Finite Group Databasebeta

← #11889754

Subgroups — #11889754

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592741C211yesmaximal, characteristic, complemented
4C3×#5033C211yesmaximal, characteristic, complemented
5#10591488C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591441C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591173C211yesmaximal, characteristic, complemented
10#10591151C211yesmaximal, characteristic, complemented
11#10591087C211yesmaximal, characteristic, complemented
12#10590590C211yesmaximal, characteristic, complemented
13#10590579C211yesmaximal, characteristic, complemented
14#10590555C211yesmaximal, characteristic, complemented
15#10590440C211yesmaximal, characteristic, complemented
16#83498—31nomaximal
17#81289—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64133C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C3×#938—21no—
25C3×#937—21no—
26C3×#936C2211yescharacteristic
27C3×C4×#67C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#883—21no—
32C3×D3×C22⋊C4—21no—
33Dic3×#67—21no—
34#63964—21no—
35#63918C2211yescharacteristic, complemented
36#63899—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63857C2211yescharacteristic
39#63846—21no—
40#63844C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63659C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#830C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61C3×#546—31no—
62#5612D311yescharacteristic
63#5543—31no—
64#5511—31no—
65C3×#480—31no—
66#5239—31no—
67#5232—31no—
68#5218—31no—
69C2×#832—31no—
70#5055—31no—
71#5054—31no—
72#5051—31no—
73#5044—31no—
74#5042—31no—
75#5042—31no—
76#5042—61no—
77#5033D311yescharacteristic, complemented
78#5018—31no—
79#5011—31no—
80#5007—31no—
81#4966—31no—
82#4890—31no—
83#4889—31no—
84#4887—31no—
85#4884—31no—
86#4776—31no—
87D3×#102—31no—
88#4767—31no—
89#4765—31no—
90#4733—31no—
91#4728—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4—41no—
103C3×#235—22no—
104C3×#235—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×D3×Dic3—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114#3757—21no—
115#3754—41no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3748—41no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
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#3719—41no—
142#3716—22no—
143D3×C3⋊C8—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235C2×D311yescharacteristic
149C3×#124—31no—
150C3×#123—61no—
151C3×C22⋊Q8—31no—
152C3×#121—21no—
153C3×#121—61no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×#120—61no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—61no—
161C2×#216—31no—
162#938—21no—
163#937—21no—
164#936C2×D311yescharacteristic
165D4×Dic3—61no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—61no—
170C4×#67—61no—
171C4×#67C2×D311yescharacteristic
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3C2×D311yescharacteristic, complemented
174#924—31no—
175#924—31no—
176#924—31no—
177#924—61no—
178#924—61no—
179C2×#208—31no—
180C2×#208—31no—
181C2×#208—61no—
182C22×C3⋊C8—31no—
183C2×Dic12—31no—
184C2×#204—31no—
185C2×D3×C8—31no—
186#897—31no—
187#897C2×D311yescharacteristic
188#896—61no—
189#893C2×D311yescharacteristic
190D3×C4⋊C4—31no—
191#890—61no—
192#889—61no—
193#888—31no—
194#887—31no—
195#883—21no—
196D3×C22⋊C4—21no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830—31no—
218#830C2×D311yescharacteristic, complemented
219#821—31no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#815—31no—
223Dic3⋊C8—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#809—31no—
230#809—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
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—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C3×#67—42no—
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#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—42no—
272C3×C4×D3—81no—
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—31no—
286#474—91no—
287#468—91no—
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×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—41no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
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—21no—
324C22×Dic3—61no—
325D3×D4—22no—
326D3×D4—41no—
327#235—22no—
328#235—41no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6C22×D311yescharacteristic
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—21no—
361#217—21no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—121no—
366#217#6711yescharacteristic
367#216—121no—
368#214—62no—
369#214—121no—
370#214—121no—
371#214—122no—
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—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—121no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398#208—121no—
399#208—121no—
400#208—122no—
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
410Dic12—121no—
411#204—62no—
412D3×C8—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—84no—
426C2×C3×D3#13712yes—
427C32×C4—21no—
428C32×C4—41no—
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—
