Finite Group Databasebeta

← #11865808

Subgroups — #11865808

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2Dic3×#239C211yesmaximal, characteristic, complemented
3C2×#63947C211yesmaximal, characteristic, complemented
4#10595152C211yesmaximal, characteristic, complemented
5#10592865C211yesmaximal, characteristic, complemented
6C3×#5163C211yesmaximal, characteristic, complemented
7#10591625C211yesmaximal, characteristic, complemented
8#10591612C211yesmaximal, characteristic, complemented
9#10591434C211yesmaximal, characteristic, complemented
10#10591428C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10590954C211yesmaximal, characteristic, complemented
13#10590752C211yesmaximal, characteristic, complemented
14#10590750C211yesmaximal, characteristic, complemented
15D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
16#83900—31nomaximal
17#80382—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24#64145C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#916—24no—
31C2×C3×#204C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33Dic3×#67—21no—
34Dic3×#67—21no—
35#63970—21no—
36#63970—21no—
37#63947—24no—
38#63898—21no—
39#63898C2211yescharacteristic
40Dic3×D12—21no—
41Dic3×D12C2211yescharacteristic
42C4×D3×Dic3—21no—
43C4×D3×Dic3C2211yescharacteristic
44#63866C2211yescharacteristic
45#63863C2211yescharacteristic
46#63841—21no—
47#63841C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic
52#63643C2211yescharacteristic
53#63641C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#821C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63565C2211yescharacteristic
62#63563C2211yescharacteristic
63C2×C3×#135—31no—
64#5832—31no—
65Dic3×#41—31no—
66C2×#950—31no—
67C2×#916—31no—
68C2×#916D311yescharacteristic, complemented
69#5716—31no—
70C4×#239—31no—
71C3×#460—31no—
72#5233—31no—
73#5185—31no—
74#5182—31no—
75#5166—31no—
76#5166—31no—
77#5166—31no—
78#5166—61no—
79#5165—31no—
80#5163D311yescharacteristic, complemented
81#5162—31no—
82#5153—31no—
83#5150—31no—
84#5113—31no—
85C2×Dic3⋊C8—31no—
86#5072—31no—
87#5031—31no—
88#4841—31no—
89D3×C4⋊C8—31no—
90#4787—31no—
91#4787—31no—
92#4772—31no—
93#4772—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239D414yescomplemented
103C3×#237—22no—
104C3×#237—22no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117#3795—22no—
118#3795—22no—
119C32×SD16—22no—
120C2×C32×C8C2311yescharacteristic
121#3757—21no—
122#3757—21no—
123#3756—22no—
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C3×#216—22no—
130C3×#215—22no—
131C3×#213—22no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×D3×C8—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3716—22no—
151#3713—22no—
152D3×C3⋊C8—22no—
153#3035—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C2×#239C2×D311yescharacteristic
157C2×#237—31no—
158C2×#237C2×D311yescharacteristic
159C2×#235—31no—
160C3×#135—64no—
161C2×C3×Q16—31no—
162C2×C3×SD16—21no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16C2×D311yescharacteristic
166C2×C3×SD16C2×D311yescharacteristic
167C2×C3×D8—31no—
168C22×C3×C8—31no—
169C3×#127—31no—
170C3×C4×Q8—31no—
171#950—64no—
172#947—31no—
173Q8×Dic3—31no—
174Q8×Dic3—31no—
175Q8×Dic3—61no—
176Q8×Dic3C2×D311yescharacteristic
177#944—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—61no—
181C2×#216C2×D311yescharacteristic
182C2×#215C2×D311yescharacteristic
183#940C2×D311yescharacteristic
184#939—61no—
185#939—61no—
186#938—61no—
187#938—61no—
188#936—31no—
189#936—31no—
190#936—31no—
191#936—61no—
192D4×Dic3—31no—
193D4×Dic3—31no—
194D4×Dic3—61no—
195D4×Dic3—61no—
196D4×Dic3—61no—
197D4×Dic3—61no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213C2×D311yescharacteristic
202C4×#67—61no—
203C4×#67—61no—
204#926—31no—
205#926—61no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—61no—
208C22×C3⋊C8—31no—
209#916—24no—
210#916—64no—
211C2×#204—31no—
212C2×#204C2×D311yescharacteristic
213C2×D3×C8—31no—
214C2×D3×C8C2×D311yescharacteristic
215#893—31no—
216#893—61no—
217#892—31no—
218#892—61no—
219C4×D12—31no—
220C4×D12—61no—
221C42×D3—31no—
222C42×D3—61no—
223#869—31no—
224C3×C4⋊C8—31no—
225C3×#102—31no—
226C3×#102—31no—
227#835—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—61no—
233#832C2×D311yescharacteristic
234#821—31no—
235#821C2×D311yescharacteristic
236#816—31no—
237#816—31no—
238#816—31no—
239#816—31no—
240#816—61no—
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic
248#810—31no—
249#810—31no—
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C32×Q8—21no—
