Finite Group Databasebeta

← #11878568

Subgroups — #11878568

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5052C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591597C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591179C211yesmaximal, characteristic, complemented
10#10591165C211yesmaximal, characteristic, complemented
11#10591071C211yesmaximal, characteristic, complemented
12#10590615C211yesmaximal, characteristic, complemented
13#10590516C211yesmaximal, characteristic, complemented
14#10590441C211yesmaximal, characteristic, complemented
15#10590423C211yesmaximal, characteristic, complemented
16#83429—31nomaximal
17#80913—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64139C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#896—21no—
31C3×#895—21no—
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×#884—21no—
36#63971—21no—
37#63958—21no—
38#63909C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63888—21no—
41#63886—21no—
42#63856C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63662C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63565C2211yescharacteristic
54#63564C2211yescharacteristic
55#63563C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5629—31no—
64#5629D311yescharacteristic, complemented
65C3×#470—31no—
66#5239—31no—
67#5238—31no—
68#5234—31no—
69#5187—31no—
70#5187—31no—
71#5135—31no—
72#5129—31no—
73#5052D311yescharacteristic, complemented
74#5048—31no—
75#5048—31no—
76#5048—31no—
77#5048—61no—
78#5047—31no—
79#5043—31no—
80#5041—31no—
81#5039—31no—
82#5037—31no—
83#5034—31no—
84#4971—31no—
85#4968—31no—
86#4863—31no—
87#4863—31no—
88#4810—31no—
89#4810—31no—
90#4805—31no—
91#4805—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×#67D411yescharacteristic
99C3×#239—41no—
100C3×#239—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×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6D411yescharacteristic
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×C22⋊C4—21no—
122#3755—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#216—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×#208—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145#3715—41no—
146#3714—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239—31no—
151C2×#239C2×D311yescharacteristic
152C2×#235—31no—
153C2×#235C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×M16—31no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C2×D311yescharacteristic
162C3×#121—31no—
163C3×#121—31no—
164C3×#121—61no—
165C3×#121—61no—
166C3×#121—61no—
167C2×C3×C4⋊C4—31no—
168#946—31no—
169#946—61no—
170#946C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—31no—
175C2×#215—61no—
176#939—61no—
177#939—61no—
178#938—61no—
179C2×#214—31no—
180C2×#213—31no—
181#930—31no—
182#930—31no—
183#930—31no—
184#930—61no—
185#930C2×D311yescharacteristic
186C2×C4⋊Dic3—31no—
187#924—31no—
188#924C2×D311yescharacteristic
189C2×#208C2×D311yescharacteristic
190C22×C3⋊C8—31no—
191C22×C3⋊C8—31no—
192C22×C3⋊C8—61no—
193C2×D24—31no—
194#896—21no—
195#896—61no—
196#895—21no—
197#895—31no—
198#895—61no—
199#895C2×D311yescharacteristic
200D3×C4⋊C4—31no—
201D3×C4⋊C4C2×D311yescharacteristic
202#884—21no—
203#884—21no—
204#884—61no—
205#884—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic
214#832—31no—
215#832—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220#821—31no—
221#821—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225(C2×D3)⋊C8—31no—
226#817—31no—
227#810—31no—
228#810C2×D311yescharacteristic
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—31no—
239#808—61no—
240#808C2×D311yescharacteristic
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—81no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67—41no—
259C3×#67—41no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—41no—
269C3×D12—42no—
270C3×D12—81no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—42no—
276C3×C4×D3—81no—
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—91no—
291#483—91no—
292#481—91no—
293#481—91no—
294#470—31no—
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—21no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
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—41no—
336#239—41no—
337#239—121no—
338#239—121no—
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—21no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3—61no—
357C2×C4×D3C22×D311yescharacteristic
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6#6711yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×Q16—121no—
362C3×M16—121no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—41no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383#217—21no—
384#217—61no—
385#216—41no—
386#215—121no—
387#215—121no—
388#215—121no—
389#215—122no—
390#214—121no—
391#213—121no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—121no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3C22×D311yescharacteristic
406C4⋊Dic3C22×D311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—21no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413#208—41no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—61no—
420C2×C3⋊C8—121no—
421C2×C3⋊C8—121no—
422C2×C3⋊C8—122no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425D24—121no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C22×D411yescharacteristic
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—21no—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4H(5,𝔽2)11yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—41no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C2×#41—31no—
455C2×#41—91no—
456C2×Q16—31no—
457C2×SD16—91no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×M16—31no—
