Finite Group Databasebeta

← #30616882

Subgroups — #30616882

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840831C211yesmaximal, characteristic
2C2×#16840801C211yesmaximal, characteristic, complemented
3C2×Q16×#6923C211yesmaximal, characteristic, complemented
4#21462306C211yesmaximal, characteristic, complemented
5#21461813C211yesmaximal, characteristic, complemented
6#21461812C211yesmaximal, characteristic, complemented
7#21461804C211yesmaximal, characteristic, complemented
8#21461783C211yesmaximal, characteristic, complemented
9#21461782C211yesmaximal, characteristic, complemented
10#21461768C211yesmaximal, characteristic, complemented
11#21461659C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#452×D61C211yesmaximal, characteristic
16#16840831—24no—
17#16840831—24no—
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20C2×Q8×#6923C2211yescharacteristic
21C2×D4×#6923—21no—
22C2×D4×#6923—21no—
23C2×D4×#6923C2211yescharacteristic
24C2×D4×#6923C2211yescharacteristic
25C2×#14519856—21no—
26C2×#14519856C2211yescharacteristic
27C22×C4⋊#6923—21no—
28C22×C4⋊#6923C2211yescharacteristic
29#16840801—24no—
30Q16×#6923—24no—
31C2×#14519846C2211yescharacteristic
32C2×#14519846C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519840C2211yescharacteristic
37C2×#14519839C2211yescharacteristic
38C2×#14519839C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40C2×#14519831C2211yescharacteristic
41C2×C8×#6923C2211yescharacteristic
42(C2×#6923)⋊Q8C2211yescharacteristic
43#16840713—21no—
44#16840713C2211yescharacteristic
45#16840712—21no—
46#16840712—21no—
47#16840711—21no—
48#16840704C2211yescharacteristic
49C4⋊C4×#6923C2211yescharacteristic
50#16840636C2211yescharacteristic
51#16840636C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54(C2×#6923)⋊C8C2211yescharacteristic
55(C2×#6923)⋊C8C2211yescharacteristic
56C2×#41×D61C2211yescharacteristic
57C2×Q16×D61C2211yescharacteristic
58C2×SD16×D61C2211yescharacteristic
59C22⋊Q8×D61C2211yescharacteristic
60#16839927C411yescharacteristic, complemented
61#16839926C411yescharacteristic, complemented
62#16839925C411yescharacteristic, complemented
63#16839924C411yescharacteristic, complemented
64#16839923C411yescharacteristic, complemented
65#16839922C411yescharacteristic, complemented
66#16839921C411yescharacteristic, complemented
67#103×D61C2211yescharacteristic
68#102×D61C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#452C411yescharacteristic, complemented
71C23×#6923—21no—
72C23×#6923—21no—
73C23×#6923—21no—
74C2×D61⋊C8C2311yescharacteristic
75C2×D61⋊C8C2311yescharacteristic
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923—22no—
79Q8×#6923—22no—
80Q8×#6923—22no—
81Q8×#6923D414yes—
82D4×#6923—28no—
83D4×#6923—28no—
84D4×#6923—22no—
85D4×#6923—22no—
86D4×#6923—22no—
87D4×#6923D414yes—
88#14519856—28no—
89#14519856—22no—
90#14519856—22no—
91C2×C4⋊#6923—28no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—22no—
96C2×C4⋊#6923—22no—
97C2×C4⋊#6923—21no—
98C2×C4⋊#6923—21no—
99C2×C4⋊#6923D411yescharacteristic
100C2×C4⋊#6923D411yescharacteristic
101C2×C4⋊#6923C2311yescharacteristic
102C2×C4⋊#6923C2311yescharacteristic
103C2×C4⋊#6923C2311yescharacteristic
104C2×C4⋊#6923C2311yescharacteristic
105C2×C22⋊#6923—21no—
106C2×C22⋊#6923—21no—
107C2×C22⋊#6923—21no—
108C2×C22⋊#6923D411yescharacteristic
109C2×C22⋊#6923D411yescharacteristic
110C2×C4×#6923—21no—
111C2×C4×#6923—21no—
112C2×C4×#6923—21no—
113C2×C4×#6923—21no—
114C2×C4×#6923C2311yescharacteristic
