Finite Group Databasebeta

← #11887120

Subgroups — #11887120

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#626C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3C3⋊D3×#102C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4761C211yesmaximal, characteristic, complemented
6#10591467C211yesmaximal, characteristic, complemented
7Dic3×#214C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590906C211yesmaximal, characteristic, complemented
10#10590843C211yesmaximal, characteristic, complemented
11#10590799C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590577C211yesmaximal, characteristic, complemented
14#10590548C211yesmaximal, characteristic, complemented
15#10590511C211yesmaximal, characteristic, complemented
16#81075—31nomaximal
17#80158—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×#626—21no—
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic, complemented
26C3×#897C2211yescharacteristic, complemented
27C3×#888C2211yescharacteristic, complemented
28#63981—21no—
29#63978—21no—
30#63977—21no—
31#63916C2211yescharacteristic
32#63911C2211yescharacteristic
33#63909C2211yescharacteristic
34C4×#626C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic, complemented
36#63887—21no—
37#63881—21no—
38#63871—21no—
39#63871C2211yescharacteristic, complemented
40#63846—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61D4×#67—31no—
62#5730—31no—
63#5635—31no—
64D4×D12—31no—
65C3×#476—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5171—31no—
69#5169—31no—
70#5163—31no—
71Dic3×SD16—31no—
72#5088—31no—
73#5048—31no—
74C4×#214—31no—
75#4864—31no—
76#4864—31no—
77#4863—31no—
78#4863—31no—
79#4848—31no—
80#4834—31no—
81#4777—31no—
82#4776—31no—
83#4776D311yescharacteristic, complemented
84D3×#102—31no—
85D3×#102—31no—
86D3×#102—31no—
87D3×#102—61no—
88#4761D311yescharacteristic, complemented
89#4760—31no—
90#4735—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96D4×C3⋊D3—22no—
97D4×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—44no—
114C2×#626D411yescharacteristic
115C2×D3×Dic3—21no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C8×C3⋊D3—41no—
122C3×#217—21no—
123C3×#214—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—41no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3717—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4C2×D311yescharacteristic
152C22×D12—61no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×C4⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#953—61no—
159#946—31no—
160#946—61no—
161#946—61no—
162Q8×Dic3—31no—
163C2×#215—31no—
164#940—31no—
165#939—61no—
166#938—31no—
167#937—61no—
168D4×Dic3C2×D311yescharacteristic
169C2×#214C2×D311yescharacteristic
170#930—31no—
171#930—61no—
172C4×#67—31no—
173C2×C4⋊Dic3—31no—
174C22×C3⋊C8—31no—
175C2×#204—31no—
176C2×#204C2×D311yescharacteristic, complemented
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8—31no—
180C2×D3×C8—61no—
181#897—31no—
182#897—61no—
183#897C2×D311yescharacteristic, complemented
184#895—31no—
185#895—31no—
186#893—61no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191#890—61no—
192#889—61no—
193#888C2×D311yescharacteristic, complemented
194#882—61no—
195#882—61no—
196#67⋊C4—61no—
197#878—61no—
198#874—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209C3×C22⋊C8—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#817—31no—
226#817C2×D311yescharacteristic, complemented
227Dic3⋊C8C2×D311yescharacteristic, complemented
228C8×Dic3—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic, complemented
236#808—31no—
237#808C2×D311yescharacteristic, complemented
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—21no—
261C4×C3⋊D3—81no—
262C3×#67—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—81no—
277#626—42no—
278#626—42no—
279#626—42no—
280#626—81no—
281#626SD1614yescomplemented
282D3×Dic3—81no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—31no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—121no—
307C2×C3×Q8—31no—
308C2×C3×Q8—61no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4—62no—
313C2×C3×D4—121no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—31no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—121no—
327C2×#67—124no—
328C22×Dic3—21no—
329C22×Dic3—61no—
330D3×D4—22no—
331D3×D4—41no—
332D3×D4—64no—
333D3×D4—62no—
334D3×D4—62no—
