Finite Group Databasebeta

← #11878606

Subgroups — #11878606

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5510C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3#10592667C211yesmaximal, characteristic, complemented
4C3×#4971C211yesmaximal, characteristic, complemented
5#10591170C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591145C211yesmaximal, characteristic, complemented
8#10590616C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590586C211yesmaximal, characteristic, complemented
11#10590577C211yesmaximal, characteristic, complemented
12#10590520C211yesmaximal, characteristic, complemented
13#10590514C211yesmaximal, characteristic, complemented
14#10590441C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#83429—31nomaximal
17#81444—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22#64139C2211yescharacteristic
23C3×#930—21no—
24C3×#930—21no—
25C3×#924C2211yescharacteristic
26C3×#897—21no—
27C3×#897C2211yescharacteristic
28C3×#897C2211yescharacteristic
29C3×#895—21no—
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32#63971—21no—
33#63958—21no—
34#63909C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63888—21no—
37#63886—21no—
38#63856C2211yescharacteristic
39C2×#3718C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63657C2211yescharacteristic
46#63636C2211yescharacteristic
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5629—31no—
64#5510D311yescharacteristic, complemented
65C3×#483—31no—
66#5239—31no—
67#5238—31no—
68#5234—31no—
69#5052—31no—
70#5048—31no—
71#5047—31no—
72#5047—31no—
73#5043—31no—
74#5041—31no—
75#5039—31no—
76#5037—31no—
77#5034—31no—
78#4971D311yescharacteristic, complemented
79#4968—31no—
80#4968—31no—
81#4968—61no—
82#4865—31no—
83#4864—31no—
84#4863—31no—
85#4862—31no—
86#4816—31no—
87#4810—31no—
88#4808—31no—
89#4807—31no—
90#4734—31no—
91#4727—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#235—41no—
100C3×#235—41no—
101C3×#235—41no—
102C3×#235—41no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6D411yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—41no—
118#3799—41no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3718—41no—
142#3717—41no—
143#3715—41no—
144#3714—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239—31no—
151C2×#235—31no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×#121—31no—
159C3×#121—31no—
160C3×#121—61no—
161C3×#121—61no—
162C3×#121—61no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C2×D311yescharacteristic
166#946—31no—
167#946—61no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#215—31no—
171C2×#215—31no—
172#939—61no—
173#939—61no—
174#938—61no—
175C2×#214—31no—
176C2×#213—31no—
177#930—21no—
178#930—21no—
179#930—31no—
180#930—31no—
181#930—31no—
182#930—61no—
183C2×C4⋊Dic3—31no—
184#924—31no—
185#924C2×D311yescharacteristic
186C2×#208—31no—
187C22×C3⋊C8—31no—
188C2×D24—31no—
189C2×#204—31no—
190C2×ΓL(1,𝔽25)—31no—
191C2×D3×C8—31no—
192#897—21no—
193#897C2×D311yescharacteristic
194#897C2×D311yescharacteristic
195#896—61no—
196#895—21no—
197#895—31no—
198#895—61no—
199#895C2×D311yescharacteristic
200#895C2×D311yescharacteristic
201D3×C4⋊C4—31no—
202#884—61no—
203#884—61no—
204C3×#106—31no—
205C3×#106—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#830—31no—
215#830—31no—
216#830—31no—
217#830—61no—
218#830C2×D311yescharacteristic
219#821—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#810—31no—
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809—61no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238#808—61no—
239#808C2×D311yescharacteristic
240#808C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—81no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—41no—
268C3×D12—81no—
269C3×D12—81no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—41no—
280#626—42no—
281#626—81no—
282#624—42no—
283D3×Dic3—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#483—31no—
291#483—91no—
292#481—91no—
293#481—91no—
294#470—91no—
295#469—91no—
296#465—91no—
297#465—91no—
298#452—91no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C2×C3×Q8—31no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—21no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—121no—
332C2×#67#6711yescharacteristic
333C2×#67#6711yescharacteristic
334C22×Dic3—61no—
335#239—121no—
336#239—121no—
337#235—41no—
338#235—41no—
339#235—41no—
340#235—41no—
341#235—121no—
342#235—121no—
343C2×D12—21no—
344C2×D12—21no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12#6711yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6#6711yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—41no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381#217—21no—
382#217—61no—
383#216—121no—
384#216—121no—
385#215—121no—
386#215—121no—
387#214—121no—
388#213—121no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—121no—
399C4⋊Dic3—21no—
400C4⋊Dic3—21no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410#208—121no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420D24—121no—
421#204—121no—
422ΓL(1,𝔽25)—121no—
423D3×C8—121no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C22×D411yescharacteristic
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4H(5,𝔽2)11yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—91no—
454C2×Q16—91no—
455C2×SD16—91no—
456C2×SD16—91no—
457C2×D8—91no—
458C2×M16—91no—
459C22×C8—91no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—61no—
464C22⋊Q8—91no—
465C22⋊Q8—181no—
