Finite Group Databasebeta

← #11889703

Subgroups — #11889703

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595246C211yesmaximal, characteristic
2#10594393C211yesmaximal, characteristic, complemented
3#10592470C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4759C211yesmaximal, characteristic, complemented
6#10591466C211yesmaximal, characteristic, complemented
7#10591440C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590907C211yesmaximal, characteristic, complemented
10#10590859C211yesmaximal, characteristic, complemented
11#10590845C211yesmaximal, characteristic, complemented
12#10590684C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590531C211yesmaximal, characteristic, complemented
15#10590510C211yesmaximal, characteristic, complemented
16#80982—31nomaximal
17#80163—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×#3743C2211yescharacteristic, complemented
21C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27#63978—21no—
28#63977—21no—
29#63962—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63916C2211yescharacteristic
32C4×#626C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63881—21no—
36#63871—21no—
37#63871C2211yescharacteristic, complemented
38#63860C2211yescharacteristic
39#63857C2211yescharacteristic
40#63846—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63637C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×Dic3⋊C8C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61#5806—31no—
62#5730—31no—
63#5635—31no—
64#5554—31no—
65C3×#474—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5174—31no—
69#5173—31no—
70#5166—31no—
71#5164—31no—
72#5089—31no—
73#5051—31no—
74#5018—31no—
75#4887—31no—
76#4886—31no—
77#4884—31no—
78#4882—31no—
79#4845—31no—
80#4836—31no—
81#4783—31no—
82#4776D311yescharacteristic, complemented
83#4774—31no—
84#4771—31no—
85#4771—31no—
86#4771—61no—
87D3×#102—31no—
88#4765—31no—
89#4759D311yescharacteristic, complemented
90#4730—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830—41no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
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×#626D411yescharacteristic
111C2×D3×Dic3—21no—
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—41no—
118C3×#217—21no—
119C3×#214—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#237—31no—
148C2×#237—61no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C3×C4⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#953—61no—
156C2×#217—61no—
157#946—31no—
158#946—61no—
159#946—61no—
160Q8×Dic3—31no—
161C2×#216—31no—
162#939—61no—
163#938—31no—
164#936—31no—
165#935—61no—
166D4×Dic3C2×D311yescharacteristic
167C2×#214C2×D311yescharacteristic
168#930—61no—
169C4×#67—31no—
170C2×(C2×D3)⋊C4—61no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173C22×C3⋊C8—31no—
174C2×Dic12—31no—
175C2×#204C2×D311yescharacteristic
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179C2×D3×C8—31no—
180#897—31no—
181#897—31no—
182#897—61no—
183#897C2×D311yescharacteristic
184#895—31no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190#890—61no—
191#889—61no—
192#888C2×D311yescharacteristic, complemented
193#886—61no—
194#882—61no—
195#67⋊C4—61no—
196#878—61no—
197#875—31no—
198C4×D12—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×C22⋊C8—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#818C2×D311yescharacteristic, complemented
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#815—31no—
227Dic3⋊C8C2×D311yescharacteristic, complemented
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#809—31no—
234#809C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C4×C3⋊D3—81no—
257#634—21no—
258#634—21no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—81no—
274#626—22no—
275#626—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—31no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—121no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C22×Dic3—21no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—121no—
320#237—64no—
321#237—62no—
322#237—62no—
323#237—121no—
324#237—121no—
325#237—122no—
326D3×D4—22no—
327D3×D4—41no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—31no—
332C2×C4×D3—31no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—21no—
340C2×Dic6—31no—
341C2×Dic6—31no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—62no—
345C3×SD16—121no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—31no—
361#217—21no—
362#217—31no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#216—121no—
368#214—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—121no—
409#204—41no—
410ΓL(1,𝔽25)—121no—
411ΓL(1,𝔽25)—121no—
412ΓL(1,𝔽25)—122no—
413D3×C8—121no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C2×C3×D3#13712yes—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—31no—
442C2×Q16—91no—
443C2×SD16—31no—
444C2×SD16—31no—
445C2×M16—91no—
446C22×C8—91no—
447C4⋊Q8—31no—
448#125—181no—
449#124—91no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—181no—
458#120—181no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—31no—
468#107—91no—
469C4⋊C8—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—91no—
482#97—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C22×D3—21no—
492C22×D3—31no—