115C2×C4×#6923C2311yescharacteristic
116#14519846—22no—
117#14519846—22no—
118#14519840—22no—
119#14519840—22no—
120#14519840—22no—
121#14519840—22no—
122#14519839—22no—
123#14519839—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126#14519831—22no—
127C8×#6923—22no—
128(C2×#6923)⋊C4—21no—
129(C2×#6923)⋊C4—21no—
130(C2×#6923)⋊C4—21no—
131(C2×#6923)⋊C4—21no—
132(C2×#6923)⋊C4—21no—
133C2×#11758226C2×C411yescharacteristic
134C2×#11758222—21no—
135C2×#11758222C2×C411yescharacteristic
136C2×#11758224—21no—
137C2×#11758224C2×C411yescharacteristic
138#41×D61—22no—
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142C2×Q8×D61C2311yescharacteristic
143C2×Q8×D61C2311yescharacteristic
144C2×D4×D61—21no—
145C2×D4×D61C2311yescharacteristic
146C22×C4×D61—21no—
147C22×C4×D61C2311yescharacteristic
148C2×Dic244C2×C411yescharacteristic, complemented
149C2×#11758202C2×C411yescharacteristic, complemented
150C2×#11758202C2×C411yescharacteristic, complemented
151Q16×D61—22no—
152Q16×D61—22no—
153C2×#11758190C2×C411yescharacteristic, complemented
154C2×#11758200C2×C411yescharacteristic, complemented
155C2×#11758201C2×C411yescharacteristic, complemented
156SD16×D61—22no—
157SD16×D61—22no—
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519757C2×C411yescharacteristic, complemented
161#14519756C2×C411yescharacteristic, complemented
162#14519755—21no—
163#14519754—21no—
164#14519753C2×C411yescharacteristic, complemented
165C4⋊C4×D61—21no—
166C4⋊C4×D61C2311yescharacteristic
167C22⋊C4×D61—21no—
168#14519702C2×C411yescharacteristic, complemented
169#14519701C2×C411yescharacteristic, complemented
170#14519700C2×C411yescharacteristic, complemented
171#14519699C2×C411yescharacteristic, complemented
172#14519698C2×C411yescharacteristic, complemented
173#14519697C2×C411yescharacteristic, complemented
174C22⋊#92418C2×C411yescharacteristic, complemented
175#14519689C2×C411yescharacteristic, complemented
176#14519689C2×C411yescharacteristic, complemented
177C2×#41×C61C2×C411yescharacteristic
178C2×Q16×C61C2×C411yescharacteristic, complemented
179C2×SD16×C61C2×C411yescharacteristic, complemented
180C22⋊Q8×C61C2×C411yescharacteristic, complemented
181#103×C61C2×C411yescharacteristic, complemented
182#102×C61C2×C411yescharacteristic, complemented
183C22⋊C8×C61C2×C411yescharacteristic, complemented
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C22×#6923—21no—
187C22×#6923—21no—
188C22×#6923—24no—
189C22×#6923—24no—
190C22×#6923—24no—
191C22×#6923—21no—
192C22×#6923—21no—
193C22×#6923—81no—
194C22×#6923—81no—
195C22×#6923—81no—
196C22×#6923—81no—
197C22×#6923—81no—
198C22×#6923—81no—
199C22×#6923C2×D411yescharacteristic
200C22×#6923C2×D411yescharacteristic
201C22×#6923C2×D411yescharacteristic
202C22×#6923C2×D411yescharacteristic
203#41×C61—22no—
204#41×C61—22no—
205C2×Q8×C61C22×C411yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61C22×C411yescharacteristic
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C22×Dic61—21no—
215C22×Dic61#4111yescharacteristic
216#11758226—22no—
217#11758226—22no—
218Q8×D61—21no—
219Q8×D61—21no—
220Q8×D61—21no—
221Q8×D61—21no—
222Q8×D61—21no—
223Q8×D61—21no—
224Q8×D61C2×D412yes—
225Q8×D61#4112yes—
226#11758224—24no—
227#11758224—24no—
228#11758224—22no—
229#11758224—22no—
230D4×D61—24no—
231D4×D61—24no—
232D4×D61—21no—
233D4×D61—21no—
234D4×D61C2×D412yes—
235D4×D61#4112yes—
236#11758222—24no—
237#11758222—24no—
238#11758222—22no—
239#11758222—22no—
240C2×D244—21no—
241C2×D244C22×C411yescharacteristic
