441no—
655#102C2×#692311yescharacteristic, complemented
656C22⋊C8—611no—
657C22⋊C8—611no—
658C22⋊C8—611no—
659C22⋊C8C2×#692311yescharacteristic, complemented
660C4×C8—1222no—
661C4×C8—2441no—
662#95—611no—
663#95—611no—
664#95—1221no—
665#95—1221no—
666#95—1221no—
667C24—611no—
668C24—1221no—
669C24—1221no—
670#41—22no—
671#41—41no—
672#41—1222no—
673#41—1222no—
674#41—1222no—
675#41—2441no—
676#41—2442no—
677#41—2442no—
678#41—2441no—
679#41—2442no—
680#41—2442no—
681#41—2441no—
682C2×Q8—612no—
683C2×Q8—612no—
684C2×Q8—611no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8C22×#692311yescharacteristic
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—611no—
692C2×D4—611no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1221no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—4881no—
710C2×D4—4881no—
711C2×D4—2442no—
712C2×D4—2442no—
713C2×D4C22×#692311yescharacteristic
714C2×D4C22×#692311yescharacteristic
715C22×C4—21no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—4881no—
739C22×C4—2442no—
740C22×C4—2442no—
741C22×C4—2442no—
742C22×C4—2442no—
743C22×C4C22×#692311yescharacteristic
744SD16—22no—
745SD16—1222no—
746SD16—1222no—
747SD16—1222no—
748D8—41no—
749D8—2441no—
750D8—2441no—
751D8—2441no—
752C2×C8—612no—
753C2×C8—611no—
754C2×C8—611no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—2442no—
765C2×C8—2442no—
766C2×C8C22×#692311yescharacteristic
767C2×C8C22×#692311yescharacteristic
768C4⋊C4—612no—
769C4⋊C4—611no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4—1221no—
773C4⋊C4—1221no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—4881no—
779C4⋊C4—2442no—
780C4⋊C4—2442no—
781C4⋊C4C22×#692311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1222no—
786C22⋊C4—1222no—
787C22⋊C4—1221no—
788C22⋊C4—4881no—
789C22⋊C4—4881no—
790C22⋊C4—4881no—
791C22⋊C4—4881no—
792C22⋊C4—2442no—
793C22⋊C4—2442no—
794C22⋊C4—2442no—
795C22⋊C4—2442no—
796C22⋊C4—2442no—
797C42—1221no—
798C42—1221no—
799C42—1221no—
800C42—1221no—
801C42—4881no—
802C42—2442no—
803C42—2442no—
804C42—2442no—
805C23—21no—
806C23—21no—
807C23—611no—
808C23—611no—
809C23—1221no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—2441no—
818C23—2441no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23D4×#692311yescharacteristic
830Q8—21no—
831Q8—612no—
832Q8—1222no—
833Q8—1222no—
834Q8—1221no—
835Q8D4×#692312yes—
836D4—21no—
837D4—21no—
838D4—21no—
839D4—21no—
840D4—42no—
841D4—81no—
842D4—1221no—
843D4—1221no—
844D4—1221no—
845D4—1221no—
846D4—4881no—
847D4—4881no—
848D4—4881no—
849D4—2442no—
850D4—2441no—
851D4—2441no—
852D4—2441no—
853D4—2441no—
854D4—2442no—
855D4—2442no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—42no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—612no—
867C2×C4—612no—
868C2×C4—611no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1222no—
873C2×C4—1222no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1222no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—4884no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2442no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4D4×#692311yescharacteristic
910C2×C4C23×#692311yescharacteristic
911C8—21no—
912C8—21no—
913C8—1222no—
914C8—1221no—
915C8—1221no—
916C8—2441no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—611no—
927C22—611no—
928C22—611no—
929C22—611no—
930C22—611no—
931C22—611no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—4881no—
936C22—4881no—
937C22—4881no—
938C22—4881no—
939C22—4881no—
940C22—4881no—
941C22—4881no—
942C22—4881no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2441no—
951C22—2441no—
952C22—2441no—
953C22C2×D4×#692311yescharacteristic
954C4—21no—
955C4—22no—
956C4—41no—
957C4—611no—
958C4—611no—
959C4—1222no—
960C4—1222no—
961C4—1221no—
962C4—1222no—
963C4—4881no—
964C4—4881no—
965C4—4881no—
966C4—2441no—
967C4—2441no—
968C4—2442no—
969C4—2441no—
970C4C2×D4×#692311yescharacteristic
971C4#1684082911yescharacteristic
972C2—41no—
973C2—81no—
974C2—81no—
975C2—611no—
976C2—611no—
977C2—611no—
978C2—611no—
979C2—4881no—
980C2—4881no—
981C2—2441no—
982C2#2146234111yescharacteristic
983C2#135×#692311yescharacteristic
984C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#449×D61C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#22877
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
2. C2×#16840752C2semidirect
3. #21462346C2semidirect
4. #21462324C2semidirect
5. #21461966C2semidirect
6. #21461909C2semidirect
7. #21461897C2semidirect
8. #21461833C2semidirect
9. #21461815C2semidirect
10. #21461814C2semidirect
11. #21461783C2semidirect
12. #21461770C2semidirect
13. #103×#6923C2semidirect
14. #21461554C2semidirect
58. #16839910C4semidirect
59. #16839909C4semidirect
60. #16839908C4semidirect
61. #16839907C4semidirect
62. #16839906C4semidirect
63. #16839905C4semidirect
64. #16839904C4semidirect
68. C61×#449C4semidirect
111. #14519840D4semidirect
123. C2×#11758226C2×C4semidirect
125. C2×#11758222C2×C4semidirect
127. C2×#11758224C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519701C2×C4semidirect
160. #14519700C2×C4semidirect
161. #14519699C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519697C2×C4semidirect
164. C22⋊#92418C2×C4semidirect
165. #14519689C2×C4semidirect
166. #14519689C2×C4semidirect
167. C2×#41×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. C22⋊C8×C61C2×C4semidirect
524. #449#6923semidirect
561. C61#22877semidirect
571. C2×#41C2×#6923semidirect
647. #103C2×#6923semidirect
655. #102C2×#6923semidirect
659. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407522
#214623462
#214623242
#214619662
#214619092
#214618972
#214618332
#214618152
#214618142
#214617832
#214617702
#103×#69232
#214615542
#449×D612
#2287761