461C22×C8—91no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—61no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8D3211yescharacteristic
468#121—31no—
469#121—31no—
470#121—61no—
471#121—61no—
472#121—61no—
473#121—91no—
474#121—91no—
475#121—181no—
476#121—181no—
477#121—181no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—91no—
480#106—31no—
481#106—91no—
482#106—91no—
483#106—91no—
484#103—31no—
485#103—31no—
486#103—91no—
487#103—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C22⋊C8—91no—
495C22⋊C8—91no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3—31no—
499C23×C3—61no—
500C23×C3D3×D411yescharacteristic
501C23×C3C2×#6711yescharacteristic
502C22×D3—21no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3C2×#6711yescharacteristic
507C22×D3C2×#6711yescharacteristic
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—41no—
513C3×Q8—41no—
514C3×Q8—61no—
515C3×Q8—61no—
516C3×Q8—121no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—121no—
520C3×D4—122no—
521C3×D4—121no—
522C3×D4—121no—
523C3×D4—241no—
524C3×D4—241no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4—241no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—41no—
555#67—41no—
556#67—81no—
557#67—122no—
558#67—241no—
559#67—241no—
560#67—241no—
561#67—242no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—241no—
569C2×Dic3C2×#6711yescharacteristic
570C2×Dic3C2×#6711yescharacteristic
571D12—21no—
572D12—21no—
573D12—41no—
574D12—42no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—81no—
580D12—121no—
581D12—121no—
582D12—122no—
583D12—241no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—42no—
589C4×D3—81no—
590C4×D3—122no—
591C4×D3—122no—
592C4×D3—241no—
593Dic6—21no—
594Dic6—21no—
595Dic6—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—62no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—61no—
605C3⋊C8—121no—
606C2×C32—41no—
607C2×C32#53411yescharacteristic
608C2×C32#57711yescharacteristic
609C2×C32#57711yescharacteristic
610C3⋊D3—81no—
611C3×D3—41no—
612C3×D3—41no—
613C3×D3—81no—
614#41—121no—
615#41—121no—
616#41—121no—
617#41—121no—
618#41—361no—
619#41—361no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8C2×D3211yescharacteristic
623C2×D4—31no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—31no—
627C2×D4—61no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4—91no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—181no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—181no—
639C22×C4—181no—
640C22×C4C2×D3211yescharacteristic
641Q16—121no—
642SD16—361no—
643SD16—361no—
644D8—361no—
645M16—121no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—91no—
649C2×C8—91no—
650C2×C8—361no—
651C4⋊C4—21no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4—91no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4C2×D3211yescharacteristic
661C22⋊C4—21no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3C2×D3×D411yescharacteristic
689C22×C3C22×#6711yescharacteristic
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—241no—
706C2×D3—241no—
707C2×D3—241no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—61no—
718C3×C4—61no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4#100411yescharacteristic
725C3×C4#100411yescharacteristic
726C3×C4#100411yescharacteristic
727C3×C4#100911yescharacteristic
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736C32#320411yescharacteristic, complemented, Sylow
737C23—31no—
738C23—31no—
739C23—61no—
740C23—181no—
741C23D3×#6711yescharacteristic
742Q8—21no—
743Q8—21no—
744Q8—61no—
745Q8—61no—
746Q8—121no—
747D4—61no—
748D4—61no—
749D4—121no—
750D4—122no—
751D4—121no—
752D4—121no—
753D4—181no—
754D4—181no—
755D4—241no—
756D4—241no—
757D4—362no—
758D4—721no—
759D4—721no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—122no—
774C2×C4—181no—
775C2×C4—241no—
776C2×C4—362no—
777C2×C4—721no—
778C2×C4D3×#6711yescharacteristic
779C2×C4C22×D3211yescharacteristic
780C8—61no—
781C8—61no—
782C8—181no—
783C8—181no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—121no—
791C2×C3—121no—
792C2×C3—241no—
793C2×C3#560511yescharacteristic
794C2×C3#577811yescharacteristic
795C2×C3#577811yescharacteristic
796C2×C3#580411yescharacteristic
797C2×C3#583611yescharacteristic
798C2×C3#583711yescharacteristic
799D3—41no—
800D3—41no—
801D3—81no—
802D3—241no—
803D3—241no—
804D3—481no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—361no—
818C22—361no—
819C22—361no—
820C22C2×D3×#6711yescharacteristic
821C4—21no—
822C4—41no—
823C4—41no—
824C4—61no—
825C4—61no—
826C4—121no—
827C4—121no—
828C4—121no—
829C4—361no—
830C4#6431311yescharacteristic
831C4#6431411yescharacteristic
832C3—21no—
833C3#8091311yescharacteristic, complemented
834C3#8342911yescharacteristic, complemented
835C2—41no—
836C2—121no—
837C2—121no—
838C2—241no—
839C2—721no—
840C2#1059530211yescharacteristic
841C2#1059531911yescharacteristic
842C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3204
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5629C2semidirect
2. #10594894C2semidirect
3. #10592747C2semidirect
4. C3×#5052C2semidirect
5. #10591657C2semidirect
6. #10591597C2semidirect
7. #10591588C2semidirect
8. #10591549C2semidirect
9. #10591179C2semidirect
10. #10591165C2semidirect
11. #10591071C2semidirect
12. #10590615C2semidirect
13. #10590516C2semidirect
14. #10590441C2semidirect
15. #10590423C2semidirect
64. #5629D3semidirect
73. #5052D3semidirect
736. C32#3204semidirect
833. C3#80913semidirect
834. C3#83429semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
#105948942
#105927472
C3×#50522
#105916572
#105915972
#105915882
#105915492
#105911792
#105911652
#105910712
#105906152
#105905162
#105904412
#105904232
#834293
#809133