Finite Group Databasebeta

← #29696720

Subgroups — #29696720

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic122C211yesmaximal, characteristic
2M16×Dic122C211yesmaximal, characteristic, complemented
3#21448291C211yesmaximal, characteristic, complemented
4#21446800C211yesmaximal, characteristic, complemented
5#21446798C211yesmaximal, characteristic, complemented
6#21446794C211yesmaximal, characteristic, complemented
7#21446763C211yesmaximal, characteristic, complemented
8#21446761C211yesmaximal, characteristic, complemented
9#21446761C211yesmaximal, characteristic, complemented
10#21445839C211yesmaximal, characteristic
11#21445837C211yesmaximal, characteristic
12#21445837C211yesmaximal, characteristic
13#21445631C211yesmaximal, characteristic
14#104×Dic61C211yesmaximal, characteristic
15C61×#1759C211yesmaximal, characteristic
16Q8×Dic122C411yescharacteristic, complemented
17#16840491C411yescharacteristic, complemented
18#16840488C411yescharacteristic, complemented
19#16840488C411yescharacteristic, complemented
20#16840471—21no—
21#16840471—21no—
22#16840471C411yescharacteristic, complemented
23#16840471C411yescharacteristic, complemented
24#16840469—21no—
25#16840469C411yescharacteristic, complemented
26D4×Dic122—21no—
27D4×Dic122C411yescharacteristic, complemented
28#16840319—21no—
29#16840319C2211yescharacteristic
30#16840315—21no—
31#16840315—21no—
32#16840315C2211yescharacteristic
33#16840315C2211yescharacteristic
34#41×Dic61C2211yescharacteristic
35#41×Dic61C2211yescharacteristic
36C2×C4×Dic122—21no—
37C2×C4×Dic122C2211yescharacteristic
38#16839892—21no—
39#16839890—21no—
40#16839890—21no—
41C8×Dic122—21no—
42#16839786C2211yescharacteristic
43#16839785C2211yescharacteristic
44#16839785C2211yescharacteristic
45C2×#14519704C2211yescharacteristic
46C2×#14519704C2211yescharacteristic
47M16×Dic61C2211yescharacteristic
48M16×Dic61C2211yescharacteristic
49#16839666—21no—
50#16839659—21no—
51#16839649—21no—
52#16839645—21no—
53C4×#11758196C2211yescharacteristic
54C4×#11758196C2211yescharacteristic
55C4×C4⋊Dic61C2211yescharacteristic
56#16839608C2211yescharacteristic
57C42×Dic61C2211yescharacteristic
58#16839523C2211yescharacteristic
59#16839523C2211yescharacteristic
60#16839523C2211yescharacteristic
61#16839523C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
64#16839522C2211yescharacteristic
65#16839522C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C2×#104×C61C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C4×M16×C61C2211yescharacteristic
72C61×#376C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C22×Dic122—21no—
76C22×Dic122D411yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79#14519777—21no—
80#14519777—21no—
81#14519777C2×C411yescharacteristic
82#14519777C2×C411yescharacteristic
83#14519776—21no—
84#14519776—21no—
85#14519776—21no—
86#14519776—21no—
87#14519776C2×C411yescharacteristic
88#14519776C2×C411yescharacteristic
89#14519776C2×C411yescharacteristic
90#14519776C2×C411yescharacteristic
91#14519769—21no—
92#14519769—21no—
93#14519769C2×C411yescharacteristic
94#14519769C2×C411yescharacteristic
95#14519768—21no—
96#14519768—21no—
97#14519768—21no—
98#14519768—21no—
99#14519768C2×C411yescharacteristic
100#14519768C2×C411yescharacteristic
101#14519768C2×C411yescharacteristic
102#14519768C2×C411yescharacteristic
103#14519756—21no—
104#14519756—21no—
105#14519756—21no—
106#14519756—21no—
107#14519756—21no—
108#14519756—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519754—21no—
114#14519754—21no—
115#14519754—21no—
116#14519754—21no—
117#14519754—21no—
118#14519754—21no—
119#14519754—21no—
120#14519754—21no—
121Q8×Dic61C2×C411yescharacteristic
122Q8×Dic61C2×C411yescharacteristic
123Q8×Dic61C2×C411yescharacteristic
124Q8×Dic61C2×C411yescharacteristic
125C4×Dic122—21no—
126C4×Dic122—21no—
127C4×Dic122—21no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×Dic122C2×C411yescharacteristic
136C4×Dic122C2×C411yescharacteristic
137C4×Dic122C2×C411yescharacteristic
138C4×Dic122C2×C411yescharacteristic
139C4×Dic122D411yescharacteristic
140C4×Dic122D411yescharacteristic
141C4×Dic122D411yescharacteristic