439C2×#41—31no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—91no—
447#125—181no—
448#124—31no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455#121—61no—
456#121D3211yescharacteristic
457#120—61no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—61no—
465#107—31no—
466#107—31no—
467#107—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C23×C3D3×D411yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3—21no—
494C22×D3—42no—
495C22×D3—42no—
496C22×D3—81no—
497C22×D3C2×#6711yescharacteristic
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×C4—241no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—22no—
541#67—42no—
542#67—42no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—81no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3—241no—
554C2×Dic3C2×#6711yescharacteristic
555C2×Dic3C2×#6711yescharacteristic
556C2×Dic3C2×#6711yescharacteristic
557D12—21no—
558D12#23712yes—
559C4×D3—21no—
560C4×D3—21no—
561C4×D3—42no—
562C4×D3—81no—
563C4×D3—241no—
564Dic6—21no—
565Dic6—21no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—121no—
571Dic6—121no—
572Dic6—241no—
573Dic6—241no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—62no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32—41no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13711yescharacteristic
588C2×C32#57611yescharacteristic
589C3×D3—22no—
590C3×D3—42no—
591C24—61no—
592#41—62no—
593#41—121no—
594C2×Q8—31no—
595C2×Q8—91no—
596C2×Q8—181no—
597C2×D4—21no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—121no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4C2×D3211yescharacteristic
611Q16—361no—
612SD16—182no—
613SD16—361no—
614M16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—361no—
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—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—62no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—244no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C22×#6711yescharacteristic
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—22no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—84no—
677C2×D3#95112yes—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
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×C4D3×#4111yescharacteristic
695C3×C4#100911yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3—241no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—21no—
710C23—31no—
711C23—61no—
712C23—122no—
713C23—122no—
714C23—241no—
715C23D3×#6711yescharacteristic
716Q8—61no—
717Q8—61no—
718Q8—181no—
719Q8—181no—
720Q8—721no—
721D4—21no—
722D4—21no—
723D4—32no—
724D4—62no—
725D4—61no—
726D4—81no—
727D4—122no—
728D4—122no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—122no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—241no—
744C2×C4—241no—
745C2×C4—721no—
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—61no—
749C8—61no—
750C8—181no—
751C8—181no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—62no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—122no—
762C2×C3—161no—
763C2×C3#565411yescharacteristic
764C2×C3#575711yescharacteristic
765C2×C3D3×#13711yescharacteristic
766C2×C3#580611yescharacteristic
767C2×C3C2×#95111yescharacteristic
768C2×C3#583511yescharacteristic
769D3—22no—
770D3—42no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—32no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—61no—
779C22—61no—
780C22—62no—
781C22—121no—
782C22—121no—
783C22—244no—
784C22C2×D3×#6711yescharacteristic
785C4—21no—
786C4—41no—
787C4—61no—
788C4—61no—
789C4—61no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—361no—
794C4—361no—
795C4D3×#23711yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#8128911yescharacteristic, complemented
799C3#8349811yescharacteristic, complemented
800C2—41no—
801C2—62no—
802C2—81no—
803C2—122no—
804C2#1059509611yescharacteristic
805C2#1059514811yescharacteristic
806C2D3×#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. #10594988C2semidirect
3. #10592741C2semidirect
4. C3×#5033C2semidirect
5. #10591488C2semidirect
6. #10591459C2semidirect
7. #10591441C2semidirect
8. D3×#832C2semidirect
9. #10591173C2semidirect
10. #10591151C2semidirect
11. #10591087C2semidirect
12. #10590590C2semidirect
13. #10590579C2semidirect
14. #10590555C2semidirect
15. #10590440C2semidirect
22. #64133C22semidirect
23. C2×#3748C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
35. #63918C22semidirect
40. #63844C22semidirect
41. C2×#3719C22semidirect
45. #63637C22semidirect
46. #63634C22semidirect
49. C3×#830C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
55. #63565C22semidirect
60. #63554C22semidirect
77. #5033D3semidirect
173. C2×C4⋊Dic3C2×D3semidirect
218. #830C2×D3semidirect
234. #807C2×D3semidirect
235. #807C2×D3semidirect
708. C32#3314semidirect
798. C3#81289semidirect
799. C3#83498semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
#105949882
#105927412
C3×#50332
#105914882
#105914592
#105914412
D3×#8322
#105911732
#105911512
#105910872
#105905902
#105905792
#105905552
#105904402
#834983
#812893