Finite Group Databasebeta

← #10701909

Subgroups — #10701909

Order 768.

1506 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5832C211yesmaximal, characteristic
2C22×C3×#104C211yesmaximal, characteristic, complemented
3C22×#837C211yesmaximal, characteristic, complemented
4C22×#825C211yesmaximal, characteristic, complemented
5C22×#805C211yesmaximal, characteristic, complemented
6#71979C211yesmaximal, characteristic, complemented
7C4×C3⋊#95C211yesmaximal, characteristic, complemented
8#11011—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13#5832—22no—
14#5832—22no—
15#5832—22no—
16#5832—22no—
17C2×#947C411yescharacteristic, complemented
18C2×#944C411yescharacteristic, complemented
19C2×#940C411yescharacteristic, complemented
20C2×#939—22no—
21C2×#936C411yescharacteristic, complemented
22C2×C4×#67—22no—
23C22×C4×Dic3C2211yescharacteristic
24C22×C4×Dic3C2211yescharacteristic
25C22×#208C2211yescharacteristic
26C2×C3×#104—22no—
27C2×C3×#104—22no—
28C2×C3×#104—22no—
29C2×#837—22no—
30C2×#837—22no—
31C2×#837—22no—
32C2×C3⋊#95—22no—
33C2×#825—22no—
34C2×#825—22no—
35C2×#825—22no—
36C2×#805—22no—
37C2×#805—22no—
38C2×#805—22no—
39#4550—22no—
40C2×#532—31no—
41C22×#104—31no—
42C22×#104—31no—
43C22×#104—31no—
44C22×#104D311yescharacteristic, complemented
45#1728—31no—
46C4×#95—31no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—21no—
57C2×C3×#41D412yes—
58C2×C3×#41D412yes—
59C22×C3×Q8C2×C411yescharacteristic
60C22×C3×D4—21no—
61C22×C3×D4C2×C411yescharacteristic
62C23×C3×C4—21no—
63C23×C3×C4—21no—
64C23×C3×C4C2311yescharacteristic
65C22×#67—21no—
66C22×#67—22no—
67C23×Dic3—21no—
68C23×Dic3D412yes—
69C2×#235—21no—
70C2×#235—21no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235—21no—
77C2×#235—21no—
78C2×#235—21no—
79C2×#235D412yes—
80C2×#235D412yes—
81C22×D12C2×C411yescharacteristic
82C22×C4×D3—21no—
83C22×Dic6C2×C411yescharacteristic
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16—21no—
87C2×C3×M16—21no—
88C2×C3×M16—21no—
89C2×C3×M16D412yescomplemented
90C22×C3×C8—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42D412yescomplemented
97C2×#217—22no—
98#947—22no—
99#947—22no—
100#944—22no—
101#944—22no—
102#940—22no—
103#940—22no—
104#939—28no—
105#939—28no—
106#936—22no—
107#936—22no—
108C4×#67—28no—
109C4×#67—28no—
110C2×(C2×D3)⋊C4—22no—
111C2×Dic3⋊C4—22no—
112C2×C4×Dic3—21no—
113C2×C4×Dic3—21no—
114C2×C4×Dic3—21no—
115C2×C4×Dic3—21no—
116C2×C4×Dic3—21no—
117C2×C4×Dic3—21no—
118C2×C4×Dic3—21no—
119C2×C4×Dic3—21no—
120C2×C4×Dic3—21no—
121C2×C4×Dic3C2×C411yescharacteristic
122C2×C4×Dic3C2×C411yescharacteristic
123C2×C4×Dic3D412yes—
124C2×C4×Dic3D412yescomplemented
125C2×#208—21no—
126C2×#208—21no—
127C2×#208—21no—
128C2×#208—21no—
129C2×#208—21no—
130C2×#208D412yescomplemented
131C22×C3⋊C8—21no—
132C3×#104—28no—
133#837—28no—
134C3⋊#95—28no—
135#825—28no—
136#805—28no—
137C22×#41—31no—
138C22×#41C2×D311yescharacteristic
139C22×M16—31no—
140C22×M16C2×D311yescharacteristic
141#532—62no—
142#532—62no—
143#532—62no—
144#532—62no—
145C2×C4⋊Q8—31no—
146C2×#127—31no—
147C2×#124—31no—
148C2×#124—31no—
149C2×#121—62no—
150C2×C4×D4—62no—
151C22×C42—31no—
152C22×C42—31no—
153C22×C42C2×D311yescharacteristic
154C2×#104—22no—
155C2×#104—22no—
156C2×#104—22no—
157C2×#104—62no—
158C2×#104—62no—
159C2×#104—62no—
160C2×#104—62no—
161C2×#104—62no—
162C2×#104—62no—
163C2×#104—62no—
164C2×#104—62no—
165C2×#104—62no—
166C2×#95—62no—
167#336—62no—
168C24×C3—21no—
169C24×C3C2×D411yescharacteristic
170C23×D3—21no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—22no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C3×#41—41no—
186C3×#41—41no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8C22⋊C412yes—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4C22⋊C412yes—
205C22×C3×C4—24no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—42no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—41no—
