Finite Group Databasebeta

← #11889712

Subgroups — #11889712

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591502C211yesmaximal, characteristic, complemented
6#10591488C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591442C211yesmaximal, characteristic, complemented
9#10591440C211yesmaximal, characteristic, complemented
10#10591414C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12#10591410C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#10591158C211yesmaximal, characteristic, complemented
15#10591103C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#80163—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#953—21no—
23C2×C3×#217—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#936C2211yescharacteristic
27C3×#935—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63982—21no—
35#67⋊Dic3—21no—
36#63918C2211yescharacteristic, complemented
37#63893—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63856C2211yescharacteristic, complemented
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3718C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5806D311yescharacteristic
63#5635—31no—
64#5543—31no—
65C3×#450—31no—
66#5239—31no—
67#5232—31no—
68#5218D311yescharacteristic, complemented
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5174—31no—
73#5173—31no—
74#5166—31no—
75#5164—31no—
76#5055—31no—
77#5054—31no—
78#5051—31no—
79#5051—31no—
80#5044—31no—
81#5042—31no—
82#5033—31no—
83#5018—31no—
84#5011—31no—
85#5007—31no—
86#4774—31no—
87#4771—31no—
88#4765—31no—
89#4759—31no—
90#4730—31no—
91#4722—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
99C22×C3⋊Dic3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#237—22no—
106C3×#237—41no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×#214—22no—
126C3×#214—41no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3718—41no—
143#3711—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C22⋊C4—61no—
162#953—21no—
163C2×#217—21no—
164#946—31no—
165Q8×Dic3—31no—
166C2×#216—31no—
167C2×#216—31no—
168#939—21no—
169#938C2×D311yescharacteristic
170#936C2×D311yescharacteristic
171#935—21no—
172D4×Dic3—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214C2×D311yescharacteristic
175C2×#214C2×D311yescharacteristic
176C4×#67C2×D311yescharacteristic
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—61no—
181#924—31no—
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×ΓL(1,𝔽25)—31no—
189#897—61no—
190D3×C4⋊C4—31no—
191#890—61no—
192#889—61no—
193#888—31no—
194#67⋊C4—61no—
195#878—61no—
196#878—61no—
197#878—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832—61no—
217#832—61no—
218#832—61no—
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#818—31no—
225#818—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229Dic3⋊C8—31no—
230#810—31no—
231#810—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—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—
256C2×C3⋊Dic3—81no—
257C3×#67—22no—
258C3×#67—42no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×C4×D3—21no—
270C3×C4×D3—21no—
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—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—21no—
297C24×C3—21no—
298C24×C3—41no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×D4—24no—
304C2×C3×D4—22no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—41no—
313C2×C3×D4—41no—
314C2×C3×D4—42no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—21no—
329C2×#67#6711yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—121no—
336#237—22no—
337#237—41no—
338C2×C4×D3—61no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C3×SD16—62no—
345C3×SD16—121no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
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—21no—
366#217—21no—
367#217—21no—
368#217—61no—
369#217#6711yescharacteristic
370#216—121no—
371#216—121no—
372#214—22no—
373#214—41no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—121no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401#208—121no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—122no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413ΓL(1,𝔽25)—121no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—84no—
423C22×C32#13712yes—
424C22×C32C22×D411yescharacteristic
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—31no—
441C22×D4D3211yescharacteristic
442C2×Q16—91no—
443C2×SD16—31no—
444C2×SD16—31no—
445C2×M16—91no—
446C22×C8—91no—
447C4⋊Q8—91no—
448#125—181no—
449#124—31no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
457#121—61no—
458#120—61no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—61no—
466#107—91no—
467#107—91no—
468#107—91no—
469C4⋊C8—91no—
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#102—91no—
480C22⋊C8—31no—
481C22⋊C8—91no—
482#97—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—42no—
