Finite Group Databasebeta

← #11887259

Subgroups — #11887259

Order 1152.

910 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
1C3×#5806C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591478C211yesmaximal, characteristic, complemented
6#10591463C211yesmaximal, characteristic, complemented
7#10591460C211yesmaximal, characteristic, complemented
8#10591441C211yesmaximal, characteristic, complemented
9#10591423C211yesmaximal, characteristic, complemented
10#10591420C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591187C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591101C211yesmaximal, characteristic, complemented
16#83494—31nomaximal
17#78759—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#953—21no—
24C2×C3×#217—21no—
25C3×#939—21no—
26C3×#938C2211yescharacteristic
27C3×#936C2211yescharacteristic
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34#63961—21no—
35#63955—21no—
36#63869C2211yescharacteristic, complemented
37#63858—21no—
38#63857C2211yescharacteristic, complemented
39#63847—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic
63#5541—31no—
64#5513—31no—
65C2×C3×#102—31no—
66#5239—31no—
67#5233—31no—
68#5218—31no—
69#5218—31no—
70#5218—61no—
71C2×#832D311yescharacteristic, complemented
72#5116—31no—
73C8×#67—31no—
74#5056—31no—
75#5054—31no—
76#5051—31no—
77#5043—31no—
78#5041—31no—
79#5035—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#5009—31no—
83#4971—31no—
84#4784—31no—
85#4783—31no—
86#4778—31no—
87#4772—31no—
88#4768—31no—
89#4767—31no—
90#4766—31no—
91#4758—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—41no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C3×#237—22no—
107C3×#237—41no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110#3757—21no—
111#3754—22no—
112#3754—41no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C22×C3×C8—31no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×#121—31no—
155C3×#121—61no—
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—61no—
161#953—21no—
162C2×#217—21no—
163C2×#216—31no—
164#939—21no—
165#938C2×D311yescharacteristic
166#936C2×D311yescharacteristic
167#935—21no—
168#935—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175C2×#214—61no—
176#929—61no—
177C4×#67C2×D311yescharacteristic
178#926—31no—
179#926—61no—
180C2×C4⋊Dic3C2×D311yescharacteristic
181#924—31no—
182#924—31no—
183#924—31no—
184#924—61no—
185#924C2×D311yescharacteristic
186C22×C3⋊C8—31no—
187C22×C3⋊C8C2×D311yescharacteristic
188C2×Dic12—31no—
189C2×D3×C8—31no—
190#898—61no—
191#897—31no—
192#892—31no—
193#890—31no—
194#889—61no—
195#889—61no—
196#887—31no—
197#879—61no—
198#877—61no—
199#870—31no—
200C4×Dic6—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—61no—
213#832—61no—
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222(C2×D3)⋊C8—31no—
223#818—31no—
224#816—31no—
225#816—31no—
226Dic3⋊C8—31no—
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—42no—
241C23×C32—42no—
242C23×C32—81no—
243C23×C32C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3—81no—
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—31no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—31no—
294C24×C3—21no—
295C24×C3—21no—
296C24×C3—41no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—31no—
300C2×C3×D4—22no—
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—41no—
308C2×C3×D4—42no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—42no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67#6711yescharacteristic
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331#237—22no—
332#237—41no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355#217—21no—
356#217—21no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365#217#6711yescharacteristic
366#216—121no—
367#214—62no—
368#214—62no—
369#214—122no—
370#214—121no—
371#214—121no—
372#214—122no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395Dic3⋊C4#6711yescharacteristic
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—41no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411Dic12—121no—
412D3×C8—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—84no—
422C22×C32#13512yes—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4D3211yescharacteristic
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—91no—
446#126—181no—
447#125—91no—
448#125—181no—
449#124—31no—
450#123—61no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—31no—
456#121—61no—
457#120—61no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461#117—91no—
