Finite Group Databasebeta

← #11887066

Subgroups — #11887066

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic, complemented
2#10594517C211yesmaximal, characteristic, complemented
3#10592582C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic, complemented
5C3×#4882C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic, complemented
7#10590940C211yesmaximal, characteristic, complemented
8#10590906C211yesmaximal, characteristic, complemented
9#10590765C211yesmaximal, characteristic, complemented
10#10590598C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590548C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590442C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#80980—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3799—21no—
22C2×#3745C2211yescharacteristic, complemented
23C2×C8×C3⋊D3C2211yescharacteristic, complemented
24#64104C2211yescharacteristic
25#64104C2211yescharacteristic, complemented
26C3×#895C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29C3×#888C2211yescharacteristic, complemented
30#63923—21no—
31#63922—21no—
32#63911C2211yescharacteristic
33#63909C2211yescharacteristic, complemented
34#63906—21no—
35C4×#626C2211yescharacteristic
36#63900C2211yescharacteristic, complemented
37#63897—21no—
38#63894C2211yescharacteristic, complemented
39#63888—21no—
40#63850—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63636C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#807C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5726—31no—
62#5609—31no—
63D4×D12—31no—
64#5507—31no—
65C3×#480—31no—
66C3×#474—31no—
67#5088—31no—
68#5038—31no—
69C4×#213—31no—
70C2×#809—31no—
71#4890D311yescharacteristic, complemented
72#4883—31no—
73#4883—31no—
74#4883—31no—
75#4883—61no—
76#4882—31no—
77#4882—31no—
78#4882D311yescharacteristic, complemented
79#4872—31no—
80#4843—31no—
81#4834—31no—
82#4786—31no—
83#4773—31no—
84#4773—31no—
85#4773—31no—
86D3×#102—31no—
87D3×#102—31no—
88D3×#102—31no—
89#4760—31no—
90#4732—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
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×#624—21no—
113C2×#624—21no—
114#3802—22no—
115#3802—41no—
116D3×D12—22no—
117D3×D12—41no—
118D3×D12—44no—
119#3799—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3752—21no—
124#3752—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3745—41no—
127C8×C3⋊D3—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3D411yescharacteristic
139#3722—21no—
140#3722—21no—
141#3722D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3714—22no—
144#3714—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C2×#239—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×#235—61no—
153C22×D12—31no—
154C22×D12—61no—
155C3×C4⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158C2×C3×C4⋊C4—31no—
159#946—61no—
160#940—31no—
161#937—61no—
162C2×#213—31no—
163C2×#213—31no—
164#930—31no—
165#930—61no—
166#929—61no—
167C4×#67—31no—
168C22×C3⋊C8—31no—
169C2×D24—31no—
170C2×D24—31no—
171C2×D24—31no—
172C2×D24—31no—
173C2×D24—61no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—61no—
178#896—61no—
179#895—31no—
180#895—31no—
181#895—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#895—61no—
186#895C2×D311yescharacteristic
187#894—61no—
188#894—61no—
189#894—61no—
190#893—31no—
191#893C2×D311yescharacteristic
192D3×C4⋊C4—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4C2×D311yescharacteristic, complemented
195#888C2×D311yescharacteristic, complemented
196#884—61no—
197#882—61no—
198#882—61no—
199#882—61no—
200#874—31no—
201C4×D12—31no—
202C4×D12—31no—
203C3×#107—21no—
204C3×#107—31no—
205C3×#107—31no—
206C3×#107C2×D311yescharacteristic, complemented
207C3×#107C2×D311yescharacteristic, complemented
208C3×C4⋊C8—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×C22⋊C8—31no—
214#832—31no—
215#832—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223Dic3⋊C8C2×D311yescharacteristic, complemented
224C8×Dic3—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809—61no—
235#809C2×D311yescharacteristic
236#809C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239C4×C3⋊C8—31no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—42no—
261C4⋊(C3⋊D3)—42no—
262C4×C3⋊D3—21no—
263C4×C3⋊D3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yescomplemented
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×Dic6—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#626—81no—
283#626D814yescomplemented
284#625—42no—
285#624—42no—
