Finite Group Databasebeta

← #11889756

Subgroups — #11889756

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5042C211yesmaximal, characteristic, complemented
5#10591488C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591170C211yesmaximal, characteristic, complemented
10#10591147C211yesmaximal, characteristic, complemented
11#10591088C211yesmaximal, characteristic, complemented
12#10590555C211yesmaximal, characteristic, complemented
13#10590518C211yesmaximal, characteristic, complemented
14#10590478C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#80823—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C3×#938—21no—
23C3×#937—21no—
24C3×#936C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#883—21no—
32C3×D3×C22⋊C4—21no—
33#63982—21no—
34#67⋊Dic3—21no—
35#63918C2211yescharacteristic, complemented
36#63893—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63856C2211yescharacteristic
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#810C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63566C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5635—31no—
63#5612D311yescharacteristic
64#5543—31no—
65C3×#468—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69C2×#832—31no—
70#5169—31no—
71#5166—31no—
72#5133—31no—
73#5127—31no—
74#5055—31no—
75#5054—31no—
76#5051—31no—
77#5047—31no—
78#5044—31no—
79#5042D311yescharacteristic, complemented
80#5033—31no—
81#5033—31no—
82#5033—61no—
83#5018—31no—
84#5011—31no—
85#5007—31no—
86#4890—31no—
87#4884—31no—
88#4817—31no—
89#4813—31no—
90D3×#102—31no—
91#4765—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×#214—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C3×#208—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3718—41no—
142#3715—22no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×M16—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×#121—21no—
156C3×#121—61no—
157C3×#121C2×D311yescharacteristic
158C3×#121C2×D311yescharacteristic
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C22⋊C4—61no—
163#946—31no—
164Q8×Dic3—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#215—31no—
168#938—21no—
169#937—21no—
170#936C2×D311yescharacteristic
171D4×Dic3—61no—
172C2×#214—31no—
173C2×#214C2×D311yescharacteristic
174C4×#67C2×D311yescharacteristic
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—61no—
179#924—31no—
180#924C2×D311yescharacteristic, complemented
181C2×#208C2×D311yescharacteristic, complemented
182C22×C3⋊C8—31no—
183C2×D3×C8—31no—
184#897—61no—
185#897C2×D311yescharacteristic
186#893C2×D311yescharacteristic
187D3×C4⋊C4—31no—
188#890—61no—
189#889—61no—
190#888—31no—
191#883—21no—
192#67⋊C4—61no—
193D3×C22⋊C4—21no—
194#878—61no—
195#878—61no—
196#878—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#107—31no—
200C3×#103—31no—
201C3×#102—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832—61no—
214#832C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219#821—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222#816—31no—
223#816—31no—
224#815—31no—
225Dic3⋊C8—31no—
226#810—31no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32—21no—
239C23×C32C2×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—21no—
247C32×D4—81no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—81no—
256C3×#67—22no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275#627—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—91no—
282#546—31no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—31no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—61no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—21no—
321C2×#67—21no—
322C2×#67#6711yescharacteristic
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—121no—
327D3×D4—22no—
328D3×D4—41no—
329#235—22no—
330#235—41no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6C22×D311yescharacteristic
339C2×Dic6C22×D311yescharacteristic
340C3×SD16—121no—
341C3×M16—121no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362#217—21no—
363#217—21no—
364#217—21no—
365#217—61no—
366#217#6711yescharacteristic
367#216—121no—
368#216—121no—
369#215—62no—
370#214—41no—
371#214—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—121no—
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4#6711yescharacteristic
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400#208—41no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13712yes—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×M16—31no—
443C22×C8—91no—
444C4⋊Q8—91no—
445#125—181no—
446#124—31no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451C22⋊Q8—181no—
452C22⋊Q8—181no—
453#121—61no—
454#121D3211yescharacteristic
455#120—61no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—181no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—61no—
463#107—31no—
464#107—91no—