335D3×D4—121no—
336D3×D4—121no—
337D3×D4—122no—
338C2×D12—31no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—61no—
346C2×D12—124no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—121no—
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—21no—
357C2×Dic6C22×D311yescharacteristic
358C3×SD16—62no—
359C3×SD16—121no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375#217—21no—
376#217—31no—
377#217—61no—
378#215—121no—
379#214—22no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—31no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—121no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416#204—41no—
417#204—121no—
418D3×C8—121no—
419D3×C8—121no—
420D3×C8—121no—
421D3×C8—122no—
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
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⋊D3—84no—
432C2×C3⋊D3C2×SD1612yes—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C2×C3×D3C2×SD1612yes—
440C32×C4—41no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—21no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3C2×SD1612yes—
451C22×D4—31no—
452C22×D4—91no—
453C22×D4—181no—
454C2×SD16—31no—
455C2×SD16—31no—
456C2×SD16—91no—
457C22×C8—91no—
458C22×C8—91no—
459C4⋊Q8—31no—
460#127—91no—
461#125—181no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466#121—91no—
467#121—91no—
468#121—181no—
469#120—181no—
470#120—181no—
471C4×Q8—91no—
472C4×D4—31no—
473C4×D4—91no—
474C4×D4—181no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477#106—31no—
478#106—31no—
479#106—91no—
480C4⋊C8—31no—
481#103—91no—
482#102—31no—
483#102—31no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102D3211yescharacteristic
491C22⋊C8—31no—
492C22⋊C8—91no—
493C4×C8—91no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C22×D3—21no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—81no—
511C22×D3—121no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—124no—
517C22×D3—242no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—242no—
521C22×D3D3×D411yescharacteristic
522C3×Q8—61no—
523C3×Q8—61no—
524C3×Q8—241no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—22no—
528C3×D4—41no—
529C3×D4—61no—
530C3×D4—61no—
531C3×D4—122no—
532C3×D4#23712yes—
533C3×D4#23912yes—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
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—122no—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549#67—34no—
550#67—42no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—124no—
556#67—122no—
557#67—241no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—42no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—241no—
569C2×Dic3D3×D411yescharacteristic
570C2×Dic3D3×D411yescharacteristic
571C2×Dic3D3×D411yescharacteristic
572D12—21no—
573D12—21no—
574D12—34no—
575D12—62no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12—122no—
582D12—122no—
583D12—122no—
584D12—241no—
585C4×D3—21no—
586C4×D3—21no—
587C4×D3—62no—
588C4×D3—62no—
589C4×D3—61no—
590C4×D3—61no—
591C4×D3—61no—
592C4×D3—61no—
593C4×D3—241no—
594C4×D3—241no—
595C4×D3—241no—
596C4×D3—242no—
597Dic6—21no—
598Dic6—21no—
599Dic6—81no—
600C3×C8—21no—
601C3×C8—21no—
602C3×C8—41no—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—121no—
610C2×C32—42no—
611C2×C32#54611yescharacteristic
612C2×C32C22×SD1611yescharacteristic
613C2×C32#57611yescharacteristic
614C3⋊D3—22no—
615C3⋊D3—81no—
616C3×D3—22no—
617C3×D3—81no—
618C24—61no—
619C24—181no—
620C2×Q8—31no—
621C2×Q8—61no—
622C2×D4—31no—
623C2×D4—61no—
624C2×D4—62no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—121no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—181no—
631C2×D4—181no—
632C2×D4—181no—
633C2×D4—182no—
634C2×D4—364no—
635C2×D4—361no—
636C2×D4C2×D3211yescharacteristic
637C22×C4—31no—
638C22×C4—61no—
639C22×C4—91no—
640C22×C4—181no—
641C22×C4—181no—
642SD16—62no—
643SD16—121no—
644SD16—361no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—91no—
648C2×C8—361no—
649C2×C8—361no—
650C2×C8C2×D3211yescharacteristic
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4—91no—
656C4⋊C4—91no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4C2×D3211yescharacteristic
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C42—31no—
670C42—181no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—32no—
675C22×C3—42no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—121no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—244no—
