Finite Group Databasebeta

← #11887065

Subgroups — #11887065

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic, complemented
2#10594373C211yesmaximal, characteristic, complemented
3#10592581C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4883C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic, complemented
7D3×#821C211yesmaximal, characteristic, complemented
8#10590753C211yesmaximal, characteristic, complemented
9#10590720C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590593C211yesmaximal, characteristic, complemented
12#10590548C211yesmaximal, characteristic, complemented
13#10590509C211yesmaximal, characteristic, complemented
14#10590452C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#80980—31nomaximal
17#80731—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3796—21no—
22#64104C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#895C2211yescharacteristic, complemented
28C3×#893C2211yescharacteristic
29C3×#888C2211yescharacteristic, complemented
30#63923—21no—
31#63922—21no—
32#63916C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63906—21no—
35C4×#626C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63887—21no—
39#63884—21no—
40#63853—21no—
41C2×#3714C2211yescharacteristic, complemented
42C2×#3713C2211yescharacteristic
43C2×#3710C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5726—31no—
62#5611—31no—
63#5609—31no—
64D4×D12—31no—
65C3×#474—31no—
66C3×#466—31no—
67#5156—31no—
68#5150—31no—
69C2×#821—31no—
70C8×#67—31no—
71#5088—31no—
72#5036—31no—
73#5033—31no—
74C4×#213—31no—
75#4890D311yescharacteristic, complemented
76#4883—31no—
77#4883D311yescharacteristic, complemented
78#4882—31no—
79#4882—31no—
80#4882—31no—
81#4882—61no—
82#4843—31no—
83#4834—31no—
84#4775—31no—
85#4773—31no—
86#4773—31no—
87D3×#102—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4760—31no—
91#4756—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114#3802—22no—
115#3802—41no—
116D3×D12—22no—
117D3×D12—41no—
118D3×D12—44no—
119#3796—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×D24—41no—
136C3×D3×C8—41no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3714—41no—
144#3713—22no—
145#3710—41no—
146#3294—91noSylow
147C2×#239—61no—
148C2×#237—61no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—31no—
152C2×D3×D4—61no—
153C22×D12—31no—
154C22×D12—61no—
155C2×C3×D8—31no—
156C22×C3×C8—31no—
157C3×C4⋊Q8—31no—
158C3×#121—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161#946—61no—
162#940—31no—
163#938—31no—
164#937—61no—
165#935—61no—
166D4×Dic3—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170#930—61no—
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173C2×D24—31no—
174C2×D24C2×D311yescharacteristic, complemented
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#895—31no—
179#895—31no—
180#895—31no—
181#895—61no—
182#895C2×D311yescharacteristic
183#895C2×D311yescharacteristic, complemented
184#894—61no—
185#894—61no—
186#893C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191#888C2×D311yescharacteristic, complemented
192#884—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196#882—61no—
197#878—61no—
198#874—31no—
199C4×D12—31no—
200C4×D12—31no—
201C3×#107—21no—
202C3×#107—31no—
203C3×#107C2×D311yescharacteristic, complemented
204C3×#107C2×D311yescharacteristic, complemented
205C3×C4⋊C8—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#830—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225Dic3⋊C8C2×D311yescharacteristic, complemented
226C8×Dic3—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—61no—
238#807C2×D311yescharacteristic, complemented
239C4×C3⋊C8—31no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—42no—
250C2×D32—81no—
251C2×D32—81no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—42no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12—42no—
274C3×D12#4112yescomplemented
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×Dic6—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—81no—
283#626D814yescomplemented
284#625—42no—
285D3×Dic3—42no—
286D3×Dic3—42no—
287C32×C8—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—91no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—31no—
297#466—31no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×Q8—61no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C2×#67—31no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327#239—124no—
328#237—124no—
329D3×D4—62no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—121no—
333D3×D4—124no—
334D3×D4—121no—
335D3×D4—121no—
336C2×D12—21no—
337C2×D12—21no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—62no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—121no—
350C2×D12—121no—
351C2×D12—124no—
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—61no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—121no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—21no—
366C3×D8—121no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—121no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385#217—31no—
386#217—61no—
387#217—61no—
388#213—62no—
389#213—62no—
390#213—121no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—121no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—21no—
409Dic3⋊C4—31no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—121no—
414C4×Dic3C22×D311yescharacteristic
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420D24—41no—
421D24—121no—
422D3×C8—41no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3C2×D812yes—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—22no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3C2×D812yes—
444D32—84no—
445D32—84no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4C2×#4111yescharacteristic
449C32×C4H(5,𝔽2)11yescharacteristic
450C3⋊Dic3—21no—
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
456C2×#41—181no—
457C22×D4—91no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—91no—
462C2×D8—91no—
463C22×C8—31no—
464C22×C8—91no—
465C4⋊Q8—31no—
466#127—91no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—31no—
472#121—91no—
473#121—91no—
474#121—181no—
475#120—181no—
476#120—181no—
477C4×D4—31no—
478C4×D4—91no—
479C4×D4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482#107—31no—
483#107—91no—
484#107D3211yescharacteristic, complemented
485C4⋊C8—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—31no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—121no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—241no—
