Finite Group Databasebeta

← #11887039

Subgroups — #11887039

Order 1152.

1047 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic, complemented
2#10594370C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic, complemented
4C3×#4774C211yesmaximal, characteristic, complemented
5C3×#4773C211yesmaximal, characteristic, complemented
6#10591498C211yesmaximal, characteristic, complemented
7#10591433C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590777C211yesmaximal, characteristic, complemented
11#10590718C211yesmaximal, characteristic, complemented
12#10590679C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590576C211yesmaximal, characteristic, complemented
15#10590471C211yesmaximal, characteristic, complemented
16#81302—31nomaximal
17#80014—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3795—21no—
22#64149C2211yescharacteristic
23#64097C2211yescharacteristic, complemented
24C3×#938C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C3×#895C2211yescharacteristic, complemented
28C3×D3×C4⋊C4C2211yescharacteristic, complemented
29#63983—21no—
30#63977—21no—
31#63971—21no—
32#63909C2211yescharacteristic
33#63908C2211yescharacteristic, complemented
34#63905—21no—
35C4×#625C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63896—21no—
39D3×C4⋊Dic3C2211yescharacteristic, complemented
40#63884—21no—
41C2×#3714C2211yescharacteristic, complemented
42C2×D3×C3⋊C8C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48#63636C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×#818C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61D4×#67—31no—
62#5611—31no—
63#5609—31no—
64#5507—31no—
65C3×#480—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5157—31no—
69#5156—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5038—31no—
73#5038—31no—
74C2×#809—31no—
75#4890—31no—
76#4883—31no—
77#4882—31no—
78#4872—31no—
79#4786—31no—
80#4774D311yescharacteristic, complemented
81#4773D311yescharacteristic, complemented
82D3×#102—31no—
83D3×#102—31no—
84#4760—31no—
85#4760—31no—
86#4760—61no—
87#4759—31no—
88#4736—31no—
89#4732—31no—
90#67⋊C8—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109D3×#67—44no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#625D411yescharacteristic
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119#3795—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#213—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143#3714—41no—
144D3×C3⋊C8—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#237—61no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×D3×D4C2×D311yescharacteristic
153C2×#235—61no—
154C22×D12—31no—
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C3×#121—31no—
158C3×#121—31no—
159C2×C3×C4⋊C4—31no—
160#953—61no—
161#940—31no—
162#940—31no—
163#940—61no—
164#939—61no—
165#938—31no—
166#938C2×D311yescharacteristic
167#937—61no—
168#937—61no—
169#935—61no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172C2×#213—31no—
173C2×#213C2×D311yescharacteristic, complemented
174#930—31no—
175#930—31no—
176#929—61no—
177C4×#67—31no—
178C4×#67—31no—
179C2×C4⋊Dic3—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182C2×D24—31no—
183C2×D24C2×D311yescharacteristic
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186#896—61no—
187#895—31no—
188#895C2×D311yescharacteristic, complemented
189#894—61no—
190#893—31no—
191#893—31no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4C2×D311yescharacteristic, complemented
194#888—31no—
195#888—31no—
196#888—61no—
197#884—61no—
198#883—61no—
199#882—61no—
200#878—61no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic, complemented
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224#818—31no—
225#818C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—61no—
237#809C2×D311yescharacteristic
238#807—31no—
239#807C2×D311yescharacteristic, complemented
240C23×C32—21no—
241C22×C3⋊D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C22×C3×D3C2×D411yescharacteristic
249C2×D32—42no—
250C2×D32—42no—
251C2×D32—81no—
252C32×D4—21no—
253C32×D4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2411yescharacteristic
256#638—42no—
257#638—81no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)—21no—
263#634—42no—
264C3×#67—42no—
265C3×#67—42no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×D12#4112yescomplemented
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—42no—
280#626—42no—
281#626—42no—
282#625—42no—
283#625D814yescomplemented
284D3×Dic3—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—31no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—31no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—62no—
