Finite Group Databasebeta

← #11878570

Subgroups — #11878570

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic, complemented
3#10592751C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591599C211yesmaximal, characteristic, complemented
7#10591586C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591175C211yesmaximal, characteristic, complemented
10#10591167C211yesmaximal, characteristic, complemented
11#10591070C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590500C211yesmaximal, characteristic, complemented
14#10590441C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83429—31nomaximal
17#80670—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23#64133C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#930C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C3×#896—21no—
31C3×#895—21no—
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×#884—21no—
36#63970—21no—
37#63970—21no—
38#63908C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63887—21no—
41#63885—21no—
42#63857C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3713C2211yescharacteristic
45#63662C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63567C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
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#5629D311yescharacteristic, complemented
64#5608—31no—
65C3×#465—31no—
66#5239—31no—
67#5238—31no—
68#5234—31no—
69#5173—31no—
70#5172—31no—
71#5114—31no—
72#5110—31no—
73#5052—31no—
74#5052—31no—
75#5052—61no—
76#5048D311yescharacteristic, complemented
77#5047—31no—
78#5043—31no—
79#5041—31no—
80#5039—31no—
81#5039—31no—
82#5037—31no—
83#5034—31no—
84#4971—31no—
85#4968—31no—
86#4863—31no—
87#4862—31no—
88#4808—31no—
89#4805—31no—
90#4781—31no—
91#4777—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
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×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6D411yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—41no—
118#3795—41no—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3757—21no—
123#3756—41no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3748—41no—
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#215—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3716—41no—
146#3713—41no—
147#3204—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×#239C2×D311yescharacteristic
151C2×#237—31no—
152C2×#235—31no—
153C2×#235C2×D311yescharacteristic
154C2×C3×SD16—31no—
155C22×C3×C8—31no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—31no—
164C3×#121—61no—
165C3×#121—61no—
166C3×#121—61no—
167C2×C3×C4⋊C4—31no—
168#946—61no—
169#946C2×D311yescharacteristic
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—61no—
173C2×#215C2×D311yescharacteristic
174#939—61no—
175#939—61no—
176#939—61no—
177#938—31no—
178#938—61no—
179#938—61no—
180C2×#214—31no—
181C2×#213—31no—
182C2×#213—31no—
183#930—31no—
184#930C2×D311yescharacteristic
185#930C2×D311yescharacteristic
186C2×C4⋊Dic3—31no—
187#924—31no—
188#924—31no—
189#924—31no—
190#924—61no—
191C2×#208—31no—
192C2×#208—31no—
193C2×#208—61no—
194C22×C3⋊C8C2×D311yescharacteristic
195C2×#204—31no—
196#897—31no—
197#896—21no—
198#895—21no—
199#895C2×D311yescharacteristic
200D3×C4⋊C4—31no—
201D3×C4⋊C4C2×D311yescharacteristic
202#884—21no—
203#884—21no—
204#884—61no—
205#878—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—31no—
216#830—31no—
217#830—31no—
218#830—31no—
219#830—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#816—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#809—31no—
232#809—31no—
233#809C2×D311yescharacteristic
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
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256#634—21no—
257#634—21no—
258C3×#67—41no—
259C3×#67—41no—
260C3×#67—81no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—41no—
271C3×D12—42no—
272C3×D12—81no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×C4×D3—81no—
279C3×Dic6—41no—
280#625—42no—
281#625—81no—
282D3×Dic3—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—91no—
295#469—91no—
296#465—31no—
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×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—31no—
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—
319C2×C3×D4—61no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67#6711yescharacteristic
334C2×#67#6711yescharacteristic
335C22×Dic3—61no—
336C22×Dic3—61no—
337#239—41no—
338#239—41no—
339#237—121no—
340#237—121no—
341#235—41no—
342#235—41no—
343#235—121no—
344#235—121no—
345C2×D12—21no—
346C2×D12—21no—
347C2×D12#6711yescharacteristic
348C2×D12C22×D311yescharacteristic
349C2×D12C22×D311yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—61no—
359C2×Dic6#6711yescharacteristic
360C3×SD16—121no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—121no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—41no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—121no—
386#216—121no—
387#216—121no—
388#216—122no—
389#215—41no—
390#214—121no—
391#213—121no—
392#213—121no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—121no—
413#208—121no—
414#208—121no—
415#208—122no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425#204—121no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32C22×D411yescharacteristic
