Finite Group Databasebeta

← #11872141

Subgroups — #11872141

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic, complemented
2#10594983C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10591468C211yesmaximal, characteristic, complemented
6#10591468C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591410C211yesmaximal, characteristic, complemented
10#10591408C211yesmaximal, characteristic, complemented
11#10591405C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591134C211yesmaximal, characteristic, complemented
14#10591090C211yesmaximal, characteristic, complemented
15#10591056C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17#79992—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×C3×#217—21no—
23C2×C3×#217—21no—
24C3×D4×Dic3—21no—
25C3×D4×Dic3—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C3×#926C2211yescharacteristic
35#63969—21no—
36#63959—21no—
37#63918C2211yescharacteristic, complemented
38#63899—21no—
39Dic3×D12C2211yescharacteristic, complemented
40#63860C2211yescharacteristic, complemented
41#63858—21no—
42#63844C2211yescharacteristic, complemented
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63576C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5798D311yescharacteristic, complemented
63#5603—31no—
64#5534—31no—
65C3×#447—31no—
66#5218—31no—
67#5218—31no—
68#5218—61no—
69#5217D311yescharacteristic
70#5153—31no—
71#5153—31no—
72#5152—31no—
73Dic3×D8—31no—
74#5035—31no—
75#5018—31no—
76C4×#214—31no—
77#5016—31no—
78#5016—31no—
79#5014—31no—
80C4×#213—31no—
81#5008—31no—
82#5007—31no—
83#5003—31no—
84#5000—31no—
85#4996—31no—
86#4761—31no—
87#4759—31no—
88#4758—31no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C2×C3×D12C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108#3757—21no—
109#3754—22no—
110#3754—22no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#217D411yescharacteristic
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3118—91noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158C2×#217—21no—
159C2×#217—21no—
160#936—31no—
161#936—61no—
162#935—61no—
163D4×Dic3—21no—
164D4×Dic3—21no—
165D4×Dic3—31no—
166D4×Dic3C2×D311yescharacteristic
167D4×Dic3C2×D311yescharacteristic
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175C2×#214—61no—
176C2×#213C2×D311yescharacteristic
177C2×#213C2×D311yescharacteristic
178#930C2×D311yescharacteristic
179#926C2×D311yescharacteristic
180#926C2×D311yescharacteristic
181#924—31no—
182#924—31no—
183#924—61no—
184#898—61no—
185#896—61no—
186#888—31no—
187#887—31no—
188#885—61no—
189#883—61no—
190#879—61no—
191#878—61no—
192#875—31no—
193C4×D12—31no—
194#869—31no—
195C4×Dic6—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#818—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#810—31no—
222#810—31no—
223#809—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—24no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—81no—
239C23×C32—81no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×D4—24no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253#634—21no—
254#634—21no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269#627—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—31no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—31no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C24×C3—21no—
291C24×C3—21no—
292C24×C3—41no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—41no—
303C2×C3×D4—42no—
304C2×C3×D4—42no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C2×#67—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—61no—
330C3×D8—62no—
331C3×D8—62no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#217—21no—
353#217—21no—
354#217—21no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—121no—
361#217#6711yescharacteristic
362#217#6711yescharacteristic
363#214—62no—
364#214—62no—
365#214—62no—
366#214—62no—
367#214—122no—
368#214—122no—
369#213—22no—
370#213—22no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3#6711yescharacteristic
380C4⋊Dic3#6711yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—21no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—84no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4D3211yescharacteristic
430C2×SD16—91no—
431C2×SD16—91no—
432C2×D8—31no—
433C2×D8—31no—
434C4⋊Q8—91no—
435#126—181no—
436#124—91no—
437#124—181no—
438#123—181no—
439C22⋊Q8—91no—
440C22⋊Q8—181no—
441#121—31no—
442C4×Q8—91no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—91no—
450#117—31no—