688C22×C3C2×D3×D411yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—32no—
693C2×D3—32no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—62no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—84no—
705C2×D3—122no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—248no—
717C2×D3D3×SD1612yes—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—32no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—61no—
724C3×C4—61no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4C2×#23711yescharacteristic
730C3×C4#100411yescharacteristic
731C3×C4C2×#23911yescharacteristic
732C3×C4#100911yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—121no—
742Dic3—121no—
743Dic3—241no—
744Dic3D3×SD1612yes—
745C32#329511yescharacteristic, complemented, Sylow
746C23—21no—
747C23—31no—
748C23—61no—
749C23—91no—
750C23—122no—
751C23—122no—
752C23—181no—
753C23—241no—
754C23—362no—
755C23—362no—
756C23—721no—
757Q8—61no—
758Q8—61no—
759Q8—241no—
760D4—21no—
761D4—61no—
762D4—61no—
763D4—94no—
764D4—122no—
765D4—181no—
766D4—181no—
767D4—362no—
768D4—362no—
769D4—362no—
770D4—362no—
771D4—721no—
772D4#379612yes—
773C2×C4—21no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—91no—
783C2×C4—122no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—181no—
787C2×C4—721no—
788C2×C4—721no—
789C2×C4C22×D3211yescharacteristic
790C8—21no—
791C8—61no—
792C8—61no—
793C8—181no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—42no—
798C2×C3—42no—
799C2×C3—62no—
800C2×C3—82no—
801C2×C3—241no—
802C2×C3#559111yescharacteristic
803C2×C3#563011yescharacteristic
804C2×C3C2×D3×SD1611yescharacteristic
805C2×C3C2×D3×SD1611yescharacteristic
806C2×C3#577411yescharacteristic
807C2×C3#577411yescharacteristic
808D3—22no—
809D3—64no—
810D3—62no—
811D3—62no—
812D3—81no—
813D3—242no—
814D3—241no—
815D3—241no—
816C22—22no—
817C22—32no—
818C22—41no—
819C22—41no—
820C22—61no—
821C22—61no—
822C22—92no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—181no—
827C22—181no—
828C22—244no—
829C22—361no—
830C22—361no—
831C22—361no—
832C22—724no—
833C22D32×D411yescharacteristic
834C4—32no—
835C4—41no—
836C4—61no—
837C4—61no—
838C4—121no—
839C4—121no—
840C4—121no—
841C4—181no—
842C4—361no—
843C4C2×#379611yescharacteristic
844C4#6431411yescharacteristic
845C3—21no—
846C3#8015811yescharacteristic, complemented
847C3#8107511yescharacteristic, complemented
848C2—42no—
849C2—62no—
850C2—182no—
851C2—241no—
852C2—721no—
853C2#1059406311yescharacteristic
854C2#1059473511yescharacteristic
855C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD4×#626C2
hypercenter#102D32
hypocenterC32#3295
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
2. #10594393C2semidirect
3. C3⋊D3×#102C2semidirect
4. C3×#4776C2semidirect
5. C3×#4761C2semidirect
6. #10591467C2semidirect
7. Dic3×#214C2semidirect
8. D3×#832C2semidirect
9. #10590906C2semidirect
10. #10590843C2semidirect
11. #10590799C2semidirect
12. #10590677C2semidirect
13. #10590577C2semidirect
14. #10590548C2semidirect
15. #10590511C2semidirect
21. C2×C8×C3⋊D3C22semidirect
22. C4⋊C4×C3⋊D3C22semidirect
25. C2×C3×#204C22semidirect
26. C3×#897C22semidirect
27. C3×#888C22semidirect
35. D3×C4⋊Dic3C22semidirect
39. #63871C22semidirect
41. Dic3×Dic6C22semidirect
42. C2×#3717C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63648C22semidirect
47. #63636C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#817C22semidirect
51. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#808C22semidirect
54. #63573C22semidirect
55. #63565C22semidirect
56. #63564C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. #63557C22semidirect
60. Dic3×C3⋊C8C22semidirect
83. #4776D3semidirect
88. #4761D3semidirect
176. C2×#204C2×D3semidirect
183. #897C2×D3semidirect
193. #888C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
226. #817C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
235. #809C2×D3semidirect
237. #808C2×D3semidirect
281. #626SD16semidirect
745. C32#3295semidirect
846. C3#80158semidirect
847. C3#81075semidirect

Maximal subgroups

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

subgroupindex
D4×#6262
#105943932
C3⋊D3×#1022
C3×#47762
C3×#47612
#105914672
Dic3×#2142
D3×#8322
#105909062
#105908432
#105907992
#105906772
#105905772
#105905482
#105905112
#810753
#801583