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
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—41no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C2×#41—31no—
455C2×#41—91no—
456C2×Q16—91no—
457C2×SD16—31no—
458C2×SD16—91no—
459C2×D8—91no—
460C2×M16—91no—
461C22×C8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—61no—
464C22⋊Q8—91no—
465C22⋊Q8—91no—
466C22⋊Q8—181no—
467C22⋊Q8D3211yescharacteristic
468#121—31no—
469#121—31no—
470#121—31no—
471#121—61no—
472#121—61no—
473#121—61no—
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—91no—
486#103—91no—
487#103—91no—
488#102—31no—
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×C3—61no—
501C23×C3D3×D411yescharacteristic
502C23×C3C2×#6711yescharacteristic
503C22×D3—21no—
504C22×D3—21no—
505C22×D3C2×#6711yescharacteristic
506C22×D3C2×#6711yescharacteristic
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—121no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—121no—
519C3×D4—122no—
520C3×D4—121no—
521C3×D4—121no—
522C3×D4—241no—
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—122no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—41no—
554#67—41no—
555#67—81no—
556#67—81no—
557#67—122no—
558#67—122no—
559#67—241no—
560#67—241no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—122no—
570C2×Dic3—241no—
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577D12—41no—
578D12—42no—
579D12—81no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—42no—
585C4×D3—81no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—41no—
589Dic6—61no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—121no—
594Dic6—121no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—62no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C2×C32—41no—
606C2×C32#53411yescharacteristic
607C2×C32#57711yescharacteristic
608C2×C32#57711yescharacteristic
609C3×D3—41no—
610C3×D3—41no—
611C3×D3—81no—
612C3×D3—81no—
613#41—121no—
614#41—121no—
615#41—121no—
616#41—121no—
617#41—361no—
618#41—361no—
619C2×Q8—31no—
620C2×Q8—91no—
621C2×Q8C2×D3211yescharacteristic
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—31no—
627C2×D4—61no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—181no—
632C2×D4—181no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—181no—
638C22×C4—181no—
639C22×C4C2×D3211yescharacteristic
640Q16—361no—
641SD16—121no—
642SD16—361no—
643D8—361no—
644M16—361no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—91no—
648C2×C8—91no—
649C2×C8—121no—
650C4⋊C4—21no—
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—91no—
656C4⋊C4—181no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4C2×D3211yescharacteristic
660C22⋊C4—21no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—61no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3C2×D3×D411yescharacteristic
691C22×C3C22×#6711yescharacteristic
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4#100411yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4#100411yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732Dic3—241no—
733C32#320411yescharacteristic, complemented, Sylow
734C23—31no—
735C23—31no—
736C23—61no—
737C23—61no—
738C23D3×#6711yescharacteristic
739Q8—21no—
740Q8—21no—
741Q8—121no—
742Q8—181no—
743Q8—181no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—121no—
749D4—122no—
750D4—121no—
751D4—121no—
752D4—241no—
753D4—241no—
754D4—241no—
755D4—362no—
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—122no—
770C2×C4—181no—
771C2×C4—181no—
772C2×C4—241no—
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—41no—
785C2×C3—41no—
786C2×C3—81no—
787C2×C3—121no—
788C2×C3—121no—
789C2×C3—241no—
790C2×C3—241no—
791C2×C3#560511yescharacteristic
792C2×C3#576211yescharacteristic
793C2×C3#577011yescharacteristic
794C2×C3#580411yescharacteristic
795C2×C3#583611yescharacteristic
796C2×C3#583711yescharacteristic
797D3—41no—
798D3—41no—
799D3—81no—
800D3—81no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—61no—
805C22—61no—
806C22—61no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22C2×D3×#6711yescharacteristic
817C4—21no—
818C4—41no—
819C4—41no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—361no—
825C4—361no—
826C4#6431311yescharacteristic
827C4#6431411yescharacteristic
828C3—21no—
829C3#8067011yescharacteristic, complemented
830C3#8342911yescharacteristic, complemented
831C2—41no—
832C2—121no—
833C2—121no—
834C2—241no—
835C2—241no—
836C2#1059530211yescharacteristic
837C2#1059531811yescharacteristic
838C2#1059546611yescharacteristic
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. #10595004C2semidirect
3. #10592751C2semidirect
4. C3×#5048C2semidirect
5. #10591655C2semidirect
6. #10591599C2semidirect
7. #10591586C2semidirect
8. #10591549C2semidirect
9. #10591175C2semidirect
10. #10591167C2semidirect
11. #10591070C2semidirect
12. #10590613C2semidirect
13. #10590500C2semidirect
14. #10590441C2semidirect
15. #10590426C2semidirect
63. #5629D3semidirect
76. #5048D3semidirect
733. C32#3204semidirect
829. C3#80670semidirect
830. C3#83429semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
#105950042
#105927512
C3×#50482
#105916552
#105915992
#105915862
#105915492
#105911752
#105911672
#105910702
#105906132
#105905002
#105904412
#105904262
#834293
#806703