286#624—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—31no—
295#480—91no—
296#474—31no—
297#466—91no—
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—61no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C2×#67—31no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324#239—124no—
325D3×D4—62no—
326D3×D4—62no—
327D3×D4—62no—
328D3×D4—121no—
329D3×D4—124no—
330D3×D4—121no—
331D3×D4—121no—
332#235—124no—
333C2×D12—21no—
334C2×D12—31no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—61no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—121no—
351C2×D12—121no—
352C2×D12—121no—
353C2×D12—124no—
354C2×D12C22×D311yescharacteristic
355C2×D12C22×D311yescharacteristic
356C2×C4×D3—21no—
357C2×C4×D3—21no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—61no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C4⋊C4C22×D311yescharacteristic
381C3×C4⋊C4C22×D311yescharacteristic
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385#217—31no—
386#213—62no—
387#213—121no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
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—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403C4⋊Dic3—31no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—31no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—121no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418D24—62no—
419D24—121no—
420D24—121no—
421D24—122no—
422D24—121no—
423D3×C8—121no—
424D3×C8—121no—
425D3×C8—121no—
426D3×C8—122no—
427C22×C32C22×D411yescharacteristic
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3C2×D812yes—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3C2×D812yes—
446D32—84no—
447D32—84no—
448C32×C4—41no—
449C32×C4—41no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
458C2×#41—181no—
459C22×D4—91no—
460C22×D4—91no—
461C22×D4—181no—
462C2×D8—91no—
463C2×D8—91no—
464C2×D8—91no—
465C22×C8—91no—
466C22×C8—91no—
467C4⋊Q8—31no—
468#127—91no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—31no—
473#121—91no—
474#121—91no—
475#121—91no—
476#121—181no—
477#120—181no—
478#120—181no—
479C4×D4—31no—
480C4×D4—91no—
481C4×D4—91no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484#107—31no—
485#107—31no—
486#107D3211yescharacteristic, complemented
487C4⋊C8—31no—
488#102—31no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—31no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—31no—
502C23×C3—61no—
503C23×C3—61no—
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—61no—
511C22×D3—61no—
512C22×D3—61no—
513C22×D3—121no—
514C22×D3—121no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3D3×D411yescharacteristic
528C3×Q8—122no—
529C3×D4—32no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
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—61no—
548C2×C3×C4—122no—
549C2×C3×C4—122no—
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552#67—34no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—241no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—61no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—21no—
568D12—21no—
569D12—21no—
570D12—34no—
571D12—42no—
572D12—61no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—121no—
582D12—121no—
583D12—121no—
584D12—122no—
585D12—122no—
586D12—122no—
587D12—122no—
588D12—122no—
589D12—122no—
590D12—122no—
591D12—242no—
592D12—242no—
593D12—241no—
594D12#23912yescomplemented
595C4×D3—21no—
596C4×D3—21no—
597C4×D3—42no—
598C4×D3—42no—
599C4×D3—61no—
600C4×D3—61no—
601C4×D3—61no—
602C4×D3—61no—
603C4×D3—121no—
604C4×D3—121no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608C4×D3—122no—
609Dic6—42no—
610C3×C8—22no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—61no—
614C3×C8—61no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—121no—
620C2×C32#54611yescharacteristic
621C2×C32C22×D811yescharacteristic
622C2×C32#57711yescharacteristic
623C3⋊D3—22no—
624C3⋊D3—81no—
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—181no—
630C24—181no—
631#41—364no—
632C2×Q8—61no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—91no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—182no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—182no—
648C2×D4—361no—
649C2×D4—364no—
650C2×D4—361no—
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—91no—
655C22×C4—181no—
656C22×C4—181no—
657D8—182no—
658D8—361no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—361no—
664C2×C8—361no—
665C2×C8C2×D3211yescharacteristic
