Finite Group Databasebeta

← #30621760

Subgroups — #30621760

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840755C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic
4Q8×C22⋊#6923C211yesmaximal, characteristic, complemented
5#21461969C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461898C211yesmaximal, characteristic, complemented
8#21461835C211yesmaximal, characteristic
9#21461815C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461783C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#21461592C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#448×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21SD16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840755—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8—21no—
34(C2×#6923)⋊Q8—21no—
35(C2×#6923)⋊Q8C2211yescharacteristic
36(C2×#6923)⋊Q8C2211yescharacteristic
37#16840714—21no—
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
54C22×Q8×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839903C411yescharacteristic, complemented
59#16839902C411yescharacteristic, complemented
60#16839902C411yescharacteristic, complemented
61#16839901C411yescharacteristic, complemented
62#16839900C411yescharacteristic, complemented
63#16839899C411yescharacteristic, complemented
64#16839899C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#448C411yescharacteristic, complemented
69C23×#6923—21no—
70C2×#11758213—21no—
71D61⋊M16—22no—
72D61⋊M16—41no—
73C2×#11758217—21no—
74C2×D61⋊C8C2311yescharacteristic
75C2×D61⋊C8C2311yescharacteristic
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⋊#6923D411yescharacteristic
97C2×C22⋊#6923D411yescharacteristic
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519846—41no—
105#14519845—22no—
106#14519840—22no—
107#14519840—22no—
108#14519840—22no—
109#14519840D414yescomplemented
110#14519839—22no—
111#14519839—41no—
112#14519831—41no—
113C8×#6923—22no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C22×Dic122—21no—
124C22×Dic122C2×C411yescharacteristic, complemented
125C2×Q8×D61—21no—
126C2×Q8×D61—21no—
127C2×Q8×D61—22no—
128C2×Q8×D61—22no—
129C2×Q8×D61—41no—
130C2×Q8×D61—41no—
131C2×Q8×D61C2×C411yescharacteristic, complemented
132C2×Q8×D61C2×C411yescharacteristic, complemented
133C2×Q8×D61C2311yescharacteristic
134C2×Q8×D61C2311yescharacteristic
135C2×D4×D61—21no—
136C2×D4×D61C2311yescharacteristic
137C22×C4×D61—21no—
138C22×C4×D61C2311yescharacteristic
139C2×#11758190C2×C411yescharacteristic
140C2×#11758190C2×C411yescharacteristic
141C2×#11758200C2×C411yescharacteristic
142C2×#11758200C2×C411yescharacteristic
143C2×#11758201C2×C411yescharacteristic
144C2×#11758201C2×C411yescharacteristic
145SD16×D61—22no—
146SD16×D61—22no—
147SD16×D61—41no—
148SD16×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#14519702C2×C411yescharacteristic, complemented
160#14519701C2×C411yescharacteristic, complemented
161#14519701C2×C411yescharacteristic, complemented
162#14519700C2×C411yescharacteristic, complemented
163#14519700C2×C411yescharacteristic, complemented
164C22⋊#92418C2×C411yescharacteristic, complemented
165#14519689C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167C22×Q8×C61C2×C411yescharacteristic, complemented
168C2×SD16×C61C2×C411yescharacteristic
169C2×SD16×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171#103×C61C2×C411yescharacteristic, complemented
172#103×C61C2×C411yescharacteristic, complemented
173C22⋊C8×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61C2×D411yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—42no—
181C22×#6923—42no—
182C22×#6923—81no—
183C22×#6923C2×D411yescharacteristic