256C32×Q8C2×D412yes—
257C32×D4—21no—
258C32×D4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265#634—21no—
266#634—21no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—24no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—24no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286#625—42no—
287D3×Dic3—22no—
288D3×Dic3—41no—
289D3×Dic3—42no—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C32×C8—21no—
293C3⋊(C3⋊C8)—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×#135—31no—
297C2×#135—91no—
298#532—91no—
299C4×#41—91no—
300#464—91no—
301#464—91no—
302#463—91no—
303#463—91no—
304#462—91no—
305#461—91no—
306#460—31no—
307#459—91no—
308C2×C4⋊C8—91no—
309#416—91no—
310#416—91no—
311C3×#41—34no—
312C3×#41—62no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×D4—21no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C2×#67—21no—
332C2×#67—21no—
333C2×#67—21no—
334C2×#67—61no—
335C2×#67—61no—
336C22×Dic3—21no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342#239—22no—
343#239#6714yescomplemented
344#237—22no—
345#237—22no—
346#237—62no—
347#237—62no—
348#235—62no—
349#235—62no—
350C2×D12—21no—
351C2×D12C22×D311yescharacteristic
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3C22×D311yescharacteristic
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
363C2×Dic6C22×D311yescharacteristic
364C3×Q16—62no—
365C3×SD16—22no—
366C3×SD16—22no—
367C3×SD16—42no—
368C3×SD16—62no—
369C3×SD16—62no—
370C3×D8—62no—
371C2×C3×C8—21no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—62no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C42—31no—
380C3×C42—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—121no—
391#217—121no—
392#216—22no—
393#216—62no—
394#216—62no—
395#216—122no—
396#215—22no—
397#214—62no—
398#213—22no—
399#213—62no—
400#213—62no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406C4⋊Dic3—21no—
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3—121no—
415C4⋊Dic3C22×D311yescharacteristic
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418C4×Dic3—21no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—61no—
429C4×Dic3—61no—
430C4×Dic3—121no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8—31no—
433C2×C3⋊C8—31no—
434C2×C3⋊C8—61no—
435C2×C3⋊C8—62no—
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D311yescharacteristic
438#204—22no—
439#204—62no—
440D3×C8—22no—
441D3×C8—62no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455C32×C4—22no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—41no—
461C3⋊Dic3—41no—
462C3×Dic3—21no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C3×Dic3#13512yescomplemented
467C2×#41—31no—
468C2×#41—31no—
469C2×#41—91no—
470#135—64no—
471#135—184no—
472C2×Q16—31no—
473C2×Q16—91no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—91no—
477C2×SD16D3211yescharacteristic
478C2×D8—31no—
479C2×D8—91no—
480C22×C8—31no—
481C22×C8—91no—
482C4⋊Q8—91no—
483#127—31no—
484#124—91no—
485#124—91no—
486#121—181no—
487#121—181no—
488C4×Q8—31no—
489C4×Q8—91no—
490C4×D4—91no—
491C4×D4—91no—
492C4×D4—181no—
493C4×D4—181no—
494C4×D4—181no—
495C4×D4—181no—
496#117—91no—
497#117—181no—
498C2×C42—91no—
499C2×C42—181no—
500C4⋊C8—31no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504#103—91no—
505#103—91no—
506#103—91no—
507#103—91no—
508#102—31no—
509#102—31no—
510#102—91no—
511#102—91no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—41no—
516C23×C3—61no—
517C23×C3—61no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3D3×D411yescharacteristic
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—22no—
524C3×Q8—41no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×Q8D3×D412yes—
528C3×Q8C2×#6712yes—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—32no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—64no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
552C2×C3×C4—64no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—122no—
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—42no—
559#67—42no—
560#67—42no—
561#67—122no—
562#67—122no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—42no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—62no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—121no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3—122no—
583C2×Dic3D3×D411yescharacteristic
584C2×Dic3D3×D411yescharacteristic
585C2×Dic3D3×D411yescharacteristic
586D12—24no—
587D12—21no—
588D12—21no—
589D12—21no—
590D12C2×#6712yes—
591C4×D3—24no—
592C4×D3—62no—
593C4×D3—121no—
594C4×D3—122no—