142C4×Dic122D411yescharacteristic
143D4×Dic61—21no—
144D4×Dic61—21no—
145D4×Dic61—21no—
146D4×Dic61—21no—
147D4×Dic61C2×C411yescharacteristic
148D4×Dic61C2×C411yescharacteristic
149D4×Dic61C2×C411yescharacteristic
150D4×Dic61C2×C411yescharacteristic
151#14519736—21no—
152#14519736—21no—
153#14519736C2311yescharacteristic
154#14519736C2311yescharacteristic
155C2×C4⋊Dic61—21no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61D411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×#11758196D411yescharacteristic
163C2×#11758196D411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61—21no—
168C2×C4×Dic61C2311yescharacteristic
169C2×C4×Dic61C2311yescharacteristic
170C2×C4×Dic61C2311yescharacteristic
171C2×C4×Dic61C2311yescharacteristic
172C4⋊#92418—21no—
173C4⋊#92418—21no—
174#14519706—21no—
175#14519706—21no—
176#14519706—21no—
177#14519706—21no—
178#14519704—22no—
179#14519704—22no—
180#14519687—21no—
181#14519687—21no—
182C8×Dic61—21no—
183C8×Dic61—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189C2×#41×C61C2311yescharacteristic
190C2×M16×C61C2311yescharacteristic
191C2×M16×C61C2311yescharacteristic
192C4×Q8×C61C2×C411yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61—21no—
196C4×D4×C61C2×C411yescharacteristic
197C4×D4×C61C2×C411yescharacteristic
198#117×C61—21no—
199#117×C61C2311yescharacteristic
200C2×C42×C61—21no—
201C2×C42×C61C2311yescharacteristic
202C2×C42×C61C2311yescharacteristic
203C2×C42×C61C2311yescharacteristic
204#104×C61—22no—
205#104×C61Q814yescomplemented
206#97×C61—21no—
207C4×C8×C61—21no—
208#95×C61—21no—
209#95×C61—21no—
210#41×C61—21no—
211#41×C61—21no—
212#41×C61C2×Q812yes—
213#41×C61#4112yes—
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2411yescharacteristic
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—42no—
242C2×Dic122—44no—
243C2×Dic122C22⋊C411yescharacteristic
244C2×Dic122C22⋊C411yescharacteristic
245C2×Dic122C22⋊C411yescharacteristic
246C2×Dic122C22⋊C411yescharacteristic
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61C2×Q812yescomplemented
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C22×C411yescharacteristic
256C4⋊C4×C61C22×C411yescharacteristic
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—21no—
266C42×C61C22×C411yescharacteristic
267C42×C61C22×C411yescharacteristic
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2×Q812yescomplemented
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—42no—
288C4⋊Dic61C22⋊C411yescharacteristic
289C4⋊Dic61C22⋊C411yescharacteristic
290C4⋊Dic61C22⋊C411yescharacteristic
291C4⋊Dic61C22⋊C411yescharacteristic
292C4⋊Dic61C22×C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—42no—
309#11758196—42no—
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—21no—
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—42no—
329C4×Dic61—42no—
330C4×Dic61C22×C411yescharacteristic
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194—21no—
342C2×#92418—21no—
343C2×#92418—21no—
344C23×C61—21no—
345C23×C61C22×D411yescharacteristic
346Q8×C61—21no—
347Q8×C61C4×Q812yes—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—21no—
351D4×C61C4×Q812yes—
352C2×C4×C61—21no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—42no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—81no—
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C23×C411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×Q811yescharacteristic
374C2×C4×C61C2×#4111yescharacteristic
375C2×C4×C612−1+411yescharacteristic
376C2×C4×C612−1+411yescharacteristic
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—21no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—42no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—42no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—81no—
394C2×Dic61—81no—
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403Dic122—22no—
404Dic122—22no—
405Dic122—41no—
406Dic122—41no—
407Dic122—42no—
408Dic122—42no—
409Dic122—42no—
410Dic122—81no—
411Dic122—81no—
412Dic122—81no—
413C8×C61—22no—
414C8×C61—41no—
415#92418—41no—
416#92418—41no—
417#22529—611nomaximal, Sylow
418C22×C61—21no—
419C22×C61—21no—