242C2×C4×D61—24no—
243C2×C4×D61—24no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C2×D411yescharacteristic
255C2×C4×D61#4111yescharacteristic
256C2×C4×D61C2411yescharacteristic
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C22×C411yescharacteristic
260C2×Dic122C22×C411yescharacteristic
261C22⋊#6923—24no—
262C22⋊#6923—24no—
263C22⋊#6923—22no—
264C22⋊#6923—22no—
265C22⋊#6923—81no—
266C2×#92420—21no—
267C2×#92420—21no—
268C4⋊#6923—24no—
269C4⋊#6923—24no—
270C4⋊#6923—22no—
271C4⋊#6923—24no—
272C4⋊#6923—22no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—21no—
276C4⋊#6923—21no—
277C4⋊#6923—21no—
278C4⋊#6923—21no—
279C4⋊#6923—42no—
280C4⋊#6923—81no—
281C4⋊#6923C2×D412yes—
282C4⋊#6923C2×D412yes—
283C4×#6923—24no—
284C4×#6923—24no—
285C4×#6923—21no—
286C4×#6923—21no—
287C4×#6923—42no—
288C4×#6923—81no—
289C4×#6923C2×D412yes—
290C4×#6923C2×D412yes—
291D61⋊C8—21no—
292D61⋊C8—21no—
293D61⋊C8—21no—
294D61⋊C8—21no—
295Q16×C61—22no—
296SD16×C61—22no—
297C2×C8×C61C22×C411yescharacteristic
298C2×C8×C61C22×C411yescharacteristic
299C4⋊C4×C61—21no—
300C4⋊C4×C61C22×C411yescharacteristic
301C22⋊C4×C61—21no—
302C22⋊Dic61—21no—
303#11758202—22no—
304#11758202—22no—
305#11758201—22no—
306#11758200—22no—
307#11758198—21no—
308#11758198—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61C22×C411yescharacteristic
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314C2×#92418C22×C411yescharacteristic
315C2×#92418C22×C411yescharacteristic
316Dic244—22no—
317#11758190—22no—
318C8×D61—21no—
319C8×D61—21no—
320C8×D61—21no—
321C8×D61—21no—
322C23×C61—21no—
323C23×C61C4×D411yescharacteristic
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—22no—
327C22×D61—21no—
328C22×D61—22no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—21no—
332C22×D61—21no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61C4×D411yescharacteristic
338C22×D61C22×D411yescharacteristic
339C2×#6923—21no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—21no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—22no—
346C2×#6923—22no—
347C2×#6923—21no—
348C2×#6923—21no—
349C2×#6923—21no—
350C2×#6923—21no—
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—41no—
360C2×#6923—41no—
361C2×#6923—84no—
362C2×#6923—84no—
363C2×#6923—84no—
364C2×#6923#12012yes—
365C2×#6923#12012yes—
366Q8×C61—21no—
367Q8×C61—21no—
368Q8×C61—21no—
369Q8×C61C4×D412yes—
370D4×C61—24no—
371D4×C61—21no—
372D4×C61C4×D412yes—
373C2×C4×C61—24no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61C4×D411yescharacteristic
380C2×C4×C61C23×C411yescharacteristic
381C22⋊D61—24no—
382C22⋊D61—24no—
383C22⋊D61—22no—
384C22⋊D61—22no—
385C2×Dic61—24no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61C4×D411yescharacteristic
392C2×Dic61C2×#4111yescharacteristic
393D244—24no—
394D244—21no—
395D244C4×D412yes—
396C4×D61—24no—
397C4×D61—24no—
398C4×D61—22no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—22no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61C22×D411yescharacteristic
411C4×D61C22×D411yescharacteristic
412C4×D61C2×#4111yescharacteristic
413C4×D61C2×#4111yescharacteristic
414Dic122—21no—
415Dic122—22no—
416Dic122—22no—
417Dic122—21no—
418Dic122—21no—
419Dic122—41no—
420Dic122—41no—
421Dic122C4×D412yes—
422#92420—41no—
423#92420—41no—
424C8×C61—21no—
425C8×C61—21no—
426#92418—21no—
427#92418—21no—
428#21465—611nomaximal, Sylow
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—22no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61C2×C4×D411yescharacteristic