595C4×D3—122no—
596C4×D3—122no—
597C4×D3#23712yes—
598C4×D3C2×#6712yes—
599Dic6—21no—
600Dic6—21no—
601Dic6—61no—
602Dic6—61no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6—121no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—41no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—61no—
615C3⋊C8—61no—
616C3⋊C8—121no—
617C2×C32—81no—
618C2×C32C2×#12111yescharacteristic
619C2×C32C2×#13511yescharacteristic
620C2×C32#57511yescharacteristic
621C3×D3—22no—
622C3×D3—42no—
623C3×D3—81no—
624#41—34no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—182no—
629#41—182no—
630C2×Q8—31no—
631C2×Q8—91no—
632C2×Q8C2×D3211yescharacteristic
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—61no—
638C2×D4—61no—
639C2×D4—181no—
640C2×D4C2×D3211yescharacteristic
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—61no—
644C22×C4—91no—
645C22×C4—91no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649Q16—62no—
650Q16—182no—
651SD16—22no—
652SD16—62no—
653SD16—62no—
654SD16—182no—
655D8—62no—
656D8—182no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8—91no—
661C2×C8—182no—
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—61no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C42—31no—
677C42—61no—
678C42—91no—
679C42—91no—
680C42—91no—
681C42—181no—
682C42—181no—
683C22×C3—21no—
684C22×C3—32no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—121no—
698C22×C3—121no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C2×D3×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—22no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3#93912yes—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—32no—
718C3×C4—32no—
719C3×C4—42no—
720C3×C4—61no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C2×D3×D411yescharacteristic
724C3×C4C2×#23711yescharacteristic
725C3×C4D3×#4111yescharacteristic
726C3×C4C22×#6711yescharacteristic
727Dic3—21no—
728Dic3—41no—
729Dic3—41no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—241no—
741Dic3—241no—
742Dic3#91612yescomplemented
743Dic3#93912yes—
744C32#303511yescharacteristic, complemented, Sylow
745C23—21no—
746C23—31no—
747C23—61no—
748C23—61no—
749Q8—21no—
750Q8—61no—
751Q8—61no—
752Q8—181no—
753Q8—181no—
754Q8D3×#6712yes—
755D4—21no—
756D4—21no—
757D4—32no—
758D4—64no—
759D4—61no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—122no—
764D4—122no—
765D4—362no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—31no—
772C2×C4—64no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—122no—
778C2×C4—182no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—362no—
782C2×C4—362no—
783C2×C4—361no—
784C2×C4—362no—
785C2×C4C22×D3211yescharacteristic
786C8—21no—
787C8—61no—
788C8—61no—
789C8—181no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—62no—
794C2×C3—81no—
795C2×C3—81no—
796C2×C3—122no—
797C2×C3—161no—
798C2×C3—241no—
799C2×C3D3×#12111yescharacteristic
800C2×C3C2×#91611yescharacteristic
801C2×C3D3×#13511yescharacteristic
802C2×C3#576811yescharacteristic
803C2×C3#577311yescharacteristic
804C2×C3C2×#93911yescharacteristic
805D3—22no—
806D3—42no—
807D3—81no—
808C22—32no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—61no—
813C22—61no—
814C22—62no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22D32×D411yescharacteristic
821C4—22no—
822C4—32no—
823C4—32no—
824C4—61no—
825C4—121no—
826C4—121no—
827C4—181no—
828C4—181no—
829C4—361no—
830C4—361no—
831C4D3×#23711yescharacteristic
832C4C2×D3×#6711yescharacteristic
833C3—21no—
834C3#8038211yescharacteristic, complemented
835C3#8390011yescharacteristic, complemented
836C2—62no—
837C2—81no—
838C2—122no—
839C2—241no—
840C2D3×#91611yescharacteristic
841C2#1059474511yescharacteristic
842C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. Dic3×#239C2semidirect
3. C2×#63947C2semidirect
4. #10595152C2semidirect
5. #10592865C2semidirect
6. C3×#5163C2semidirect
7. #10591625C2semidirect
8. #10591612C2semidirect
9. #10591434C2semidirect
10. #10591428C2semidirect
11. #10591420C2semidirect
12. #10590954C2semidirect
13. #10590752C2semidirect
14. #10590750C2semidirect
15. D3×Dic3⋊C8C2semidirect
68. C2×#916D3semidirect
80. #5163D3semidirect
102. C3×#239D4semidirect
343. #239#67semidirect
466. C3×Dic3#135semidirect
742. Dic3#916semidirect
744. C32#3035semidirect
834. C3#80382semidirect
835. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
Dic3×#2392
C2×#639472
#105951522
#105928652
C3×#51632
#105916252
#105916122
#105914342
#105914282
#105914202
#105909542
#105907522
#105907502
D3×Dic3⋊C82
#839003
#803823