184C22×#6923C2×D411yescharacteristic
185C22×#6923C2×D411yescharacteristic
186C22×#6923C2×D411yescharacteristic
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—41no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×Q8×C61C22×C411yescharacteristic
192C2×D4×C61—21no—
193C2×D4×C61C22×C411yescharacteristic
194C22×C4×C61—21no—
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—21no—
200C22×Dic61#4111yescharacteristic
201Q8×D61—21no—
202Q8×D61—21no—
203Q8×D61—22no—
204Q8×D61—21no—
205Q8×D61—21no—
206Q8×D61—21no—
207Q8×D61—21no—
208Q8×D61—22no—
209Q8×D61—41no—
210Q8×D61—41no—
211Q8×D61—42no—
212Q8×D61—42no—
213Q8×D61—42no—
214Q8×D61—42no—
215Q8×D61C2×D412yes—
216Q8×D61#4112yes—
217D4×D61—21no—
218D4×D61—21no—
219D4×D61—21no—
220D4×D61—21no—
221D4×D61—81no—
222D4×D61—81no—
223C2×D244—21no—
224C2×D244C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61C22×C411yescharacteristic
237C2×C4×D61C2×D411yescharacteristic
238C2×C4×D61#4111yescharacteristic
239C2×C4×D61C2411yescharacteristic
240C2×Dic122—21no—
241C2×Dic122—22no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—41no—
247C2×Dic122—42no—
248C2×Dic122—42no—
249C2×Dic122C22×C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251C22⋊#6923—22no—
252C22⋊#6923—41no—
253C22⋊#6923—42no—
254C22⋊#6923—42no—
255C22⋊#6923—42no—
256C22⋊#6923—42no—
257C22⋊#6923—81no—
258#11758217—42no—
259C2×#92420—21no—
260C2×#92420—21no—
261C4⋊#6923—21no—
262C4⋊#6923—21no—
263C4⋊#6923—21no—
264C4⋊#6923—21no—
265C4⋊#6923—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—42no—
269C4⋊#6923—42no—
270C4⋊#6923—81no—
271C4⋊#6923C2×D412yes—
272C4×#6923—21no—
273C4×#6923—21no—
274C4×#6923—21no—
275C4×#6923—21no—
276C4×#6923—42no—
277C4×#6923—42no—
278C4×#6923—42no—
279C4×#6923—81no—
280#11758213—42no—
281D61⋊C8—21no—
282D61⋊C8—21no—
283D61⋊C8—21no—
284D61⋊C8C2×D412yes—
285SD16×C61—22no—
286SD16×C61—41no—
287C2×C8×C61C22×C411yescharacteristic
288C2×C8×C61C22×C411yescharacteristic
289C4⋊C4×C61C22×C411yescharacteristic
290C22⋊C4×C61—21no—
291C22⋊Dic61—21no—
292#11758201—22no—
293#11758201—41no—
294#11758200—22no—
295#11758200—41no—
296#11758198—21no—
297#11758198—21no—
298C4⋊Dic61C22×C411yescharacteristic
299#11758196—21no—
300C2×#92418C22×C411yescharacteristic
301C2×#92418C22×C411yescharacteristic
302#11758190—22no—
303#11758190—41no—
304C8×D61—21no—
305C8×D61—21no—
306C8×D61—21no—
307C8×D61—21no—
308C23×C61—21no—
309C23×C61C4×D411yescharacteristic
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—41no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61C4×D411yescharacteristic
324C22×D61C22×D411yescharacteristic
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—21no—
328C2×#6923—22no—
329C2×#6923—21no—
330C2×#6923—21no—
331C2×#6923—21no—
332C2×#6923—21no—
333C2×#6923—21no—
334C2×#6923—21no—
335C2×#6923—21no—
336C2×#6923—21no—
337C2×#6923—41no—
338C2×#6923—41no—
339C2×#6923—41no—
340C2×#6923—41no—
341C2×#6923—41no—
342C2×#6923—41no—
343C2×#6923—41no—
344C2×#6923—41no—
345C2×#6923—41no—
346C2×#6923—41no—
347C2×#6923—41no—
348C2×#6923—84no—
349C2×#6923#13712yes—
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—21no—
353Q8×C61—42no—
354Q8×C61C4×D412yes—
355D4×C61—21no—
356D4×C61—21no—
357D4×C61—81no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—42no—
364C2×C4×C61C4×D411yescharacteristic
365C2×C4×C61C23×C411yescharacteristic
366C22⋊D61—41no—
367C22⋊D61—41no—
368C22⋊D61—81no—
369C22⋊D61—81no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—42no—
376C2×Dic61C4×D411yescharacteristic
377C2×Dic61C2×#4111yescharacteristic
378D244—21no—
379D244—21no—
380D244—81no—