521C22×D3—241no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3D3×D411yescharacteristic
525C3×Q8—122no—
526C3×D4—32no—
527C3×D4—61no—
528C3×D4—61no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—122no—
533C3×D4—122no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—34no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—241no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569D12—21no—
570D12—21no—
571D12—21no—
572D12—21no—
573D12—21no—
574D12—34no—
575D12—42no—
576D12—42no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—121no—
582D12—121no—
583D12—122no—
584D12—122no—
585D12—122no—
586D12—122no—
587D12—122no—
588D12—242no—
589D12—241no—
590D12#23912yescomplemented
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—42no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—61no—
598C4×D3—121no—
599C4×D3—121no—
600C4×D3—122no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—122no—
604C4×D3—242no—
605Dic6—42no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—41no—
609C3×C8—61no—
610C3×C8—61no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8—61no—
614C3⋊C8—61no—
615C3⋊C8—121no—
616C2×C32#54611yescharacteristic
617C2×C32C22×D811yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3⋊D3—81no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—181no—
626C24—181no—
627#41—364no—
628C2×Q8—61no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—91no—
635C2×D4—91no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4—181no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—182no—
644C2×D4—361no—
645C2×D4—364no—
646C2×D4—361no—
647C22×C4—31no—
648C22×C4—61no—
649C22×C4—91no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653D8—121no—
654D8—182no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—121no—
660C2×C8—361no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4C2×D3211yescharacteristic
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—62no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—22no—
697C2×D3—32no—
698C2×D3—32no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—62no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—61no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—121no—
715C2×D3—121no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—241no—
721C2×D3—241no—
722C2×D3—241no—
723C2×D3—244no—
724C2×D3—244no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3D3×D812yes—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—32no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—61no—
736C3×C4—61no—
737C3×C4—81no—
738C3×C4—81no—
739C3×C4—121no—
740C3×C4#100411yescharacteristic
741C3×C4C2×#23911yescharacteristic
742C3×C4D3×#4111yescharacteristic
743C3×C4#100911yescharacteristic
744Dic3—21no—
745Dic3—21no—
746Dic3—41no—
747Dic3—61no—
748Dic3—61no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752Dic3—241no—
753Dic3D3×D812yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—31no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—91no—
760C23—181no—
761C23—362no—
762C23—362no—
763C23—362no—
764C23—362no—
765C23—721no—
766C23—721no—
767Q8—122no—
768D4—32no—
769D4—61no—
770D4—61no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—94no—
775D4—122no—
776D4—122no—
777D4—181no—
778D4—181no—
779D4—362no—
780D4—362no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—721no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—31no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—91no—
794C2×C4—122no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—362no—
799C2×C4—362no—
800C2×C4—362no—
801C2×C4C22×D3211yescharacteristic
802C8—21no—
803C8—61no—
804C8—61no—
805C8—181no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—62no—
810C2×C3—122no—
811C2×C3—241no—
812C2×C3—241no—
813C2×C3#561011yescharacteristic
814C2×C3#563011yescharacteristic
815C2×C3C2×D3×D811yescharacteristic
816C2×C3C2×D3×D811yescharacteristic
817C2×C3#577011yescharacteristic
818C2×C3#577811yescharacteristic
819D3—22no—
820D3—42no—
821D3—62no—
822D3—62no—
823D3—81no—
824D3—81no—
825D3—122no—
826D3—241no—
827D3—241no—
828D3—481no—
829C22—32no—
830C22—61no—
831C22—61no—
832C22—62no—
833C22—92no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—181no—
843C22—181no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22—724no—
849C22D32×D411yescharacteristic
850C4—32no—
851C4—41no—
852C4—41no—
853C4—61no—
854C4—61no—
855C4—121no—
856C4—181no—
857C4—361no—
858C4#6430711yescharacteristic
859C4D3×#23911yescharacteristic
860C3—21no—
861C3#8073111yescharacteristic, complemented
862C3#8098011yescharacteristic, complemented
863C2—62no—
864C2—122no—
865C2—182no—
866C2—241no—
867C2—241no—
868C2—721no—
869C2#1059462211yescharacteristic
870C2D32×D811yescharacteristic
871C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594621C2semidirect
2. #10594373C2semidirect
3. #10592581C2semidirect
4. C3×#4890C2semidirect
5. C3×#4883C2semidirect
6. #10590945C2semidirect
7. D3×#821C2semidirect
8. #10590753C2semidirect
9. #10590720C2semidirect
10. #10590595C2semidirect
11. #10590593C2semidirect
12. #10590548C2semidirect
13. #10590509C2semidirect
14. #10590452C2semidirect
15. #10590438C2semidirect
23. C4⋊C4×C3⋊D3C22semidirect
24. C2×C3×D24C22semidirect
25. C2×C3×D3×C8C22semidirect
27. C3×#895C22semidirect
29. C3×#888C22semidirect
32. #63916C22semidirect
36. Dic3×D12C22semidirect
37. D3×C4⋊Dic3C22semidirect
41. C2×#3714C22semidirect
43. C2×#3710C22semidirect
44. C32×#107C22semidirect
45. #63648C22semidirect
46. #63647C22semidirect
47. #63636C22semidirect
48. #63634C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#807C22semidirect
55. #63564C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
75. #4890D3semidirect
77. #4883D3semidirect
174. C2×D24C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
183. #895C2×D3semidirect
191. #888C2×D3semidirect
203. C3×#107C2×D3semidirect
204. C3×#107C2×D3semidirect
225. Dic3⋊C8C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
238. #807C2×D3semidirect
274. C3×D12#41semidirect
283. #626D8semidirect
484. #107D32semidirect
590. D12#239semidirect
754. C32#3294semidirect
861. C3#80731semidirect
862. C3#80980semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105943732
#105925812
C3×#48902
C3×#48832
#105909452
D3×#8212
#105907532
#105907202
#105905952
#105905932
#105905482
#105905092
#105904522
#105904382
#809803
#807313