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—22no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—42no—
446C2×D61—41no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—42no—
450C2×D61C2×#12011yescharacteristic
451C2×D61#52511yescharacteristic
452C2×D61#57611yescharacteristic
453C2×D61#57711yescharacteristic
454C2×D61#57811yescharacteristic
455C2×D61#57811yescharacteristic
456#6923—22no—
457#6923—22no—
458#6923—41no—
459#6923—41no—
460#6923—42no—
461#6923—42no—
462#6923—81no—
463#6923—81no—
464C4×C61—22no—
465C4×C61—21no—
466C4×C61—41no—
467C4×C61—41no—
468C4×C61C2×C4×D411yescharacteristic
469C4×C61C2×C4×D411yescharacteristic
470Dic61—22no—
471Dic61—21no—
472Dic61—41no—
473Dic61—41no—
474Dic61#52511yescharacteristic
475Dic61#52511yescharacteristic
476C2×#520—611no—
477C2×#452—611no—
478C2×#440—611no—
479C2×C4×Q16—611no—
480#2323—611no—
481#1878—611no—
482#1877—611no—
483#1872—611no—
484#1863—611no—
485#1862—611no—
486#1852—611no—
487#1788—611no—
488#1763—611no—
489C4×#102—611no—
490#1750—611no—
491C2×C61—41no—
492C2×C61—42no—
493C2×C61C4×#12011yescharacteristic
494C2×C61#294711yescharacteristic
495C2×C61#295111yescharacteristic
496D61—41no—
497D61—42no—
498D61#301111yescharacteristic
499D61#301211yescharacteristic
500D61#312011yescharacteristic
501D61#312411yescharacteristic
502C22×#41—611no—
503C22×Q16—611no—
504C22×SD16—611no—
505C2×C22⋊Q8—611no—
506#520—1224no—
507#520—1224no—
508C2×C4×Q8—611no—
509C2×C4×Q8—611no—
510C2×C4×Q8—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×C4×D4—1221no—
514C2×C4×D4—1221no—
515C2×#117—611no—
516C2×#117—1221no—
517C22×C4⋊C4—611no—
518C22×C4⋊C4—1221no—
519#452—611no—
520#452—611no—
521#452—611no—
522#452—611no—
523#452—611no—
524#452—611no—
525#452—611no—
526#452#692311yescharacteristic, complemented
527#440—1224no—
528C4×Q16—1224no—
529C2×#107—611no—
530C2×#107—611no—
531C2×#103—611no—
532C2×#103—611no—
533C2×#103—611no—
534C2×#103—611no—
535C2×#103—611no—
536C2×#102—611no—
537C2×#102—611no—
538C2×#102—611no—
539C2×C22⋊C8—611no—
540C2×C22⋊C8—611no—
541C2×#97—611no—
542C2×C4×C8—611no—
543#391—611no—
544#389—611no—
545#389—1221no—
546#388—1221no—
547#388—1221no—
548#387—1221no—
549#380—611no—
550C4×C4⋊C4—611no—
551#340—611no—
552#340—611no—
553#340—611no—
554#340—611no—
555#336—611no—
556#336—611no—
557C61#2146511yescharacteristic, complemented, Sylow
558C2×#41—611no—
559C2×#41—611no—
560C2×#41—611no—
561C2×#41—1221no—
562C2×#41—1221no—
563C2×#41—1222no—
564C2×#41—1222no—
565C2×#41—1222no—
566C2×#41—1222no—
567C2×#41C2×#692311yescharacteristic
568C22×Q8—611no—
569C22×Q8—611no—
570C22×D4—611no—
571C22×D4—1221no—
572C23×C4—611no—
573C23×C4—1221no—
574C23×C4—1221no—
575C23×C4—1221no—
576C23×C4—1221no—
577C2×Q16—611no—
578C2×Q16—611no—
579C2×Q16—611no—
580C2×Q16—1222no—
581C2×Q16—1222no—
582C2×Q16C2×#692311yescharacteristic, complemented
583C2×SD16—611no—
584C2×SD16—611no—
585C2×SD16—611no—
586C2×SD16—1222no—
587C2×SD16—1222no—
588C2×SD16C2×#692311yescharacteristic, complemented
589C22×C8—611no—
590C22×C8—611no—
591C22×C8—611no—
592C22×C8—611no—
593C22⋊Q8—611no—
594C22⋊Q8—611no—
595C22⋊Q8—611no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8C2×#692311yescharacteristic, complemented
599C4×Q8—614no—
600C4×Q8—1222no—
601C4×Q8—1222no—
602C4×Q8—1222no—
603C4×Q8—1222no—
604C4×Q8—1222no—
605C4×D4—614no—
606C4×D4—1222no—
607C4×D4—1222no—
608C4×D4—1222no—
609C4×D4—1228no—
610C4×D4—1228no—
611#117—1222no—
612#117—1222no—
613#117—1228no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—611no—
