Finite Group Databasebeta

← #11887038

Subgroups — #11887038

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#10595293C211yesmaximal, characteristic, complemented
2#10594373C211yesmaximal, characteristic, complemented
3#10592473C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591455C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10Dic3×D24C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590680C211yesmaximal, characteristic, complemented
13#10590593C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#81576—31nomaximal
17#80014—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×#3802C2211yescharacteristic
21C2×#3796—21no—
22#64147C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic, complemented
26C2×C3×D24C2211yescharacteristic
27C3×#895C2211yescharacteristic, complemented
28C3×#888C2211yescharacteristic, complemented
29#63983—21no—
30#63976—21no—
31#63970—21no—
32#63916C2211yescharacteristic, complemented
33#63908C2211yescharacteristic
34C4×#626C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63887—21no—
39#63884—21no—
40#63853—21no—
41C2×#3713C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61D4×#67—31no—
62#5726—31no—
63#5717—31no—
64#5611—31no—
65C3×#486—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5157—31no—
69#5156—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5087—31no—
73#5072—31no—
74#5038—31no—
75#4775—31no—
76#4775—31no—
77#4774—31no—
78#4774—31no—
79#4774—31no—
80#4774—61no—
81#4773—31no—
82#4773D311yescharacteristic, complemented
83D3×#102—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4760D311yescharacteristic, complemented
87#4759—31no—
88#4736—31no—
89#67⋊C8—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×#67—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×D12C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109D3×#67—44no—
110C2×#626—21no—
111C2×#626D411yescharacteristic
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3796—44no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122#3757—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#213—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3713—41no—
144#3710—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×#67—61no—
149C2×#239—61no—
150C2×#237—61no—
151C2×D3×D4—31no—
152C2×D3×D4—31no—
153C2×D3×D4—61no—
154C2×D3×D4C2×D311yescharacteristic
155C2×C3×D8—31no—
156C2×C3×D8—31no—
157C3×C4⋊Q8—31no—
158C3×#127—31no—
159C3×#121—31no—
160#953—61no—
161#946—61no—
162#940C2×D311yescharacteristic
163#939—61no—
164#938—31no—
165#938—31no—
166#938—31no—
167#938—31no—
168#938—61no—
169#938—61no—
170#937—61no—
171#937—61no—
172#937—61no—
173#935—61no—
174D4×Dic3—31no—
175D4×Dic3—31no—
176C2×#213—31no—
177C2×#213—31no—
178C2×#213C2×D311yescharacteristic, complemented
179#930—31no—
180C4×#67—31no—
181C2×C4⋊Dic3—31no—
182C22×C3⋊C8—31no—
183C2×D24C2×D311yescharacteristic
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187#895—31no—
188#895C2×D311yescharacteristic, complemented
189#894—61no—
190#894—61no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—61no—
195#888C2×D311yescharacteristic, complemented
196#883—61no—
197#878—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic, complemented
207C3×#102C2×D311yescharacteristic, complemented
208C3×C22⋊C8—31no—
209C3×C4×C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic, complemented
218#821—31no—
219#821—31no—
220#821—31no—
221#821C2×D311yescharacteristic, complemented
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—61no—
225(C2×D3)⋊C8C2×D311yescharacteristic, complemented
226#818—31no—
227#818—31no—
228#818—31no—
229#818—61no—
230Dic3⋊C8—31no—
231C8×Dic3C2×D311yescharacteristic, complemented
232#809—31no—
233#809C2×D311yescharacteristic
234#809C2×D311yescharacteristic, complemented
235#807—31no—
236#807—31no—
237#807—31no—
238#807—61no—
239C4⋊(C3⋊C8)—31no—
240C23×C32—21no—
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—81no—
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—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—21no—
261C4×C3⋊D3—21no—
262C4×C3⋊D3—42no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12—42no—
276C3×D12#4112yescomplemented
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×Dic6—42no—