420C22×C61—22no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61C22×C22⋊C411yescharacteristic
424C22×C61#54811yescharacteristic
425C22×C61D4×Q811yescharacteristic
426C4×C61—22no—
427C4×C61—21no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—42no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—81no—
435C4×C61C2×C4×Q811yescharacteristic
436C4×C61#51911yescharacteristic
437C4×C61#54811yescharacteristic
438C4×C61D4×Q811yescharacteristic
439Dic61—21no—
440Dic61—21no—
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—21no—
446Dic61—42no—
447Dic61—41no—
448Dic61—41no—
449Dic61—41no—
450Dic61—41no—
451Dic61—81no—
452Dic61#42112yes—
453Q8×#41—611no—
454Q8×M16—611no—
455#2295—611no—
456#1995—611no—
457#1995—611no—
458#1994—611no—
459#1986—611no—
460#1986—611no—
461#1986—611no—
462#1806—611no—
463#1806—611no—
464#1806—611no—
465#1759—611no—
466#1759D6111yescharacteristic
467C4×#104—611no—
468C2×C61—21no—
469C2×C61—21no—
470C2×C61—42no—
471C2×C61Q8×C22⋊C411yescharacteristic
472C2×C61C2×#42111yescharacteristic
473C2×C61#290111yescharacteristic
474Q82—611no—
475#557—611no—
476#557—611no—
477#557—611no—
478#554—611no—
479#554—611no—
480#554—611no—
481#554—1221no—
482#554—1221no—
483#554—1221no—
484D4×Q8—611no—
485D4×Q8—1221no—
486#533—611no—
487#533—611no—
488#533—611no—
489#533—1221no—
490#533—1221no—
491#533—1221no—
492C4×#41—611no—
493C4×#41—611no—
494C4×#41C2×D6111yescharacteristic
495C2×C4×Q8—611no—
496C2×C4×Q8—1221no—
497#446—1221no—
498#446—1221no—
499#446—1221no—
500C8×Q8—1221no—
501#423—611no—
502#423—611no—
503#423—611no—
504C2×#104—611no—
505C2×#104—611no—
506C2×#104C2×D6111yescharacteristic
507C2×#104C2×D6111yescharacteristic
508C4×M16—611no—
509C4×M16—611no—
510C4×M16C2×D6111yescharacteristic
511#391—1221no—
512#389—1221no—
513#387—1221no—
514#387—1221no—
515C4×C4⋊C4—611no—
516C4×C4⋊C4—611no—
517C4×C4⋊C4—611no—
518#376—611no—
519#376C2×D6111yescharacteristic
520C43—611no—
521#339—611no—
522#339—611no—
523#339—611no—
524#339—611no—
525#339—611no—
526#339—611no—
527#339—611no—
528#339—611no—
529#339—611no—
530#339—611no—
531#339C2×D6111yescharacteristic
532#339C2×D6111yescharacteristic
533C61#2252911yescharacteristic, complemented, Sylow
534C2×#41C22×D6111yescharacteristic
535C22×Q8—611no—
536C22×Q8—1221no—
537C2×M16—611no—
538C2×M16—611no—
539C2×M16C22×D6111yescharacteristic
540C2×M16C22×D6111yescharacteristic
541C4⋊Q8—611no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—611no—
545C4⋊Q8—611no—
546C4⋊Q8—611no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8—1221no—
552C4⋊Q8—1221no—
553#125—611no—
554#125—611no—
555#125—611no—
556#125—611no—
557#125—611no—
558#125—611no—
559#125—1221no—
560#125—1221no—
561#125—1221no—
562#125—1221no—
563#125—1221no—
564#125—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—611no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—1221no—
596C4×Q8—1221no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×Q8—1221no—
600C4×Q8—1221no—
601C4×Q8—1221no—
602C4×Q8—1221no—
603C4×Q8—1221no—
604C4×Q8—1221no—
605C4×Q8C4×D6111yescharacteristic
606C4×Q8C4×D6111yescharacteristic
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—611no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—1221no—
614C4×D4—1221no—
615C4×D4—1221no—
616C4×D4—1221no—
617C4×D4C4×D6111yescharacteristic
618C4×D4C4×D6111yescharacteristic
619#117—21no—
620#117—611no—
621#117—611no—
622#117—1221no—
623#117—1221no—
624#117C22×D6111yescharacteristic
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4—1221no—
631C2×C4⋊C4—1221no—
632C2×C4⋊C4—1221no—
633C2×C4⋊C4—1221no—
634C2×C42—21no—
635C2×C42—611no—
636C2×C42—611no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—1221no—
640C2×C42—1221no—
641C2×C42—1221no—
642C2×C42—1221no—
643C2×C42C22×D6111yescharacteristic
644C2×C42C22×D6111yescharacteristic
645C2×C42C22×D6111yescharacteristic
646C4⋊C8—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652#104—22no—
653#104—1222no—
654#104—1222no—
655#104Dic12214yescomplemented
656#97—21no—
657#97—1221no—
658#97—1221no—
659C4×C8—21no—
660C4×C8—1221no—
661C4×C8—1221no—
662#95—21no—
663#95—21no—
664#95—1221no—
665#95—1221no—
666#95—1221no—
667#95—1221no—
668#95—1221no—
669#41—21no—