616C2×C4⋊C4—611no—
617C2×C4⋊C4—611no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—1221no—
622C2×C4⋊C4—1222no—
623C2×C4⋊C4—1222no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1228no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C22⋊C4—611no—
631C2×C22⋊C4—611no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—1221no—
639C2×C42—1221no—
640C2×C42—1221no—
641C2×C42—1221no—
642#107—1222no—
643#107—1222no—
644#103—611no—
645#103—611no—
646#103—611no—
647#103—1222no—
648#103—1222no—
649#103—1222no—
650#103—1222no—
651#103C2×#692311yescharacteristic, complemented
652#102—611no—
653#102—611no—
654#102—611no—
655#102—1222no—
656#102—1222no—
657#102C2×#692311yescharacteristic, complemented
658C22⋊C8—611no—
659C22⋊C8—611no—
660C22⋊C8—611no—
661C22⋊C8—1221no—
662C22⋊C8—1221no—
663C22⋊C8C2×#692311yescharacteristic, complemented
664#97—1222no—
665C4×C8—1222no—
666#95—1221no—
667#95—1221no—
668#95—1221no—
669#95—1221no—
670#95—1221no—
671C24—611no—
672C24—1221no—
673#41—22no—
674#41—22no—
675#41—1222no—
676#41—1222no—
677#41—1224no—
678#41—1224no—
679#41—1222no—
680#41—1224no—
681#41—1224no—
682#41—1222no—
683#41—1222no—
684#41—1222no—
685C2×Q8—612no—
686C2×Q8—612no—
687C2×Q8—611no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—1221no—
693C2×Q8—1221no—
694C2×Q8—1221no—
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8C22×#692311yescharacteristic
698C2×Q8C22×#692311yescharacteristic
699C2×D4—21no—
700C2×D4—612no—
701C2×D4—612no—
702C2×D4—611no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1224no—
708C2×D4—1224no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4C22×#692311yescharacteristic
712C22×C4—21no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1224no—
729C22×C4—1224no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1224no—
734C22×C4—1221no—
735C22×C4—1224no—
736C22×C4—1224no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—4881no—
742C22×C4—4881no—
743C22×C4—4881no—
744C22×C4—4881no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4C22×#692311yescharacteristic
748Q16—22no—
749Q16—1222no—
750Q16—1222no—
751Q16—1222no—
752SD16—22no—
753SD16—1222no—
754SD16—1222no—
755SD16—1222no—
756C2×C8—611no—
757C2×C8—611no—
758C2×C8—1221no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8C22×#692311yescharacteristic
769C2×C8C22×#692311yescharacteristic
770C4⋊C4—21no—
771C4⋊C4—612no—
772C4⋊C4—612no—
773C4⋊C4—611no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1222no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1222no—
781C4⋊C4—1224no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1224no—
787C4⋊C4—1224no—
788C4⋊C4—1221no—
789C4⋊C4—4881no—
790C4⋊C4—2442no—
791C4⋊C4C22×#692311yescharacteristic
792C22⋊C4—21no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1222no—
796C22⋊C4—1222no—
797C22⋊C4—1224no—
798C22⋊C4—1224no—
799C22⋊C4—1221no—
800C22⋊C4—4881no—
801C42—612no—
802C42—612no—
803C42—1221no—
804C42—1221no—
805C42—1224no—
806C42—1224no—
807C42—4881no—
808C42—2442no—
809C23—21no—
810C23—611no—
811C23—611no—
812C23—1222no—
813C23—1221no—
814C23—1221no—
815C23—1222no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23D4×#692311yescharacteristic
826Q8—21no—
827Q8—21no—
828Q8—21no—
829Q8—612no—
830Q8—1222no—
831Q8—1222no—
832Q8—1221no—
833Q8—1221no—
834Q8—1221no—
835Q8—2441no—
836Q8—2441no—
837Q8D4×#692312yes—
838D4—24no—
839D4—21no—
840D4—612no—
841D4—1224no—
842D4—1222no—
843D4—1222no—
844D4—1224no—
845D4—1224no—
846D4—1221no—