216C22×C3×C4—41no—
217C22×C3×C4C22×C411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4#4111yescharacteristic
228C22×C3×C4#4111yescharacteristic
229C22×C3×C4#4111yescharacteristic
230C22×C3×C4#4111yescharacteristic
231C2×#67—28no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—44no—
235C2×#67—41no—
236C2×#67—41no—
237C2×#67—41no—
238C2×#67—41no—
239C2×#67—44no—
240C22×Dic3—24no—
241C22×Dic3—21no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—24no—
246C22×Dic3—42no—
247C22×Dic3—42no—
248C22×Dic3—41no—
249C22×Dic3—41no—
250C22×Dic3C22⋊C412yes—
251C22×Dic3C22⋊C412yes—
252#235—22no—
253#235—22no—
254#235—22no—
255#235—22no—
256#235—22no—
257#235—22no—
258#235—22no—
259#235—22no—
260#235—41no—
261#235—41no—
262#235—41no—
263#235—41no—
264#235—41no—
265#235—41no—
266#235—41no—
267#235—41no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12—21no—
272C2×D12—21no—
273C2×D12C22⋊C412yes—
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—41no—
277C2×C4×D3—41no—
278C2×C4×D3—41no—
279C2×C4×D3—41no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6C22⋊C412yes—
286C3×M16—22no—
287C3×M16—22no—
288C3×M16—41no—
289C3×M16—41no—
290C2×C3×C8—22no—
291C2×C3×C8—41no—
292C2×C3×C8—41no—
293C3×C42—22no—
294C3×C42—22no—
295C3×C42—41no—
296C3×C42—41no—
297#217—28no—
298(C2×D3)⋊C4—28no—
299Dic3⋊C4—28no—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3—22no—
307C4×Dic3—22no—
308C4×Dic3—41no—
309C4×Dic3—41no—
310#208—22no—
311#208—22no—
312#208—41no—
313#208—41no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—41no—
316C2×C3⋊C8—41no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—32no—
328C2×#41—32no—
329C2×#41—61no—
330C2×#41—61no—
331C2×#41—61no—
332C2×#41—61no—
333C2×#41—61no—
334C2×#41—61no—
335C2×#41—61no—
336C2×#41—61no—
337C2×#41—61no—
338C2×#41—61no—
339C2×#41D1212yes—
340C2×#41#6712yes—
341C22×Q8—31no—
342C22×Q8C4×D311yescharacteristic
343C22×D4—21no—
344C22×D4—31no—
345C22×D4—62no—
346C22×D4—61no—
347C22×D4C4×D311yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—32no—
351C23×C4—61no—
352C23×C4—61no—
353C23×C4C22×D311yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—32no—
360C2×M16—61no—
361C2×M16—61no—
362C2×M16—61no—
363C2×M16—61no—
364C2×M16—61no—
365C2×M16#6712yescomplemented
366C22×C8—21no—
367C22×C8—61no—
368C4⋊Q8—62no—
369C4⋊Q8—62no—
370#127—62no—
371#127—62no—
372#124—62no—
373#124—62no—
374#124—62no—
375#124—62no—
376#121—68no—
377#121—68no—
378C4×D4—68no—
379C4×D4—68no—
380C2×C4⋊C4—62no—
381C2×C22⋊C4—62no—
382C2×C22⋊C4—62no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—32no—
391C2×C42—32no—
392C2×C42—61no—
393C2×C42—61no—
394C2×C42—61no—
395C2×C42—61no—
396C2×C42—61no—
397C2×C42—61no—
398C2×C42—61no—
399C2×C42—61no—
400C2×C42—61no—
401C2×C42#6712yescomplemented
402#104—28no—
403#104—68no—
404#104—68no—
405#104—68no—
406#95—68no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—22no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—42no—
413C23×C3—42no—
414C23×C3C2×C22⋊C411yescharacteristic
415C23×C3#12011yescharacteristic
416C23×C3#12011yescharacteristic
417C23×C3#12111yescharacteristic
418C23×C3#12111yescharacteristic
419C23×C3#12411yescharacteristic
420C23×C3#12711yescharacteristic
421C22×D3—22no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—42no—
425C22×D3—42no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—42no—
433C3×D4—42no—
434C3×D4—42no—
435C3×D4—42no—
436C3×D4—41no—
437C3×D4—41no—
438C2×C3×C4—24no—
439C2×C3×C4—22no—
440C2×C3×C4—42no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4C2×C22⋊C411yescharacteristic
451C2×C3×C4C2×C22⋊C411yescharacteristic
452C2×C3×C4C4×D411yescharacteristic
453C2×C3×C4C4×D411yescharacteristic
454C2×C3×C4C4×D411yescharacteristic
455C2×C3×C4C4×D411yescharacteristic
456C2×C3×C4#12011yescharacteristic