462#117—181no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—61no—
465#107—91no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—42no—
491C23×C3—42no—
492C23×C3—44no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—82no—
496C23×C3—81no—
497C23×C3—81no—
498C23×C3—82no—
499C23×C3D3×D411yescharacteristic
500C23×C3C2×#6711yescharacteristic
501C22×D3C2×#6711yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—22no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—42no—
515C3×D4—42no—
516C3×D4—44no—
517C3×D4—62no—
518C3×D4—122no—
519C3×D4—241no—
520C3×D4#23512yes—
521C3×D4#23712yes—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4—122no—
541C2×C3×C4—241no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—22no—
547#67—42no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—81no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3C2×#6711yescharacteristic
563C2×Dic3C2×#6711yescharacteristic
564C2×Dic3C2×#6711yescharacteristic
565C4×D3—21no—
566C4×D3—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—121no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—22no—
586C2×C32—42no—
587C2×C32—81no—
588C2×C32#54611yescharacteristic
589C2×C32C2×#13511yescharacteristic
590C2×C32#57711yescharacteristic
591C3×D3—41no—
592C24—21no—
593#41—62no—
594#41—121no—
595C2×Q8—31no—
596C2×Q8—91no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—31no—
600C2×D4—41no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4C2×D3211yescharacteristic
604C2×D4C2×D3211yescharacteristic
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4C2×D3211yescharacteristic
610Q16—361no—
611SD16—182no—
612SD16—361no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—91no—
616C2×C8—91no—
617C2×C8—121no—
618C2×C8—361no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C42—181no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—84no—
674C22×C3—84no—
675C22×C3—88no—
676C22×C3#91212yes—
677C22×C3#95012yes—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C22×#6711yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4C2×#23511yescharacteristic
696C3×C4C2×#23711yescharacteristic
697C3×C4#100411yescharacteristic
698C3×C4#100411yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712C32#329611yescharacteristic, complemented, Sylow
713C23—21no—
714C23—21no—
715C23—31no—
716C23—42no—
717C23—42no—
718C23—81no—
719C23D3×#6711yescharacteristic
720Q8—61no—
721Q8—61no—
722Q8—181no—
723Q8—181no—
724D4—21no—
725D4—21no—
726D4—21no—
727D4—42no—
728D4—62no—
729D4—122no—
730D4—241no—
731D4#380412yes—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—241no—
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—61no—
751C8—61no—
752C8—181no—
753C8—181no—
754C2×C3—22no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—42no—
760C2×C3—42no—
761C2×C3—42no—
762C2×C3—82no—
763C2×C3—82no—
764C2×C3—81no—
765C2×C3—81no—
766C2×C3—121no—
767C2×C3#549011yescharacteristic
768C2×C3C2×#91211yescharacteristic
769C2×C3#576211yescharacteristic
770C2×C3#580611yescharacteristic
771C2×C3C2×#95011yescharacteristic
772C2×C3#583611yescharacteristic
773D3—41no—
774C22—21no—
775C22—21no—
776C22—22no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—84no—
786C22#6393312yes—
787C22C2×D3×#6711yescharacteristic
788C4—21no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—361no—
797C4—361no—
798C4C2×#380411yescharacteristic
799C4#6433011yescharacteristic
800C3—21no—
801C3#7875911yescharacteristic, complemented
802C3#8349411yescharacteristic, complemented
803C2—22no—
804C2—42no—
805C2—81no—
806C2—121no—
807C2#1059510511yescharacteristic
808C2C2×#6393311yescharacteristic
809C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594849C2semidirect
3. #10592917C2semidirect
4. C2×C3×#832C2semidirect
5. #10591478C2semidirect
6. #10591463C2semidirect
7. #10591460C2semidirect
8. #10591441C2semidirect
9. #10591423C2semidirect
10. #10591420C2semidirect
11. #10591411C2semidirect
12. #10591401C2semidirect
13. #10591187C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591101C2semidirect
36. #63869C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
41. #63841C22semidirect
42. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63574C22semidirect
53. #63574C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. C2×#832D3semidirect
712. C32#3296semidirect
801. C3#78759semidirect
802. C3#83494semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105948492
#105929172
C2×C3×#8322
#105914782
#105914632
#105914602
#105914412
#105914232
#105914202
#105914112
#105914012
#105911872
C3⋊C8×#672
#105911012
#834943
#787593