316C2×C3×D4—61no—
317C2×C3×D4—121no—
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—121no—
336C2×#67—121no—
337C2×#67—124no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341#237—124no—
342D3×D4—22no—
343D3×D4—41no—
344D3×D4—62no—
345D3×D4—121no—
346D3×D4—124no—
347#235—124no—
348C2×D12—21no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—121no—
356C2×D12C22×D311yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3C22×D311yescharacteristic
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6—61no—
365C2×Dic6—61no—
366C2×Dic6—121no—
367C3×D8—62no—
368C3×D8—121no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C22×D311yescharacteristic
374C3×C4⋊C4—21no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—61no—
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C22×D311yescharacteristic
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382#217—21no—
383#217—31no—
384#217—31no—
385#217—61no—
386#217—61no—
387#217—61no—
388#213—41no—
389#213—121no—
390(C2×D3)⋊C4—21no—
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—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3C22×D311yescharacteristic
403C4⋊Dic3C22×D311yescharacteristic
404Dic3⋊C4—21no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—121no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—61no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—22no—
422D24—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—22no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—84no—
443C2×C3×D3C2×D812yes—
444C2×C3×D3C2×D812yes—
445D32—84no—
446C32×C4—41no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3⋊Dic3C2×D812yes—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C2×#41—181no—
457C22×D4—31no—
458C22×D4—91no—
459C22×D4—181no—
460C2×D8—31no—
461C2×D8—31no—
462C2×D8—91no—
463C22×C8—91no—
464C22×C8—91no—
465C4⋊Q8—91no—
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—91no—
478C4×D4—91no—
479C4×D4—91no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—31no—
483#107—31no—
484#107—91no—
485C4⋊C8—91no—
486#102—31no—
487#102—31no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102D3211yescharacteristic, complemented
496C22⋊C8—31no—
497C22⋊C8—31no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—122no—
507C23×C3—122no—
508C23×C3—241no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—42no—
512C22×D3—42no—
513C22×D3—61no—
514C22×D3—61no—
515C22×D3—81no—
516C22×D3—121no—
517C22×D3—122no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—241no—
522C22×D3—241no—
523C22×D3D3×D411yescharacteristic
524C22×D3D3×D411yescharacteristic
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—32no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—61no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C3×D4—122no—
537C3×D4—122no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—41no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—122no—
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—34no—
554#67—34no—
555#67—42no—
556#67—42no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—242no—
564#67—241no—
565#67—241no—
566#67—242no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—122no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3D3×D411yescharacteristic
582C2×Dic3D3×D411yescharacteristic
583D12—21no—
584D12—21no—
585D12—21no—
586D12—42no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—61no—
591D12—121no—
592D12—121no—
593D12—122no—
594D12—122no—
595D12#23712yescomplemented
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—42no—
601C4×D3—122no—
602C4×D3—122no—
603C4×D3—122no—
604Dic6—122no—
605Dic6—122no—
606Dic6—242no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—41no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—121no—
617C2×C32—81no—
618C2×C32#54611yescharacteristic
619C2×C32C22×D811yescharacteristic
620C2×C32#57711yescharacteristic
621C3⋊D3—81no—
622C3×D3—22no—
623C3×D3—22no—
624C3×D3—42no—
625C3×D3—81no—
626C24—61no—
627C24—181no—
628#41—364no—
629C2×Q8—181no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—61no—
633C2×D4—61no—
634C2×D4—62no—
635C2×D4—61no—
636C2×D4—91no—
637C2×D4—91no—
638C2×D4—121no—
639C2×D4—181no—
640C2×D4—182no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—361no—
646C2×D4—364no—
647C2×D4C2×D3211yescharacteristic
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—61no—
651C22×C4—181no—
652C22×C4—181no—
653C22×C4—181no—
654D8—62no—
655D8—121no—
656D8—361no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—91no—
660C2×C8—361no—
661C2×C8—361no—