492C23×C3—42no—
493C23×C3—44no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—82no—
497C23×C3—81no—
498C23×C3—81no—
499C23×C3—82no—
500C23×C3D3×D411yescharacteristic
501C23×C3C2×#6711yescharacteristic
502C22×D3C2×#6711yescharacteristic
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×D4—22no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—42no—
518C3×D4—42no—
519C3×D4—44no—
520C3×D4—62no—
521C3×D4—122no—
522C3×D4—241no—
523C3×D4#23712yes—
524C3×D4#23712yes—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4—241no—
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—22no—
549#67—42no—
550#67—81no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—42no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—81no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3—242no—
567C2×Dic3C2×#6711yescharacteristic
568C2×Dic3C2×#6711yescharacteristic
569C2×Dic3C2×#6711yescharacteristic
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
575Dic6—21no—
576Dic6—21no—
577Dic6—241no—
578Dic6—241no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8—121no—
589C2×C32—22no—
590C2×C32—42no—
591C2×C32—81no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13711yescharacteristic
594C2×C32#57611yescharacteristic
595C3×D3—41no—
596C24—21no—
597#41—62no—
598#41—121no—
599C2×Q8—31no—
600C2×Q8—31no—
601C2×Q8—181no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—31no—
605C2×D4—41no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4C2×D3211yescharacteristic
609C2×D4C2×D3211yescharacteristic
610C22×C4—31no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4C2×D3211yescharacteristic
616Q16—361no—
617SD16—62no—
618SD16—121no—
619M16—361no—
620C2×C8—31no—
621C2×C8—31no—
622C2×C8—91no—
623C2×C8—91no—
624C2×C8—361no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—91no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—181no—
646C42—31no—
647C42—181no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—84no—
678C22×C3—84no—
679C22×C3—88no—
680C22×C3#91512yes—
681C22×C3#95112yes—
682C22×C3C2×D3×D411yescharacteristic
683C22×C3C22×#6711yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C3×C4—22no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4C2×#23711yescharacteristic
700C3×C4C2×#23711yescharacteristic
701C3×C4#100411yescharacteristic
702C3×C4#100411yescharacteristic
703Dic3—21no—
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716C32#331411yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—31no—
720C23—42no—
721C23—42no—
722C23—81no—
723C23D3×#6711yescharacteristic
724Q8—61no—
725Q8—61no—
726Q8—61no—
727Q8—61no—
728Q8—721no—
729D4—21no—
730D4—21no—
731D4—21no—
732D4—42no—
733D4—62no—
734D4—122no—
735D4—241no—
736D4#380512yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—122no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—241no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—181no—
759C8—181no—
760C2×C3—24no—
761C2×C3—22no—
762C2×C3—22no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—82no—
769C2×C3—82no—
770C2×C3—81no—
771C2×C3—81no—
772C2×C3—121no—
773C2×C3#559111yescharacteristic
774C2×C3C2×#91511yescharacteristic
775C2×C3#577411yescharacteristic
776C2×C3#580611yescharacteristic
777C2×C3C2×#95111yescharacteristic
778C2×C3#583511yescharacteristic
779D3—41no—
780C22—21no—
781C22—21no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—84no—
792C22#6392912yes—
793C22C2×D3×#6711yescharacteristic
794C4—21no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—121no—
802C4—361no—
803C4—361no—
804C4C2×#380511yescharacteristic
805C4#6433011yescharacteristic
806C3—21no—
807C3#8016311yescharacteristic, complemented
808C3#8349811yescharacteristic, complemented
809C2—22no—
810C2—42no—
811C2—81no—
812C2—121no—
813C2#1059509711yescharacteristic
814C2C2×#6392911yescharacteristic
815C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5806C2
hypercenterC22×D4D32
hypocenterC32#3314
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. #10594993C2semidirect
3. C2×#63659C2semidirect
4. C3×#5218C2semidirect
5. #10591502C2semidirect
6. #10591488C2semidirect
7. #10591461C2semidirect
8. #10591442C2semidirect
9. #10591440C2semidirect
10. #10591414C2semidirect
11. #10591413C2semidirect
12. #10591410C2semidirect
13. #10591188C2semidirect
14. #10591158C2semidirect
15. #10591103C2semidirect
36. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. Dic3×Dic6C22semidirect
42. C2×#3718C22semidirect
43. C2×#3711C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
68. #5218D3semidirect
716. C32#3314semidirect
807. C3#80163semidirect
808. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
#105949932
C2×#636592
C3×#52182
#105915022
#105914882
#105914612
#105914422
#105914402
#105914142
#105914132
#105914102
#105911882
#105911582
#105911032
#834983
#801633