280#626—42no—
281#626D814yescomplemented
282#625—42no—
283#625—42no—
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—31no—
294#480—91no—
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×Q8—61no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—62no—
320C2×C3×D4—121no—
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C22×D311yescharacteristic
323C22×C3×C4—31no—
324C2×#67—21no—
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—31no—
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—124no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340#239—124no—
341#237—124no—
342D3×D4—22no—
343D3×D4—41no—
344D3×D4—62no—
345D3×D4—62no—
346D3×D4—121no—
347D3×D4—121no—
348D3×D4—124no—
349C2×D12—21no—
350C2×D12—31no—
351C2×D12—61no—
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
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—62no—
367C3×D8—121no—
368C2×C3×C8—21no—
369C2×C3×C8—31no—
370C2×C3×C8—31no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—21no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C22⋊C4—61no—
379C3×C42—31no—
380#217—31no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—121no—
388#213—41no—
389#213—121no—
390#213—121no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—61no—
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⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D24—22no—
422D3×C8—121no—
423D3×C8—121no—
424D3×C8—121no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
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×D3—84no—
444C2×C3×D3C2×D812yes—
445D32—84no—
446C32×C4—41no—
447C32×C4C2×#4111yescharacteristic
448C32×C4H(5,𝔽2)11yescharacteristic
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—41no—
455C3×Dic3C2×D812yes—
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—31no—
466#127—31no—
467#123—181no—
468#123—181no—
469C22⋊Q8—181no—
470#121—31no—
471#121—91no—
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—91no—
481C2×C4⋊C4—91no—
482#107—91no—
483#107—91no—
484#107—91no—
485C4⋊C8—91no—
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#102D3211yescharacteristic, complemented
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—31no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—41no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—122no—
507C23×C3—122no—
508C23×C3—241no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—42no—
515C22×D3—42no—
516C22×D3—61no—
517C22×D3—81no—
518C22×D3—122no—
519C22×D3—122no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—241no—
523C22×D3—241no—
524C22×D3D3×D411yescharacteristic
525C3×Q8—122no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—32no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—241no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554#67—34no—
555#67—42no—
556#67—42no—
557#67—81no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—122no—
564#67—122no—
565#67—242no—
566C2×Dic3—21no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—122no—
577C2×Dic3—122no—
578C2×Dic3—122no—
579C2×Dic3D3×D411yescharacteristic
580C2×Dic3D3×D411yescharacteristic
581C2×Dic3D3×D411yescharacteristic
582D12—21no—
583D12—21no—
584D12—21no—
585D12—21no—
586D12—21no—
587D12—34no—
588D12—42no—
589D12—122no—
590D12#23712yescomplemented
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—61no—
597C4×D3—121no—
598C4×D3—121no—
599C4×D3—122no—
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—81no—
617C2×C32#54611yescharacteristic
618C2×C32C22×D811yescharacteristic
619C2×C32#57711yescharacteristic
620C3⋊D3—22no—
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624C3×D3—81no—
625C24—61no—
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—61no—
635C2×D4—61no—
636C2×D4—62no—
637C2×D4—91no—
638C2×D4—121no—
639C2×D4—181no—
640C2×D4—181no—
641C2×D4—182no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—361no—
645C2×D4—364no—
646C2×D4C2×D3211yescharacteristic
647C22×C4—31no—
648C22×C4—91no—
649C22×C4—181no—
650C22×C4—181no—
651C22×C4—181no—
652C22×C4—181no—
653D8—62no—
654D8—121no—
655D8—361no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—91no—
659C2×C8—361no—
660C2×C8—361no—
661C2×C8C2×D3211yescharacteristic
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4C2×D3211yescharacteristic