451#117—31no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454#107—91no—
455#107—91no—
456#106—91no—
457#106—91no—
458C4⋊C8—91no—
459C4⋊C8—91no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—31no—
469C22⋊C8—91no—
470#97—91no—
471C4×C8—91no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—44no—
482C23×C3—61no—
483C23×C3—81no—
484C23×C3—81no—
485C23×C3—81no—
486C23×C3—81no—
487C23×C3—82no—
488C23×C3—82no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—21no—
492C3×D4—24no—
493C3×D4—24no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—44no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—241no—
506C3×D4#23512yes—
507C3×D4#23512yes—
508C3×D4#23712yes—
509C3×D4#23712yes—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4—241no—
528C2×C3×C4—241no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—81no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—81no—
542C2×Dic3—81no—
543C2×Dic3—81no—
544C2×Dic3—81no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—241no—
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12—21no—
554C4×D3—241no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—121no—
560Dic6—121no—
561Dic6—241no—
562Dic6—241no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8—121no—
573C2×C32—41no—
574C2×C32—42no—
575C2×C32—42no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—81no—
580C24—21no—
581C2×Q8—91no—
582C2×Q8—181no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4C2×D3211yescharacteristic
589C2×D4C2×D3211yescharacteristic
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—182no—
597SD16—182no—
598D8—62no—
599D8—62no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—91no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—31no—
627C42—61no—
628C42—181no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—42no—
644C22×C3—42no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—84no—
658C22×C3—84no—
659C22×C3—88no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×#6711yescharacteristic
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C2×#23511yescharacteristic
681C3×C4C2×#23511yescharacteristic
682C3×C4C2×#23711yescharacteristic
683C3×C4C2×#23711yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#311811yescharacteristic, complemented, Sylow
698C23—24no—
699C23—21no—
700C23—21no—
701C23—61no—
702C23—81no—
703C23—81no—
704C23D3×#6711yescharacteristic
705Q8—181no—
706Q8—181no—
707Q8—721no—
708D4—24no—
709D4—21no—
710D4—21no—
711D4—61no—
712D4—61no—
713D4—241no—
714D4#380412yes—
715D4#380412yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—241no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—61no—
735C8—61no—
736C8—181no—
737C8—181no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—41no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—41no—
746C2×C3—42no—
747C2×C3—42no—
748C2×C3—82no—
749C2×C3—82no—
750C2×C3—241no—
751C2×C3#558611yescharacteristic
752C2×C3#575711yescharacteristic
753C2×C3#577511yescharacteristic
754C2×C3#579111yescharacteristic
755C2×C3#583511yescharacteristic
756C2×C3#583611yescharacteristic
757D3—81no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—84no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22C2×D3×#6711yescharacteristic
772C4—21no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4—361no—
782C4C2×#380411yescharacteristic
783C4C2×#380411yescharacteristic
784C3—21no—
785C3#7999211yescharacteristic, complemented
786C3#8254111yescharacteristic, complemented
787C2—41no—
788C2—42no—
789C2—42no—
790C2—241no—
791C2#1059509611yescharacteristic
792C2#1059510611yescharacteristic
793C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC22×D4D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5798C2semidirect
2. #10594983C2semidirect
3. #10592917C2semidirect
5. #10591468C2semidirect
6. #10591468C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10591410C2semidirect
10. #10591408C2semidirect
11. #10591405C2semidirect
12. #10591401C2semidirect
13. #10591134C2semidirect
14. #10591090C2semidirect
15. #10591056C2semidirect
37. #63918C22semidirect
39. Dic3×D12C22semidirect
40. #63860C22semidirect
42. #63844C22semidirect
49. #63576C22semidirect
50. #63575C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5798D3semidirect
697. C32#3118semidirect
785. C3#79992semidirect
786. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105949832
#105929172
C3×#52172
#105914682
#105914302
Dic3×#2132
#105914102
#105914082
#105914052
#105914012
#105911342
#105910902
#105910562
#825413
#799923