465#107—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479#97—91no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—21no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—81no—
495C22×D3C2×#6711yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—32no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—62no—
508C3×D4—61no—
509C3×D4—81no—
510C3×D4—81no—
511C3×D4—82no—
512C3×D4—122no—
513C3×D4—122no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—241no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—22no—
540#67—42no—
541#67—42no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—241no—
554C2×Dic3—242no—
555C2×Dic3C2×#6711yescharacteristic
556C2×Dic3C2×#6711yescharacteristic
557C2×Dic3C2×#6711yescharacteristic
558D12—21no—
559D12#23712yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—42no—
563C4×D3—81no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—241no—
570Dic6—241no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—121no—
580C3⋊C8—121no—
581C2×C32—41no—
582C2×C32—81no—
583C2×C32#54611yescharacteristic
584C2×C32C2×#13711yescharacteristic
585C2×C32#57611yescharacteristic
586C3×D3—22no—
587C3×D3—42no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8—31no—
592C2×Q8—31no—
593C2×Q8—181no—
594C2×D4—21no—
595C2×D4—31no—
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—62no—
599C2×D4—61no—
600C2×D4—121no—
601C2×D4C2×D3211yescharacteristic
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4C2×D3211yescharacteristic
608Q16—361no—
609SD16—121no—
610SD16—182no—
611M16—121no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—91no—
616C2×C8—361no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4C2×D3211yescharacteristic
629C22⋊C4—21no—
630C22⋊C4—31no—
631C22⋊C4—31no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—181no—
638C42—31no—
639C42—181no—
640C22×C3—22no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—32no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3C2×D3×D411yescharacteristic
667C22×C3C22×#6711yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—84no—
674C2×D3#95112yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4#100411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—21no—
707C23—31no—
708C23—61no—
709C23—122no—
710C23—122no—
711C23—241no—
712C23D3×#6711yescharacteristic
713Q8—61no—
714Q8—61no—
715Q8—61no—
716Q8—61no—
717Q8—721no—
718D4—21no—
719D4—21no—
720D4—32no—
721D4—62no—
722D4—61no—
723D4—81no—
724D4—122no—
725D4—122no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—122no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—241no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—42no—
753C2×C3—41no—
754C2×C3—41no—
755C2×C3—62no—
756C2×C3—81no—
757C2×C3—81no—
758C2×C3—122no—
759C2×C3—161no—
760C2×C3#561011yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3D3×#13711yescharacteristic
763C2×C3#580611yescharacteristic
764C2×C3C2×#95111yescharacteristic
765C2×C3#583511yescharacteristic
766D3—22no—
767D3—42no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—32no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—61no—
776C22—61no—
777C22—62no—
778C22—121no—
779C22—121no—
780C22—244no—
781C22C2×D3×#6711yescharacteristic
782C4—21no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—361no—
791C4—361no—
792C4D3×#23711yescharacteristic
793C4#6431311yescharacteristic
794C3—21no—
795C3#8082311yescharacteristic, complemented
796C3#8349811yescharacteristic, complemented
797C2—41no—
798C2—62no—
799C2—81no—
800C2—122no—
801C2#1059509711yescharacteristic
802C2#1059515011yescharacteristic
803C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5612C2
hypercenter#121D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594993C2semidirect
3. #10592732C2semidirect
4. C3×#5042C2semidirect
5. #10591488C2semidirect
6. #10591458C2semidirect
7. #10591442C2semidirect
8. D3×#832C2semidirect
9. #10591170C2semidirect
10. #10591147C2semidirect
11. #10591088C2semidirect
12. #10590555C2semidirect
13. #10590518C2semidirect
14. #10590478C2semidirect
15. #10590440C2semidirect
21. C2×C4⋊(C3⋊Dic3)C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#208C22semidirect
35. #63918C22semidirect
40. Dic3×Dic6C22semidirect
41. C2×#3718C22semidirect
46. #63657C22semidirect
47. #63634C22semidirect
48. #63634C22semidirect
50. C3×#810C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63566C22semidirect
55. #63565C22semidirect
60. #63554C22semidirect
79. #5042D3semidirect
180. #924C2×D3semidirect
181. C2×#208C2×D3semidirect
227. #810C2×D3semidirect
235. #807C2×D3semidirect
705. C32#3314semidirect
795. C3#80823semidirect
796. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
#105949932
#105927322
C3×#50422
#105914882
#105914582
#105914422
D3×#8322
#105911702
#105911472
#105910882
#105905552
#105905182
#105904782
#105904402
#834983
#808233