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C4⋊C4—181no—
672C4⋊C4C2×D3211yescharacteristic
673C4⋊C4C2×D3211yescharacteristic
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—62no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—22no—
698C2×D3—32no—
699C2×D3—32no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—121no—
711C2×D3—121no—
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—121no—
721C2×D3—121no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—241no—
725C2×D3—241no—
726C2×D3—241no—
727C2×D3—241no—
728C2×D3—241no—
729C2×D3—241no—
730C2×D3—244no—
731C2×D3—244no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3D3×D812yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—32no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—81no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×#23911yescharacteristic
749C3×C4D3×#4111yescharacteristic
750C3×C4#100911yescharacteristic
751C3×C4#100911yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—41no—
755Dic3—41no—
756Dic3—61no—
757Dic3—61no—
758Dic3—121no—
759Dic3D3×D812yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—31no—
762C23—61no—
763C23—61no—
764C23—91no—
765C23—181no—
766C23—181no—
767C23—362no—
768C23—362no—
769C23—362no—
770C23—362no—
771C23—721no—
772C23—721no—
773Q8—122no—
774D4—32no—
775D4—61no—
776D4—61no—
777D4—61no—
778D4—94no—
779D4—122no—
780D4—181no—
781D4—181no—
782D4—181no—
783D4—181no—
784D4—362no—
785D4—362no—
786D4—362no—
787D4—362no—
788D4—362no—
789D4—362no—
790D4—721no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—91no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—362no—
806C2×C4—362no—
807C2×C4C22×D3211yescharacteristic
808C8—21no—
809C8—61no—
810C8—61no—
811C8—181no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—62no—
816C2×C3—122no—
817C2×C3—241no—
818C2×C3#563011yescharacteristic
819C2×C3#565411yescharacteristic
820C2×C3C2×D3×D811yescharacteristic
821C2×C3C2×D3×D811yescharacteristic
822C2×C3#577811yescharacteristic
823C2×C3#577811yescharacteristic
824D3—22no—
825D3—42no—
826D3—62no—
827D3—62no—
828D3—81no—
829D3—122no—
830D3—241no—
831D3—241no—
832D3—241no—
833D3—241no—
834D3—481no—
835D3—481no—
836C22—32no—
837C22—61no—
838C22—61no—
839C22—62no—
840C22—92no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—181no—
847C22—181no—
848C22—361no—
849C22—361no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—361no—
854C22—724no—
855C22—724no—
856C22D32×D411yescharacteristic
857C4—32no—
858C4—41no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—121no—
863C4—121no—
864C4—181no—
865C4#6430811yescharacteristic
866C4D3×#23911yescharacteristic
867C3—21no—
868C3#8098011yescharacteristic, complemented
869C3#8130211yescharacteristic, complemented
870C2—62no—
871C2—122no—
872C2—182no—
873C2—241no—
874C2—721no—
875C2—721no—
876C2#1059462011yescharacteristic
877C2D32×D811yescharacteristic
878C2#1059476711yescharacteristic
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. #10594517C2semidirect
3. #10592582C2semidirect
4. C3×#4890C2semidirect
5. C3×#4882C2semidirect
6. #10590947C2semidirect
7. #10590940C2semidirect
8. #10590906C2semidirect
9. #10590765C2semidirect
10. #10590598C2semidirect
11. D3×#809C2semidirect
12. #10590576C2semidirect
13. #10590548C2semidirect
14. #10590456C2semidirect
15. #10590442C2semidirect
22. C2×#3745C22semidirect
23. C2×C8×C3⋊D3C22semidirect
25. #64104C22semidirect
28. C3×D3×C4⋊C4C22semidirect
29. C3×#888C22semidirect
33. #63909C22semidirect
36. #63900C22semidirect
38. #63894C22semidirect
42. C2×#3714C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#107C22semidirect
45. #63636C22semidirect
46. #63636C22semidirect
48. C3×#821C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#807C22semidirect
54. C3×#807C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. #4890D3semidirect
78. #4882D3semidirect
194. D3×C4⋊C4C2×D3semidirect
195. #888C2×D3semidirect
206. C3×#107C2×D3semidirect
207. C3×#107C2×D3semidirect
219. #821C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
223. Dic3⋊C8C2×D3semidirect
236. #809C2×D3semidirect
237. #807C2×D3semidirect
238. #807C2×D3semidirect
273. C3×D12#41semidirect
283. #626D8semidirect
486. #107D32semidirect
594. D12#239semidirect
760. C32#3294semidirect
868. C3#80980semidirect
869. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105945172
#105925822
C3×#48902
C3×#48822
#105909472
#105909402
#105909062
#105907652
#105905982
D3×#8092
#105905762
#105905482
#105904562
#105904422
#813023
#809803