847D4D4×#692312yes—
848C2×C4—24no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—611no—
855C2×C4—611no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—612no—
860C2×C4—612no—
861C2×C4—611no—
862C2×C4—1221no—
863C2×C4—1221no—
864C2×C4—1222no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1222no—
868C2×C4—1224no—
869C2×C4—1224no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1224no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—4884no—
891C2×C4—4884no—
892C2×C4—4884no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
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×C4D4×#692311yescharacteristic
908C2×C4C23×#692311yescharacteristic
909C8—21no—
910C8—21no—
911C8—1221no—
912C8—1221no—
913C8—2441no—
914C8—2441no—
915C22—21no—
916C22—22no—
917C22—21no—
918C22—21no—
919C22—41no—
920C22—41no—
921C22—611no—
922C22—611no—
923C22—611no—
924C22—611no—
925C22—611no—
926C22—611no—
927C22—1222no—
928C22—1221no—
929C22—1221no—
930C22—1221no—
931C22—2441no—
932C22—2442no—
933C22—2441no—
934C22—2441no—
935C22—2441no—
936C22—2442no—
937C22—2442no—
938C22—2442no—
939C22—2441no—
940C22—2441no—
941C22C2×D4×#692311yescharacteristic
942C4—21no—
943C4—22no—
944C4—41no—
945C4—41no—
946C4—611no—
947C4—611no—
948C4—1222no—
949C4—1222no—
950C4—1221no—
951C4—1222no—
952C4—4881no—
953C4—4881no—
954C4—2441no—
955C4—2441no—
956C4—2442no—
957C4—2442no—
958C4—2441no—
959C4—2441no—
960C4C2×D4×#692311yescharacteristic
961C4C2×D4×#692311yescharacteristic
962C2—41no—
963C2—42no—
964C2—611no—
965C2—611no—
966C2—611no—
967C2—611no—
968C2—2441no—
969C2—2442no—
970C2#120×#692311yescharacteristic
971C2#2146257711yescharacteristic
972C2#2146258111yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#452#6923
hypocenterC61#21465
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. C2×#16840801C2semidirect
3. C2×Q16×#6923C2semidirect
4. #21462306C2semidirect
5. #21461813C2semidirect
6. #21461812C2semidirect
7. #21461804C2semidirect
8. #21461783C2semidirect
9. #21461782C2semidirect
10. #21461768C2semidirect
12. #21461592C2semidirect
13. #102×#6923C2semidirect
14. #21461550C2semidirect
60. #16839927C4semidirect
61. #16839926C4semidirect
62. #16839925C4semidirect
63. #16839924C4semidirect
64. #16839923C4semidirect
65. #16839922C4semidirect
66. #16839921C4semidirect
70. C61×#452C4semidirect
148. C2×Dic244C2×C4semidirect
149. C2×#11758202C2×C4semidirect
150. C2×#11758202C2×C4semidirect
153. C2×#11758190C2×C4semidirect
154. C2×#11758200C2×C4semidirect
155. C2×#11758201C2×C4semidirect
160. #14519757C2×C4semidirect
161. #14519756C2×C4semidirect
164. #14519753C2×C4semidirect
168. #14519702C2×C4semidirect
169. #14519701C2×C4semidirect
170. #14519700C2×C4semidirect
171. #14519699C2×C4semidirect
172. #14519698C2×C4semidirect
173. #14519697C2×C4semidirect
174. C22⋊#92418C2×C4semidirect
175. #14519689C2×C4semidirect
176. #14519689C2×C4semidirect
178. C2×Q16×C61C2×C4semidirect
179. C2×SD16×C61C2×C4semidirect
180. C22⋊Q8×C61C2×C4semidirect
181. #103×C61C2×C4semidirect
182. #102×C61C2×C4semidirect
183. C22⋊C8×C61C2×C4semidirect
526. #452#6923semidirect
557. C61#21465semidirect
582. C2×Q16C2×#6923semidirect
588. C2×SD16C2×#6923semidirect
598. C22⋊Q8C2×#6923semidirect
651. #103C2×#6923semidirect
657. #102C2×#6923semidirect
663. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408312
C2×#168408012
C2×Q16×#69232
#214623062
#214618132
#214618122
#214618042
#214617832
#214617822
#214617682
#214616592
#214615922
#102×#69232
#214615502
#452×D612
#2146561