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4#12011yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12111yescharacteristic
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4#12111yescharacteristic
469C2×C3×C4#12111yescharacteristic
470C2×C3×C4#12111yescharacteristic
471C2×C3×C4#12111yescharacteristic
472C2×C3×C4#12311yescharacteristic
473C2×C3×C4#12311yescharacteristic
474C2×C3×C4#12311yescharacteristic
475C2×C3×C4#12311yescharacteristic
476C2×C3×C4#12411yescharacteristic
477C2×C3×C4#12711yescharacteristic
478#67—416no—
479#67—42no—
480#67—42no—
481#67—42no—
482#67—42no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—44no—
491C2×Dic3—44no—
492C2×Dic3—42no—
493C2×Dic3—44no—
494C2×Dic3—44no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—42no—
498C2×Dic3#10414yescomplemented
499D12—22no—
500D12—22no—
501D12—41no—
502D12—41no—
503C4×D3—42no—
504C4×D3—42no—
505C4×D3—42no—
506C4×D3—42no—
507Dic6—22no—
508Dic6—22no—
509Dic6—41no—
510Dic6—41no—
511C3×C8—42no—
512C3⋊C8—42no—
513C24—21no—
514C24—61no—
515C24D3×D411yescharacteristic
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—62no—
533#41—62no—
534#41—62no—
535#41—62no—
536#41—62no—
537#41—62no—
538#41—62no—
539#41—62no—
540#41—121no—
541#41—121no—
542#41—121no—
543#41—121no—
544#41—121no—
545#41—121no—
546#41—121no—
547#41—121no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—32no—
554C2×Q8—61no—
555C2×Q8—61no—
556C2×Q8—61no—
557C2×Q8—61no—
558C2×Q8—61no—
559C2×Q8(C2×D3)⋊C412yes—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—32no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—68no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—61no—
580C2×D4—124no—
581C2×D4—124no—
582C2×D4—121no—
583C2×D4—121no—
584C2×D4—121no—
585C2×D4—121no—
586C2×D4(C2×D3)⋊C412yes—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—61no—
604C22×C4—62no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—122no—
610C22×C4—122no—
611C22×C4—121no—
612C22×C4—121no—
613C22×C4—121no—
614C22×C4—121no—
615C22×C4—121no—
616C22×C4—121no—
617C22×C4C2×C4×D311yescharacteristic
618C22×C4C2×D1211yescharacteristic
619C22×C4#23511yescharacteristic
620C22×C4#23511yescharacteristic
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4D3×D411yescharacteristic
624C22×C4D3×D411yescharacteristic
625C22×C4D3×D411yescharacteristic
626C22×C4#23711yescharacteristic
627C22×C4#23711yescharacteristic
628C22×C4C2×#6711yescharacteristic
629C22×C4C2×#6711yescharacteristic
630C22×C4C2×#6711yescharacteristic
631M16—22no—
632M16—22no—
633M16—41no—
634M16—41no—
635M16—62no—
636M16—62no—
637M16—121no—
638M16—121no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—62no—
643C2×C8—121no—
644C2×C8—121no—
645C4⋊C4—68no—
646C22⋊C4—68no—
647C22⋊C4—68no—
648C42—22no—
649C42—22no—
650C42—41no—
651C42—41no—
652C42—61no—
653C42—61no—
654C42—62no—
655C42—61no—
656C42—61no—
657C42—62no—
658C42—62no—
659C42—62no—
660C42—121no—
661C42—121no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—42no—
671C22×C3—44no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—82no—
675C22×C3#37911yescharacteristic
676C22×C3#39011yescharacteristic
677C22×C3#39011yescharacteristic
678C22×C3#39211yescharacteristic
679C22×C3#39211yescharacteristic
680C22×C3#39411yescharacteristic
681C22×C3#39411yescharacteristic
682C22×C3C2×#10412yes—
683C22×C3#42112yes—
684C2×D3—42no—
685C2×D3—44no—
686C2×D3—81no—
687C2×D3—81no—
688C2×D3—82no—
689C3×C4—44no—
690C3×C4—42no—
691C3×C4#38611yescharacteristic
692C3×C4#38611yescharacteristic
693C3×C4#38611yescharacteristic
694C3×C4#38611yescharacteristic
695C3×C4#39211yescharacteristic
696C3×C4#39211yescharacteristic
697C3×C4#39411yescharacteristic
698C3×C4#39411yescharacteristic
699Dic3—24no—
700Dic3—44no—
701Dic3—42no—
702Dic3—42no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—62no—
711C23—121no—
712C23—121no—
713C23—122no—
714C23—122no—