670C22⋊C4—61no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C42—31no—
679C22×C3—21no—
680C22×C3—32no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—244no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—32no—
708C2×D3—32no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—62no—
718C2×D3—61no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—84no—
723C2×D3—121no—
724C2×D3—121no—
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—61no—
734C3×C4—61no—
735C3×C4—81no—
736C3×C4—121no—
737C3×C4C2×#23711yescharacteristic
738C3×C4#100411yescharacteristic
739C3×C4D3×#4111yescharacteristic
740C3×C4#100911yescharacteristic
741Dic3—21no—
742Dic3—21no—
743Dic3—41no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—121no—
749Dic3—121no—
750Dic3—121no—
751Dic3—241no—
752Dic3—241no—
753Dic3D3×D812yes—
754C32#329411yescharacteristic, complemented, Sylow
755C23—21no—
756C23—31no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—91no—
761C23—122no—
762C23—122no—
763C23—241no—
764C23—362no—
765C23—362no—
766C23—721no—
767Q8—122no—
768D4—21no—
769D4—21no—
770D4—32no—
771D4—61no—
772D4—61no—
773D4—61no—
774D4—61no—
775D4—61no—
776D4—94no—
777D4—122no—
778D4—122no—
779D4—122no—
780D4—241no—
781D4—362no—
782D4—362no—
783D4—362no—
784D4—362no—
785C2×C4—21no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—91no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—362no—
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—81no—
811C2×C3—81no—
812C2×C3—122no—
813C2×C3—161no—
814C2×C3—241no—
815C2×C3—241no—
816C2×C3#559111yescharacteristic
817C2×C3#567611yescharacteristic
818C2×C3C2×D3×D811yescharacteristic
819C2×C3C2×D3×D811yescharacteristic
820C2×C3#576211yescharacteristic
821C2×C3#577511yescharacteristic
822D3—22no—
823D3—42no—
824D3—62no—
825D3—62no—
826D3—81no—
827D3—81no—
828D3—122no—
829C22—32no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—61no—
834C22—61no—
835C22—62no—
836C22—92no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—181no—
846C22—181no—
847C22—244no—
848C22—724no—
849C22D32×D411yescharacteristic
850C4—32no—
851C4—41no—
852C4—61no—
853C4—61no—
854C4—121no—
855C4—181no—
856C4—361no—
857C4—361no—
858C4#6430711yescharacteristic
859C4D3×#23711yescharacteristic
860C3—21no—
861C3#8001411yescharacteristic, complemented
862C3#8157611yescharacteristic, complemented
863C2—62no—
864C2—81no—
865C2—122no—
866C2—182no—
867C2—241no—
868C2—241no—
869C2#1059428111yescharacteristic
870C2D32×D811yescharacteristic
871C2#1059474911yescharacteristic
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. #10595293C2semidirect
2. #10594373C2semidirect
3. #10592473C2semidirect
4. C3×#4773C2semidirect
5. C3×#4760C2semidirect
6. #10591455C2semidirect
7. #10591428C2semidirect
8. D3×#832C2semidirect
9. #10590945C2semidirect
10. Dic3×D24C2semidirect
11. #10590721C2semidirect
12. #10590680C2semidirect
13. #10590593C2semidirect
14. #10590499C2semidirect
15. #10590463C2semidirect
23. C4⋊C4×C3⋊D3C22semidirect
25. C2×C3×#213C22semidirect
27. C3×#895C22semidirect
28. C3×#888C22semidirect
32. #63916C22semidirect
36. Dic3×D12C22semidirect
37. D3×C4⋊Dic3C22semidirect
41. C2×#3713C22semidirect
42. C2×#3710C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#102C22semidirect
45. #63659C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63634C22semidirect
49. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×C8×Dic3C22semidirect
54. C3×#809C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
82. #4773D3semidirect
86. #4760D3semidirect
178. C2×#213C2×D3semidirect
188. #895C2×D3semidirect
195. #888C2×D3semidirect
206. C3×#102C2×D3semidirect
207. C3×#102C2×D3semidirect
217. #832C2×D3semidirect
221. #821C2×D3semidirect
225. (C2×D3)⋊C8C2×D3semidirect
231. C8×Dic3C2×D3semidirect
234. #809C2×D3semidirect
276. C3×D12#41semidirect
281. #626D8semidirect
495. #102D32semidirect
590. D12#237semidirect
754. C32#3294semidirect
861. C3#80014semidirect
862. C3#81576semidirect

Maximal subgroups

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

subgroupindex
#105952932
#105943732
#105924732
C3×#47732
C3×#47602
#105914552
#105914282
D3×#8322
#105909452
Dic3×D242
#105907212
#105906802
#105905932
#105904992
#105904632
#815763
#800143