Finite Group Databasebeta

← #11872977

Subgroups — #11872977

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5682C211yesmaximal, characteristic, complemented
2#10593887C211yesmaximal, characteristic, complemented
3#10592753C211yesmaximal, characteristic, complemented
4C3×#5057C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591566C211yesmaximal, characteristic, complemented
7#10591551C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591519C211yesmaximal, characteristic
10Dic3×#213C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10590284C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83461—31nomaximal
17#80510—31nomaximal
18C2×#3795C2211yescharacteristic
19C32×#124C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#886—21no—
30C3×#885—21no—
31C3×#879—21no—
32C3×#878—21no—
33C3×C4×D12C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×#869C2211yescharacteristic
36#63902—21no—
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63879—21no—
40#63878—21no—
41D3×Dic3⋊C4—21no—
42#63844C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×C4⋊(C3⋊C8)C2211yescharacteristic
49#63576C2211yescharacteristic
50#63576C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#542—31no—
62#5682D311yescharacteristic, complemented
63#5546—31no—
64#5523—31no—
65C3×#463—31no—
66#5173—31no—
67#5164—31no—
68#5158—31no—
69Dic3×D8—31no—
70#5091—31no—
71#5087—31no—
72#5057D311yescharacteristic, complemented
73#5054—31no—
74#5054—31no—
75#5054—61no—
76#5047—31no—
77#5044—31no—
78#5037—31no—
79#5033—31no—
80C4×#216—31no—
81#5026—31no—
82#5018—31no—
83C4×#213—31no—
84#5007—31no—
85#5000—31no—
86#4850—31no—
87#4840—31no—
88#4811—31no—
89#4790—31no—
90#4774—31no—
91#4757—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×#625—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3795—22no—
106#3795—22no—
107C32×C22⋊C4—21no—
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110#3756—22no—
111#3754—22no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#215—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3124—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#124—21no—
149C3×#124—61no—
150C3×#124C2×D311yescharacteristic
151C3×#124C2×D311yescharacteristic
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#946C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—61no—
165C2×#215C2×D311yescharacteristic
166#938C2×D311yescharacteristic
167D4×Dic3—31no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—61no—
172C2×#213C2×D311yescharacteristic
173C4×#67—61no—
174C2×C4⋊Dic3—31no—
175C2×Dic3⋊C4—61no—
176#892—61no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179#887—31no—
180#886—21no—
181#885—21no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184#67⋊C4—61no—
185#879—21no—
186#878—21no—
187#877—61no—
188C4×D12—31no—
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191#869C2×D311yescharacteristic
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—31no—
195C4×Dic6—61no—
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#102—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#818—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218C8×Dic3—31no—
219#810—31no—
220#810—31no—
221#809—31no—
222#809—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C32×D4—21no—
241C32×D4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248#634—21no—
249#634#4112yes—
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263C3×Dic6—81no—
264#625—24no—
265D3×Dic3—24no—
266D3×Dic3—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#542—31no—
273#520—91no—
274#484—91no—
275#480—91no—
276#477—91no—
277#474—91no—
278#464—91no—
279#463—31no—
280#452—91no—
281#449—91no—
282#440—91no—
283#440—91no—
284C4×Q16—91no—
285C4×D8—91no—
286#433—91no—
287C2×C3×Q8—21no—
288C2×C3×Q8—61no—
289C2×C3×Q8C22×D311yescharacteristic
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C2×#67—21no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—21no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306#237—62no—
307#237—62no—
308#235—62no—
309#235—62no—
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—21no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—21no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×SD16—62no—
321C3×D8—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—21no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—31no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—21no—
345C3×C42—31no—
346C3×C42—61no—
347C3×C42C22×D311yescharacteristic
348C3×C42C22×D311yescharacteristic
349#217—21no—
350#217—21no—
351#217—61no—
352#216—62no—
353#216—62no—
354#216—122no—
355#215—22no—
356#214—62no—
357#214—62no—
358#214—122no—
359#213—22no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4#6711yescharacteristic
364(C2×D3)⋊C4#6711yescharacteristic
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—121no—
381Dic3⋊C4#6711yescharacteristic
382Dic3⋊C4#6711yescharacteristic
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—121no—
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C2×#41—91no—
422C2×Q16—91no—
423C2×SD16—31no—
424C2×SD16—91no—
425C2×D8—31no—
426C4⋊Q8—31no—