381C4×D61—21no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—21no—
385C4×D61—21no—
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—42no—
390C4×D61—42no—
391C4×D61—41no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61C22×D411yescharacteristic
396C4×D61C2×#4111yescharacteristic
397C4×D61H(5,𝔽2)11yescharacteristic
398C4×D61H(5,𝔽2)11yescharacteristic
399Dic122—21no—
400Dic122—22no—
401Dic122—22no—
402Dic122—21no—
403Dic122—21no—
404Dic122—42no—
405Dic122—42no—
406Dic122—42no—
407Dic122—41no—
408Dic122—41no—
409Dic122C4×D412yes—
410#92420—22no—
411#92420—41no—
412C8×C61—21no—
413C8×C61—21no—
414#92418—21no—
415#92418—21no—
416#22885—611nomaximal, Sylow
417C22×C61—21no—
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61C2×C4×D411yescharacteristic
424C2×D61—21no—
425C2×D61—21no—
426C2×D61—21no—
427C2×D61—41no—
428C2×D61—41no—
429C2×D61—41no—
430C2×D61—41no—
431C2×D61—41no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—81no—
435C2×D61—81no—
436C2×D61—81no—
437C2×D61—81no—
438C2×D61D4211yescharacteristic
439C2×D61#54611yescharacteristic
440C2×D61C2×#13711yescharacteristic
441C2×D61#57511yescharacteristic
442C2×D61#57711yescharacteristic
443C2×D61#57711yescharacteristic
444#6923—22no—
445#6923—41no—
446#6923—42no—
447#6923—41no—
448#6923—41no—
449#6923—81no—
450#6923—81no—
451#6923—81no—
452C4×C61—22no—
453C4×C61—21no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61C2×C4×D411yescharacteristic
457C4×C61#51811yescharacteristic
458Dic61—22no—
459Dic61—21no—
460Dic61—41no—
461Dic61—41no—
462Dic61#54611yescharacteristic
463Dic61#55111yescharacteristic
464C2×#448—611no—
465C2×C4×SD16—611no—
466C2×#419—611no—
467#2363—611no—
468Q8×C22⋊C4—611no—
469#1973—611no—
470#1933—611no—
471#1927—611no—
472#1895—611no—
473#1880—611no—
474#1877—611no—
475#1863—611no—
476#1854—611no—
477#1763—611no—
478#1753—611no—
479C2×C61—41no—
480C2×C61—81no—
481C2×C61#235811yescharacteristic
482C2×C61C4×#13711yescharacteristic
483C2×C61#294911yescharacteristic
484D61—41no—
485D61—81no—
486D61#326611yescharacteristic
487D61#327111yescharacteristic
488D61#332611yescharacteristic
489D61#332911yescharacteristic
490C23×Q8—611no—
491C22×SD16—611no—
492C22×SD16—611no—
493C22×M16—611no—
494C2×#121—611no—
495C2×C4×Q8—611no—
496C2×C4×Q8—611no—
497C2×C4×D4—611no—
498C2×#117—611no—
499#448—611no—
500#448—611no—
501#448—611no—
502#448—611no—
503#448—611no—
504#448—611no—
505#448—611no—
506#448#692311yescharacteristic, complemented
507C4×SD16—1224no—
508C2×#107—611no—
509C2×#106—611no—
510#419—1224no—
511C2×#103—611no—
512C2×#103—611no—
513C2×#103—611no—
514C2×#103—611no—
515C2×#103—611no—
516C2×#103—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×C22⋊C8—611no—
520C2×#97—611no—
521C2×C4×C8—611no—
522#391—611no—
523#391—611no—
524#391—1221no—
525#391—1221no—
526#390—611no—
527#390—1221no—
528#389—611no—
529#388—1221no—
530#386—1221no—
531#380—611no—
532#380—1221no—
533C4×C4⋊C4—611no—
534C4×C22⋊C4—611no—
535C4×C22⋊C4—1221no—
536C4×C22⋊C4—1221no—
537#340—611no—
538#340—611no—
539#340—611no—
540#340—611no—
541#336—611no—
542#336—611no—
543C61#2288511yescharacteristic, complemented, Sylow
544C22×Q8—611no—
545C22×Q8—611no—
546C22×Q8—611no—
547C22×Q8—611no—
548C22×Q8—611no—
549C22×Q8—1221no—
550C22×Q8—1221no—
551C22×Q8—1221no—
552C22×Q8—1222no—
553C22×Q8—1222no—
554C22×Q8—2441no—
555C22×Q8—2441no—
556C22×Q8C2×#692311yescharacteristic, complemented
557C22×D4—611no—
558C22×D4—1221no—
559C23×C4—611no—
560C23×C4—1221no—
561C23×C4—1221no—
562C2×SD16—611no—
563C2×SD16—611no—
564C2×SD16—611no—
565C2×SD16—611no—
566C2×SD16—611no—
567C2×SD16—611no—
568C2×SD16—1222no—
569C2×SD16—1222no—
570C2×SD16—2441no—