493C22×D3—31no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—61no—
497C22×D3—81no—
498C22×D3D3×D411yescharacteristic
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—241no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—122no—
509C3×D4#23712yes—
510C3×D4#23912yes—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—241no—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—42no—
527#67—62no—
528#67—122no—
529#67—122no—
530#67—124no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—81no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—124no—
548C2×Dic3—241no—
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552D12—21no—
553D12—21no—
554D12—62no—
555D12—241no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—62no—
559C4×D3—62no—
560C4×D3—61no—
561C4×D3—61no—
562C4×D3—61no—
563C4×D3—61no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—242no—
568Dic6—21no—
569Dic6—21no—
570Dic6—62no—
571Dic6—61no—
572Dic6—61no—
573Dic6—61no—
574Dic6—61no—
575Dic6—81no—
576Dic6—121no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C2×C32—42no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13711yescharacteristic
590C2×C32#57611yescharacteristic
591C3⋊D3—41no—
592C3×D3—22no—
593C3×D3—81no—
594C24—61no—
595#41—182no—
596#41—361no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8—91no—
600C2×D4—31no—
601C2×D4—61no—
602C2×D4—62no—
603C2×D4—91no—
604C2×D4—121no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4C2×D3211yescharacteristic
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—91no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614Q16—361no—
615SD16—62no—
616SD16—121no—
617M16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—361no—
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4C2×D3211yescharacteristic
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—181no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—244no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—62no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—84no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3#91512yes—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23711yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4C2×#23911yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—62no—
703Dic3—61no—
704Dic3—61no—
705Dic3—122no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711C32#331411yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—61no—
715C23—91no—
716C23—122no—
717C23—122no—
718C23—241no—
719Q8—61no—
720Q8—61no—
721Q8—181no—
722Q8—181no—
723Q8—241no—
724D4—21no—
725D4—61no—
726D4—61no—
727D4—122no—
728D4—182no—
729D4—362no—
730D4—721no—
731D4#379612yes—
732C2×C4—21no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—91no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—241no—
747C2×C4—362no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4C22×D3211yescharacteristic
751C8—21no—
752C8—61no—
753C8—61no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—42no—
759C2×C3—42no—
760C2×C3—62no—
761C2×C3—82no—
762C2×C3—241no—
763C2×C3#559111yescharacteristic
764C2×C3#563011yescharacteristic
765C2×C3#575711yescharacteristic
766C2×C3C2×#91511yescharacteristic
767C2×C3#577411yescharacteristic
768C2×C3D3×#13711yescharacteristic
769D3—22no—
770D3—81no—
771D3—122no—
772D3—121no—
773D3—121no—
774C22—22no—
775C22—32no—
776C22—41no—
777C22—41no—
778C22—61no—
779C22—61no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22—244no—
787C22D32×D411yescharacteristic
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—181no—
796C4—361no—
797C4—361no—
798C4C2×#379611yescharacteristic
799C4#6431411yescharacteristic
800C3—21no—
801C3#8016311yescharacteristic, complemented
802C3#8098211yescharacteristic, complemented
803C2—42no—
804C2—62no—
805C2—241no—
806C2—361no—
807C2#1059406311yescharacteristic
808C2#1059473211yescharacteristic
809C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595246C2
hypercenter#102D32
hypocenterC32#3314
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. #10592470C2semidirect
4. C3×#4776C2semidirect
5. C3×#4759C2semidirect
6. #10591466C2semidirect
7. #10591440C2semidirect
8. D3×#832C2semidirect
9. #10590907C2semidirect
10. #10590859C2semidirect
11. #10590845C2semidirect
12. #10590684C2semidirect
13. #10590579C2semidirect
14. #10590531C2semidirect
15. #10590510C2semidirect
20. C2×#3743C22semidirect
21. C4⋊C4×C3⋊D3C22semidirect
26. C3×#888C22semidirect
37. #63871C22semidirect
41. Dic3×Dic6C22semidirect
42. C2×#3719C22semidirect
46. #63643C22semidirect
47. #63637C22semidirect
50. C3×#818C22semidirect
51. C3×Dic3⋊C8C22semidirect
53. C3×#807C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63565C22semidirect
59. #63557C22semidirect
60. #63554C22semidirect
82. #4776D3semidirect
89. #4759D3semidirect
192. #888C2×D3semidirect
221. #818C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
236. #807C2×D3semidirect
711. C32#3314semidirect
801. C3#80163semidirect
802. C3#80982semidirect

Maximal subgroups

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

subgroupindex
#105952462
#105943932
#105924702
C3×#47762
C3×#47592
#105914662
#105914402
D3×#8322
#105909072
#105908592
#105908452
#105906842
#105905792
#105905312
#105905102
#809823
#801633