715C23D3×C22⋊C411yescharacteristic
716C23#88211yescharacteristic
717C23#88411yescharacteristic
718C23#88511yescharacteristic
719C23#93711yescharacteristic
720C23#93911yescharacteristic
721C23#94011yescharacteristic
722Q8—22no—
723Q8—22no—
724Q8—41no—
725Q8—41no—
726Q8—62no—
727Q8—62no—
728Q8—121no—
729Q8—121no—
730D4—22no—
731D4—22no—
732D4—42no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—41no—
737D4—41no—
738D4—62no—
739D4—62no—
740D4—1216no—
741D4—122no—
742D4—122no—
743D4—122no—
744D4—122no—
745D4—121no—
746D4—121no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—34no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—64no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—124no—
768C2×C4—124no—
769C2×C4—122no—
770C2×C4—124no—
771C2×C4—124no—
772C2×C4—121no—
773C2×C4—121no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4D3×C22⋊C411yescharacteristic
780C2×C4#67⋊C411yescharacteristic
781C2×C4#67⋊C411yescharacteristic
782C2×C4#88211yescharacteristic
783C2×C4#88211yescharacteristic
784C2×C4#88311yescharacteristic
785C2×C4#88311yescharacteristic
786C2×C4#88411yescharacteristic
787C2×C4#88411yescharacteristic
788C2×C4#88411yescharacteristic
789C2×C4#88511yescharacteristic
790C2×C4#88611yescharacteristic
791C2×C4C2×(C2×D3)⋊C411yescharacteristic
792C2×C4C4×#6711yescharacteristic
793C2×C4C4×#6711yescharacteristic
794C2×C4#92911yescharacteristic
795C2×C4#93011yescharacteristic
796C2×C4#93011yescharacteristic
797C2×C4#93711yescharacteristic
798C2×C4#93711yescharacteristic
799C2×C4#93711yescharacteristic
800C2×C4#93811yescharacteristic
801C2×C4#93811yescharacteristic
802C2×C4#93911yescharacteristic
803C2×C4#93911yescharacteristic
804C2×C4#93911yescharacteristic
805C2×C4#94011yescharacteristic
806C2×C4#95311yescharacteristic
807C8—42no—
808C8—122no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—82no—
814C2×C3#143811yescharacteristic
815C2×C3#178912yes—
816C2×C3#196211yescharacteristic
817C2×C3#196311yescharacteristic
818C2×C3#198012yes—
819D3—82no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—42no—
829C22—44no—
830C22—81no—
831C22—81no—
832C22—82no—
833C22—122no—
834C22—124no—
835C22—241no—
836C22—241no—
837C22—242no—
838C22D3×#10412yes—
839C22#482112yes—
840C22#495511yescharacteristic
841C22#495711yescharacteristic
842C22#495711yescharacteristic
843C22#495911yescharacteristic
844C22#496011yescharacteristic
845C22#496111yescharacteristic
846C22#522311yescharacteristic
847C4—44no—
848C4—42no—
849C4—64no—
850C4—124no—
851C4—122no—
852C4—122no—
853C4#495611yescharacteristic
854C4#495611yescharacteristic
855C4#495811yescharacteristic
856C4#495911yescharacteristic
857C4#496011yescharacteristic
858C4#496111yescharacteristic
859C4#521311yescharacteristic
860C4#522311yescharacteristic
861C3#1101111yescharacteristic, complemented, Sylow
862C2—21no—
863C2—21no—
864C2—21no—
865C2—21no—
866C2—82no—
867C2—242no—
868C2#7035611yescharacteristic
869C2#7035711yescharacteristic
870C2#7035812yes—
871C2#7038012yes—
872C2#7155011yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#104C2
socleC23×C3C2×C22⋊C4
prime radicalC2×#5832C2
cosocleC23×C3×C4C23
hypercenterC22×#104D3
hypocenterC3#11011
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×C3×#104C2semidirect
3. C22×#837C2semidirect
4. C22×#825C2semidirect
5. C22×#805C2semidirect
6. #71979C2semidirect
7. C4×C3⋊#95C2semidirect
17. C2×#947C4semidirect
18. C2×#944C4semidirect
19. C2×#940C4semidirect
21. C2×#936C4semidirect
44. C22×#104D3semidirect
89. C2×C3×M16D4semidirect
96. C2×C3×C42D4semidirect
124. C2×C4×Dic3D4semidirect
130. C2×#208D4semidirect
365. C2×M16#67semidirect
401. C2×C42#67semidirect
498. C2×Dic3#104semidirect
861. C3#11011semidirect

Maximal subgroups

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

subgroupindex
C2×#58322
C22×C3×#1042
C22×#8372
C22×#8252
C22×#8052
#719792
C4×C3⋊#952
#110113