571C2×SD16—2441no—
572C2×SD16C2×#692311yescharacteristic
573C2×SD16C2×#692311yescharacteristic
574C2×M16—1222no—
575C2×M16—1221no—
576C2×M16—1221no—
577C2×M16—2441no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582#121—611no—
583#121—611no—
584#121—611no—
585#121—1221no—
586#121—1221no—
587#121C2×#692311yescharacteristic
588C4×Q8—1222no—
589C4×Q8—1222no—
590C4×Q8—2441no—
591C4×Q8—2441no—
592C4×D4—1222no—
593C4×D4—2441no—
594#117—1222no—
595#117—2441no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C22⋊C4—611no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C22⋊C4—1221no—
611C2×C22⋊C4—1221no—
612C2×C42—611no—
613C2×C42—611no—
614C2×C42—1221no—
615C2×C42—1221no—
616C2×C42—1221no—
617C2×C42—1221no—
618#107—2441no—
619#106—1222no—
620#103—614no—
621#103—611no—
622#103—611no—
623#103—611no—
624#103—611no—
625#103—611no—
626#103—611no—
627#103—1222no—
628#103—1222no—
629#103—1222no—
630#103C2×#692311yescharacteristic, complemented
631#103C2×#692311yescharacteristic, complemented
632#102—1222no—
633#102—2441no—
634C22⋊C8—611no—
635C22⋊C8—611no—
636C22⋊C8—611no—
637C22⋊C8C2×#692311yescharacteristic, complemented
638#97—2441no—
639C4×C8—1222no—
640#95—611no—
641#95—611no—
642#95—1221no—
643#95—1221no—
644#95—1221no—
645#95—1221no—
646#95—1221no—
647#95—1221no—
648#95—1221no—
649C24—611no—
650C24—1221no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—41no—
654C2×Q8—612no—
655C2×Q8—612no—
656C2×Q8—611no—
657C2×Q8—611no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8—1221no—
661C2×Q8—1221no—
662C2×Q8—1222no—
663C2×Q8—1221no—
664C2×Q8—1221no—
665C2×Q8—1221no—
666C2×Q8—1221no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1222no—
671C2×Q8—1222no—
672C2×Q8—2441no—
673C2×Q8—2442no—
674C2×Q8—2442no—
675C2×Q8—2442no—
676C2×Q8—2442no—
677C2×Q8—2441no—
678C2×Q8—2441no—
679C2×Q8—2442no—
680C2×Q8—2442no—
681C2×Q8C22×#692311yescharacteristic
682C2×Q8C22×#692311yescharacteristic
683C2×D4—21no—
684C2×D4—611no—
685C2×D4—1221no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—4881no—
694C2×D4—4881no—
695C2×D4C22×#692311yescharacteristic
696C22×C4—21no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—611no—
704C22×C4—611no—
705C22×C4—611no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—1221no—
710C22×C4—1221no—
711C22×C4—1221no—
712C22×C4—1221no—
713C22×C4—1221no—
714C22×C4—1221no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—4881no—
721C22×C4—2442no—
722C22×C4—2442no—
723C22×C4—2442no—
724C22×C4—2442no—
725C22×C4C22×#692311yescharacteristic
726SD16—22no—
727SD16—41no—
728SD16—1222no—
729SD16—1222no—
730SD16—1222no—
731SD16—2441no—
732SD16—2441no—
733SD16—2441no—
734M16—2442no—
735M16—2442no—
736C2×C8—612no—
737C2×C8—611no—
738C2×C8—611no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8C22×#692311yescharacteristic
749C2×C8C22×#692311yescharacteristic
750C4⋊C4—612no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—4881no—
761C4⋊C4—2442no—
762C4⋊C4—2442no—
763C4⋊C4C22×#692311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1222no—
768C22⋊C4—1221no—
769C22⋊C4—4881no—
770C22⋊C4—2441no—
771C22⋊C4—2442no—
772C22⋊C4—2442no—
773C22⋊C4—2442no—
774C22⋊C4—2442no—
775C42—1221no—
776C42—1221no—
777C42—1221no—
778C42—1221no—
779C42—4881no—
780C42—2442no—
781C42—2442no—
782C42—2442no—
783C23—21no—
784C23—611no—
785C23—611no—
786C23—1221no—
787C23—1221no—
788C23—1221no—
789C23—1221no—
790C23—1221no—
791C23—1221no—
792C23—1221no—
793C23—2441no—
794C23—2441no—
795C23—2441no—
796C23—2441no—
797C23—2441no—
798C23—2441no—
799C23D4×#692311yescharacteristic
800Q8—21no—
801Q8—21no—
802Q8—21no—
803Q8—42no—
804Q8—612no—