670#41—21no—
671#41C2×Dic12212yes—
672#41#1175822212yes—
673C2×Q8—611no—
674C2×Q8—611no—
675C2×Q8—611no—
676C2×Q8—611no—
677C2×Q8—1221no—
678C2×Q8—1221no—
679C2×Q8—1221no—
680C2×Q8—1221no—
681C2×Q8—1221no—
682C2×Q8—1221no—
683C2×Q8—2442no—
684C2×Q8—2444no—
685C2×Q8C2×C4×D6111yescharacteristic
686C2×D4—21no—
687C2×D4C2×C4×D6111yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4D4×D6111yescharacteristic
704C22×C4D4×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706M16—21no—
707M16—21no—
708M16—21no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—1221no—
713M16C2×Dic12212yescomplemented
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—1221no—
717C2×C8—1221no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—611no—
729C4⋊C4—611no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—2442no—
759C4⋊C4—2442no—
760C4⋊C4—2442no—
761C4⋊C4C2×C4×D6111yescharacteristic
762C4⋊C4C2×C4×D6111yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—21no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—611no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42—1221no—
795C42—1221no—
796C42—2442no—
797C42—2442no—
798C42C2×Dic12212yescomplemented
799C42C2×C4×D6111yescharacteristic
800C42C2×C4×D6111yescharacteristic
801C42D4×D6111yescharacteristic
802C42D4×D6111yescharacteristic
803C23—21no—
804C23C2×D4×D6111yescharacteristic
805Q8—21no—
806Q8—1222no—
807Q8—1222no—
808Q8—4881no—
809Q8—4881no—
810Q8—4881no—
811Q8—2441no—
812Q8—2441no—
813Q8—2442no—
814Q8—2442no—
815Q8—2442no—
816Q8C4×Dic12212yes—
817D4—22no—
818D4—22no—
819D4—21no—
820D4C4×Dic12212yes—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—81no—
836C2×C4—611no—
837C2×C4—611no—
838C2×C4—611no—
839C2×C4—611no—
840C2×C4—611no—
841C2×C4—611no—
842C2×C4—611no—
843C2×C4—611no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1221no—
847C2×C4—1221no—
848C2×C4—1221no—
849C2×C4—1221no—
850C2×C4—4881no—
851C2×C4—4881no—
852C2×C4—2442no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2442no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4—2441no—
862C2×C4C22⋊C4×D6111yescharacteristic
863C2×C4C22⋊C4×D6111yescharacteristic
864C2×C4C22⋊C4×D6111yescharacteristic
865C2×C4C22⋊C4×D6111yescharacteristic
866C2×C4C22×C4×D6111yescharacteristic
867C2×C4C2×D4×D6111yescharacteristic
868C2×C4C22×Dic12211yescharacteristic
869C2×C4C2×#1175822211yescharacteristic
870C2×C4#1451982411yescharacteristic
871C2×C4#1451982411yescharacteristic
872C8—22no—
873C8—41no—
874C8—2441no—
875C8—2441no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—41no—
880C22—41no—
881C22C2×C22⋊C4×D6111yescharacteristic
882C22#1684042111yescharacteristic
883C22D4×Dic12211yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—22no—
889C4—42no—
890C4—41no—
891C4—41no—
892C4—81no—
893C4—612no—
894C4—1221no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—1221no—
901C4—4881no—
902C4—2442no—
903C4—2441no—
904C4—2441no—
905C4—2441no—
906C4—2441no—
907C4C2×C4×Dic12211yescharacteristic
908C4#1684023911yescharacteristic
909C4#1684042111yescharacteristic
910C4D4×Dic12211yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2C22⋊C4×Dic12211yescharacteristic
915C2#421×D6111yescharacteristic
916C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×C61C23
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#22529
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. M16×Dic122C2semidirect
3. #21448291C2semidirect
4. #21446800C2semidirect
5. #21446798C2semidirect
6. #21446794C2semidirect
7. #21446763C2semidirect
8. #21446761C2semidirect
9. #21446761C2semidirect
16. Q8×Dic122C4semidirect
17. #16840491C4semidirect
18. #16840488C4semidirect
19. #16840488C4semidirect
22. #16840471C4semidirect
23. #16840471C4semidirect
25. #16840469C4semidirect
27. D4×Dic122C4semidirect
205. #104×C61Q8semidirect
250. M16×C61C2×Q8semidirect
270. C42×C61C2×Q8semidirect
533. C61#22529semidirect
655. #104Dic122semidirect
713. M16C2×Dic122semidirect
798. C42C2×Dic122semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1222
M16×Dic1222
#214482912
#214468002
#214467982
#214467942
#214467632
#214467612
#214458392
#214458372
#214456312
#104×Dic612
C61×#17592
#2252961