427#126—61no—
428#124—61no—
429#124D3211yescharacteristic
430#123—61no—
431C22⋊Q8—31no—
432C22⋊Q8—61no—
433#121—31no—
434C4×Q8—31no—
435C4×Q8—91no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—91no—
440C4×D4—181no—
441C4×D4—181no—
442#117—31no—
443#117—181no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—181no—
446#107—91no—
447#107—91no—
448#107—91no—
449#107—91no—
450C4⋊C8—31no—
451C4⋊C8—91no—
452#103—31no—
453#103—91no—
454#103—91no—
455#103—91no—
456#102—31no—
457#102—91no—
458#102—91no—
459#102—91no—
460C22⋊C8—91no—
461C22⋊C8—91no—
462#97—91no—
463C4×C8—91no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—31no—
467C23×C3—41no—
468C23×C3—61no—
469C22×D3—21no—
470C22×D3C2×#6711yescharacteristic
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—241no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—32no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—61no—
486C3×D4—241no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—241no—
502C2×C3×C4—241no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C2×#6711yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—64no—
510#67—64no—
511#67—81no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—64no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—81no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—241no—
524C2×Dic3—241no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—21no—
529D12#23712yes—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—64no—
533C4×D3—81no—
534C4×D3—241no—
535C4×D3—241no—
536Dic6—32no—
537Dic6—32no—
538Dic6—62no—
539Dic6—61no—
540Dic6—61no—
541Dic6—81no—
542Dic6—121no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C3⋊C8—121no—
553C2×C32—81no—
554C2×C32#52511yescharacteristic
555C2×C32#57611yescharacteristic
556C2×C32#57811yescharacteristic
557C3×D3—41no—
558C3×D3—42no—
559#41—182no—
560#41—182no—
561C2×Q8—61no—
562C2×Q8—91no—
563C2×Q8C2×D3211yescharacteristic
564C2×D4—31no—
565C2×D4—61no—
566C2×D4—181no—
567C2×D4C2×D3211yescharacteristic
568C22×C4—31no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574Q16—182no—
575SD16—62no—
576SD16—182no—
577D8—62no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—91no—
581C2×C8—91no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—91no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—181no—
603C42—31no—
604C42—61no—
605C42—181no—
606C42—181no—
607C42C2×D3211yescharacteristic
608C22×C3—21no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—62no—
618C22×C3—61no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×#6711yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4D3×#4111yescharacteristic
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—41no—
657Dic3—41no—
658Dic3—41no—
659Dic3—62no—
660Dic3—62no—
661Dic3—122no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665C32#312411yescharacteristic, complemented, Sylow
666C23—21no—
667C23—31no—
668C23—61no—
669Q8—21no—
670Q8—21no—
671Q8—92no—
672Q8—181no—
673Q8—241no—
674D4—21no—
675D4—21no—
676D4—32no—
677D4—61no—
678D4—184no—
679D4—241no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—184no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—241no—
693C2×C4—241no—
694C2×C4—721no—
695C2×C4—721no—
696C2×C4D3×#6711yescharacteristic
697C2×C4D3×#6711yescharacteristic
698C2×C4C22×D3211yescharacteristic
699C8—61no—
700C8—61no—
701C8—181no—
702C8—181no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—81no—
707C2×C3—81no—
708C2×C3—122no—
709C2×C3—121no—
710C2×C3—161no—
711C2×C3#560611yescharacteristic
712C2×C3#577111yescharacteristic
713C2×C3#577411yescharacteristic
714C2×C3#582811yescharacteristic
715C2×C3#583511yescharacteristic
716C2×C3#583811yescharacteristic
717D3—41no—
718D3—42no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22—62no—
726C22—121no—
727C22—121no—
728C22C2×D3×#6711yescharacteristic
729C4—21no—
730C4—21no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—182no—
739C4—361no—
740C4D3×#23711yescharacteristic
741C4#6431211yescharacteristic
742C3—21no—
743C3#8051011yescharacteristic, complemented
744C3#8346111yescharacteristic, complemented
745C2—81no—
746C2—121no—
747C2—122no—
748C2#1059530111yescharacteristic
749C2#1059545411yescharacteristic
750C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radical#10591519C2
hypercenter#124D32
hypocenterC32#3124
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5682C2semidirect
2. #10593887C2semidirect
3. #10592753C2semidirect
4. C3×#5057C2semidirect
5. #10591655C2semidirect
6. #10591566C2semidirect
7. #10591551C2semidirect
8. #10591537C2semidirect
10. Dic3×#213C2semidirect
11. #10591413C2semidirect
12. #10591405C2semidirect
13. #10590284C2semidirect
14. #10590269C2semidirect
15. #10590253C2semidirect
62. #5682D3semidirect
72. #5057D3semidirect
665. C32#3124semidirect
743. C3#80510semidirect
744. C3#83461semidirect

Maximal subgroups

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

subgroupindex
C3×#56822
#105938872
#105927532
C3×#50572
#105916552
#105915662
#105915512
#105915372
#105915192
Dic3×#2132
#105914132
#105914052
#105902842
#105902692
#105902532
#834613
#805103