805Q8—1222no—
806Q8—1222no—
807Q8—1221no—
808Q8—1221no—
809Q8—1221no—
810Q8—2442no—
811Q8—2442no—
812Q8—2441no—
813Q8—2441no—
814Q8—2442no—
815Q8D4×#692312yes—
816D4—21no—
817D4—21no—
818D4—81no—
819D4—1221no—
820D4—1221no—
821D4—4881no—
822D4—4881no—
823D4—4881no—
824D4—2441no—
825D4—2441no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—42no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—611no—
835C2×C4—611no—
836C2×C4—611no—
837C2×C4—612no—
838C2×C4—611no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1222no—
843C2×C4—1222no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—1221no—
851C2×C4—1221no—
852C2×C4—1221no—
853C2×C4—1221no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1222no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—1221no—
861C2×C4—1221no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—4884no—
865C2×C4—2442no—
866C2×C4—2442no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2442no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4D4×#692311yescharacteristic
884C2×C4C23×#692311yescharacteristic
885C8—21no—
886C8—21no—
887C8—1222no—
888C8—1221no—
889C8—1221no—
890C8—2441no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—611no—
898C22—611no—
899C22—611no—
900C22—611no—
901C22—611no—
902C22—611no—
903C22—1221no—
904C22—1221no—
905C22—1221no—
906C22—4881no—
907C22—4881no—
908C22—4881no—
909C22—4881no—
910C22—2441no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22—2441no—
915C22—2441no—
916C22—2441no—
917C22C2×D4×#692311yescharacteristic
918C4—21no—
919C4—22no—
920C4—41no—
921C4—41no—
922C4—611no—
923C4—611no—
924C4—1222no—
925C4—1221no—
926C4—1222no—
927C4—4881no—
928C4—4881no—
929C4—4881no—
930C4—2441no—
931C4—2441no—
932C4—2441no—
933C4—2442no—
934C4—2441no—
935C4—2441no—
936C4C2×D4×#692311yescharacteristic
937C4#1684082911yescharacteristic
938C2—41no—
939C2—81no—
940C2—611no—
941C2—611no—
942C2—611no—
943C2—611no—
944C2—4881no—
945C2—2441no—
946C2#2146234111yescharacteristic
947C2#137×#692311yescharacteristic
948C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#448C4
socleC22×C61C2×C4×D4
prime radical#121×D61C22
cosocleC2×C4×D61C24
hypercenter#448#6923
hypocenterC61#22885
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
2. C2×#16840755C2semidirect
4. Q8×C22⋊#6923C2semidirect
5. #21461969C2semidirect
6. #21461908C2semidirect
7. #21461898C2semidirect
9. #21461815C2semidirect
10. #21461812C2semidirect
11. #21461783C2semidirect
12. #21461770C2semidirect
13. #21461592C2semidirect
14. #21461562C2semidirect
58. #16839903C4semidirect
59. #16839902C4semidirect
60. #16839902C4semidirect
61. #16839901C4semidirect
62. #16839900C4semidirect
63. #16839899C4semidirect
64. #16839899C4semidirect
68. C61×#448C4semidirect
109. #14519840D4semidirect
124. C22×Dic122C2×C4semidirect
131. C2×Q8×D61C2×C4semidirect
132. C2×Q8×D61C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519702C2×C4semidirect
160. #14519701C2×C4semidirect
161. #14519701C2×C4semidirect
162. #14519700C2×C4semidirect
163. #14519700C2×C4semidirect
164. C22⋊#92418C2×C4semidirect
165. #14519689C2×C4semidirect
166. #14519689C2×C4semidirect
167. C22×Q8×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
172. #103×C61C2×C4semidirect
173. C22⋊C8×C61C2×C4semidirect
506. #448#6923semidirect
543. C61#22885semidirect
556. C22×Q8C2×#6923semidirect
630. #103C2×#6923semidirect
631. #103C2×#6923semidirect
637. 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×#168407552
#214623462
Q8×C22⋊#69232
#214619692
#214619082
#214618982
#214618352
#214618152
#214618122
#214617832
#214617702
#214615922
#214615622
#448×D612
#2288561