466#121—31no—
467#121—31no—
468#121—61no—
469#121—61no—
470#121—61no—
471#121—91no—
472#121—91no—
473#121—181no—
474#121—181no—
475#121—181no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4D3211yescharacteristic
478#106—31no—
479#106—31no—
480#106—91no—
481#106—91no—
482#103—31no—
483#103—31no—
484#103—91no—
485#103—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—61no—
498C23×C3D3×D411yescharacteristic
499C23×C3C2×#6711yescharacteristic
500C22×D3—21no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—121no—
504C22×D3C2×#6711yescharacteristic
505C22×D3C2×#6711yescharacteristic
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8—121no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—121no—
514C3×D4—121no—
515C3×D4—121no—
516C3×D4—122no—
517C3×D4—241no—
518C3×D4—241no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—81no—
543C2×C3×C4—81no—
544C2×C3×C4—82no—
545C2×C3×C4—122no—
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—41no—
551#67—41no—
552#67—42no—
553#67—122no—
554#67—241no—
555#67—241no—
556#67—241no—
557#67—242no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3—241no—
565C2×Dic3C2×#6711yescharacteristic
566C2×Dic3C2×#6711yescharacteristic
567D12—21no—
568D12—21no—
569D12—41no—
570D12—61no—
571D12—61no—
572D12—61no—
573D12—61no—
574D12—81no—
575D12—81no—
576D12—121no—
577D12—121no—
578D12—122no—
579D12—241no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—42no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—21no—
589Dic6—21no—
590Dic6—21no—
591Dic6—21no—
592Dic6—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C3⋊C8—121no—
603C2×C32—41no—
604C2×C32#53411yescharacteristic
605C2×C32#57711yescharacteristic
606C2×C32#57711yescharacteristic
607C3⋊D3—81no—
608C3×D3—41no—
609C3×D3—41no—
610C3×D3—81no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—121no—
615#41—361no—
616#41—361no—
617C2×Q8—31no—
618C2×Q8—31no—
619C2×Q8—31no—
620C2×D4—31no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—91no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—181no—
631C22×C4—21no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—61no—
635C22×C4—181no—
636C22×C4—181no—
637C22×C4C2×D3211yescharacteristic
638Q16—361no—
639SD16—361no—
640SD16—361no—
641D8—361no—
642M16—361no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—91no—
646C2×C8—91no—
647C2×C8—361no—
648C4⋊C4—21no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—91no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4C2×D3211yescharacteristic
657C4⋊C4C2×D3211yescharacteristic
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C2×D3×D411yescharacteristic
686C22×C3C22×#6711yescharacteristic
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—241no—
703C2×D3—241no—
704C2×D3—241no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—81no—
717C3×C4—81no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4#100411yescharacteristic
722C3×C4#100411yescharacteristic
723C3×C4#100911yescharacteristic
724C3×C4#100911yescharacteristic
725Dic3—21no—
726Dic3—21no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—121no—
731Dic3—121no—
732Dic3—241no—
733C32#320411yescharacteristic, complemented, Sylow
734C23—31no—
735C23—31no—
736C23—61no—
737C23—181no—
738C23D3×#6711yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—61no—
743Q8—121no—
744D4—61no—
745D4—61no—
746D4—121no—
747D4—121no—
748D4—121no—
749D4—122no—
750D4—181no—
751D4—181no—
752D4—241no—
753D4—241no—
754D4—362no—
755D4—721no—
756D4—721no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—81no—
771C2×C4—122no—
772C2×C4—181no—
773C2×C4—362no—
774C2×C4—721no—
775C2×C4D3×#6711yescharacteristic
776C2×C4C22×D3211yescharacteristic
777C8—61no—
778C8—61no—
779C8—181no—
780C8—181no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—42no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—121no—
788C2×C3—121no—
789C2×C3—241no—
790C2×C3#565311yescharacteristic
791C2×C3#576211yescharacteristic
792C2×C3#577811yescharacteristic
793C2×C3#580411yescharacteristic
794C2×C3#583611yescharacteristic
795C2×C3#583711yescharacteristic
796D3—41no—
797D3—41no—
798D3—81no—
799D3—241no—
800D3—241no—
801D3—481no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—361no—
815C22—361no—
816C22—361no—
817C22C2×D3×#6711yescharacteristic
818C4—21no—
819C4—41no—
820C4—41no—
821C4—61no—
822C4—61no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—361no—
827C4#6430711yescharacteristic
828C4#6430711yescharacteristic
829C3—21no—
830C3#8144411yescharacteristic, complemented
831C3#8342911yescharacteristic, complemented
832C2—41no—
833C2—121no—
834C2—121no—
835C2—241no—
836C2—721no—
837C2#1059506211yescharacteristic
838C2#1059510511yescharacteristic
839C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5510C2semidirect
2. #10594894C2semidirect
3. #10592667C2semidirect
4. C3×#4971C2semidirect
5. #10591170C2semidirect
6. #10591163C2semidirect
7. #10591145C2semidirect
8. #10590616C2semidirect
9. #10590615C2semidirect
10. #10590586C2semidirect
11. #10590577C2semidirect
12. #10590520C2semidirect
13. #10590514C2semidirect
14. #10590441C2semidirect
15. #10590439C2semidirect
64. #5510D3semidirect
78. #4971D3semidirect
733. C32#3204semidirect
830. C3#81444semidirect
831. C3#83429semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
#105948942
#105926672
C3×#49712
#105911702
#105911632
#105911452
#105906162
#105906152
#105905862
#105905772
#105905202
#105905142
#105904412
#105904392
#834293
#814443