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—61no—
666C4⋊C4—91no—
667C4⋊C4—91no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—91no—
680C22×C3—21no—
681C22×C3—32no—
682C22×C3—32no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—244no—
703C22×C3C2×D3×D411yescharacteristic
704C22×C3C2×D3×D411yescharacteristic
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—22no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—84no—
716C2×D3—121no—
717C2×D3—121no—
718C2×D3—121no—
719C2×D3—121no—
720C2×D3—121no—
721C2×D3—121no—
722C2×D3—241no—
723C2×D3—241no—
724C2×D3—241no—
725C2×D3—244no—
726C2×D3—244no—
727C2×D3D3×D812yes—
728C2×D3D3×D812yes—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—81no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4C2×#23711yescharacteristic
739C3×C4#100411yescharacteristic
740C3×C4D3×#4111yescharacteristic
741C3×C4#100911yescharacteristic
742Dic3—21no—
743Dic3—21no—
744Dic3—32no—
745Dic3—32no—
746Dic3—41no—
747Dic3—41no—
748Dic3—62no—
749Dic3—62no—
750Dic3—61no—
751Dic3—61no—
752Dic3—121no—
753Dic3—121no—
754Dic3—241no—
755C32#329411yescharacteristic, complemented, Sylow
756C23—21no—
757C23—31no—
758C23—31no—
759C23—61no—
760C23—61no—
761C23—122no—
762C23—122no—
763C23—181no—
764C23—241no—
765C23—362no—
766C23—362no—
767C23—721no—
768Q8—362no—
769D4—21no—
770D4—21no—
771D4—32no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—94no—
776D4—122no—
777D4—122no—
778D4—122no—
779D4—181no—
780D4—181no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—362no—
785D4—721no—
786C2×C4—21no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—122no—
798C2×C4—181no—
799C2×C4—362no—
800C2×C4—362no—
801C2×C4—362no—
802C2×C4C22×D3211yescharacteristic
803C8—21no—
804C8—61no—
805C8—61no—
806C8—181no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—62no—
811C2×C3—62no—
812C2×C3—81no—
813C2×C3—81no—
814C2×C3—122no—
815C2×C3—161no—
816C2×C3—241no—
817C2×C3#559111yescharacteristic
818C2×C3#565411yescharacteristic
819C2×C3C2×D3×D811yescharacteristic
820C2×C3C2×D3×D811yescharacteristic
821C2×C3#577511yescharacteristic
822C2×C3#577811yescharacteristic
823D3—22no—
824D3—22no—
825D3—42no—
826D3—81no—
827D3—241no—
828D3—241no—
829D3—481no—
830C22—32no—
831C22—32no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—61no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—62no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—244no—
846C22—361no—
847C22—361no—
848C22—361no—
849C22—724no—
850C22D32×D411yescharacteristic
851C4—41no—
852C4—61no—
853C4—61no—
854C4—92no—
855C4—121no—
856C4—121no—
857C4—181no—
858C4—361no—
859C4#6430711yescharacteristic
860C4D3×#23711yescharacteristic
861C3—21no—
862C3#8001411yescharacteristic, complemented
863C3#8130211yescharacteristic, complemented
864C2—62no—
865C2—62no—
866C2—81no—
867C2—122no—
868C2—241no—
869C2—721no—
870C2#1059427411yescharacteristic
871C2D32×D811yescharacteristic
872C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595288C2semidirect
2. #10594370C2semidirect
3. #10592459C2semidirect
4. C3×#4774C2semidirect
5. C3×#4773C2semidirect
6. #10591498C2semidirect
7. #10591433C2semidirect
8. D3×#832C2semidirect
9. #10590944C2semidirect
10. #10590777C2semidirect
11. #10590718C2semidirect
12. #10590679C2semidirect
13. D3×#809C2semidirect
14. #10590576C2semidirect
15. #10590471C2semidirect
23. #64097C22semidirect
25. C2×C3×#213C22semidirect
27. C3×#895C22semidirect
28. C3×D3×C4⋊C4C22semidirect
33. #63908C22semidirect
37. #63898C22semidirect
39. D3×C4⋊Dic3C22semidirect
41. C2×#3714C22semidirect
42. C2×D3×C3⋊C8C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63648C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. #63636C22semidirect
49. C3×#832C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×#818C22semidirect
54. C3×#807C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
60. #63562C22semidirect
80. #4774D3semidirect
81. #4773D3semidirect
173. C2×#213C2×D3semidirect
188. #895C2×D3semidirect
193. D3×C4⋊C4C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
216. #832C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
225. #818C2×D3semidirect
239. #807C2×D3semidirect
274. C3×D12#41semidirect
283. #625D8semidirect
495. #102D32semidirect
595. D12#237semidirect
755. C32#3294semidirect
862. C3#80014semidirect
863. C3#81302semidirect

Maximal subgroups

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

subgroupindex
#105952882
#105943702
#105924592
C3×#47742
C3×#47732
#105914982
#105914332
D3×#8322
#105909442
#105907772
#105907182
#105906792
D3×#8092
#105905762
#105904712
#813023
#800143