Finite Group Databasebeta

← #10702000

Subgroups — #10702000

Order 768.

1334 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#950C211yesmaximal, characteristic
2C22×C3×#104C211yesmaximal, characteristic, complemented
3C2×#5234C211yesmaximal, characteristic, complemented
4C2×#5129C211yesmaximal, characteristic, complemented
5C22×#805C211yesmaximal, characteristic, complemented
6C2×#4558C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11025—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C2×#950—22no—
14C2×#950—22no—
15C2×#950—22no—
16C2×#950—22no—
17C2×#950—22no—
18C2×#950—22no—
19C22×#216C411yescharacteristic, complemented
20C22×#215C411yescharacteristic, complemented
21C22×#214C411yescharacteristic, complemented
22C22×#213C411yescharacteristic, complemented
23C22×#208C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C2×C3×#104—22no—
27C2×C3×#104—22no—
28C2×C3×#104—22no—
29#5234—22no—
30#5234—22no—
31C2×#830—22no—
32#5129—22no—
33#5129—22no—
34C2×(C2×D3)⋊C8—22no—
35C2×#805—22no—
36C2×#805—22no—
37C2×#805—22no—
38#4558—22no—
39#4524—22no—
40C22×#135—31no—
41C22×#104—31no—
42C22×#104D311yescharacteristic, complemented
43C2×#408—31no—
44C2×#408—31no—
45C2×#341—31no—
46C2×#336—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—
66C2×#235—21no—
67C2×#235—21no—
68C2×#235—21no—
69C2×#235—21no—
70C2×#235—21no—
71C2×#235—21no—
72C2×#235—21no—
73C2×#235—21no—
74C2×#235—21no—
75C2×#235—21no—
76C2×#235D412yes—
77C2×#235D412yes—
78C22×D12C2×C411yescharacteristic
79C22×C4×D3—21no—
80C22×Dic6C2×C411yescharacteristic
81C2×C3×M16—21no—
82C2×C3×M16—21no—
83C2×C3×M16—21no—
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16D412yes—
87C22×C3×C8—21no—
88C2×C3×C42—21no—
89C2×C3×C42—21no—
90C2×C3×C42—21no—
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42D412yes—
94#950—28no—
95#950—28no—
96#950—28no—
97#950—28no—
98C2×#216—22no—
99C2×#216—22no—
100C2×#216—22no—
101C2×#215—22no—
102C2×#215—22no—
103C2×#215—22no—
104C2×#214—22no—
105C2×#214—22no—
106C2×#214—22no—
107C2×#213—22no—
108C2×#213—22no—
109C2×#213—22no—
110C2×#208—21no—
111C2×#208—21no—
112C2×#208—21no—
113C2×#208—21no—
114C2×#208—21no—
115C2×#208D412yes—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8—21no—
120C22×C3⋊C8—21no—
121C22×C3⋊C8—21no—
122C22×C3⋊C8—21no—
123C22×C3⋊C8—21no—
124C22×C3⋊C8—21no—
125C22×C3⋊C8—21no—
126C22×C3⋊C8—21no—
127C22×C3⋊C8C2×C411yescharacteristic
128C22×C3⋊C8C2×C411yescharacteristic
129C22×C3⋊C8D412yes—
130C22×C3⋊C8D412yes—
131C22×C3⋊C8D412yes—
132C3×#104—28no—
133#830—28no—
134(C2×D3)⋊C8—28no—
135#805—28no—
136C22×#41—31no—
137C22×#41C2×D311yescharacteristic
138C2×#135—62no—
139C2×#135—62no—
140C2×#135—62no—
141C2×#135—62no—
142C2×#135—62no—
143C2×#135—62no—
144C22×Q16—31no—
145C22×SD16—31no—
146C22×SD16—31no—
147C22×D8—31no—
148C22×M16—31no—
149C22×M16C2×D311yescharacteristic
150C23×C8—31no—
151C23×C8—31no—
152C22×C42C2×D311yescharacteristic
153C2×#104—22no—
154C2×#104—22no—
155C2×#104—22no—
156C2×#104—62no—
157C2×#104—62no—
158C2×#104—62no—
159#408—62no—
160#408—62no—
161#408—62no—
162#408—62no—
163C2×C22⋊C8—62no—
164C2×C22⋊C8—62no—
165#341—62no—
166#336—62no—
167C24×C3—21no—
168C24×C3#4111yescharacteristic
169C23×D3—21no—
170C3×#41—22no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—22no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—22no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—41no—
185C3×#41—41no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8C22⋊C412yes—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—41no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4C22⋊C412yes—
204C22×C3×C4—24no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—42no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—41no—
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
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
230C2×#67—22no—
231C2×#67—22no—
232C2×#67—41no—
233C2×#67—41no—
234C2×#67—41no—
235C2×#67—41no—
236C22×Dic3—21no—
237#235—22no—
238#235—22no—
239#235—22no—
240#235—22no—
241#235—22no—
242#235—22no—
243#235—22no—
244#235—22no—
245#235—41no—
246#235—41no—
247#235—41no—
248#235—41no—
249#235—41no—
250#235—41no—
251#235—41no—
252#235—41no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12C22⋊C412yes—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—41no—
262C2×C4×D3—41no—
263C2×C4×D3—41no—
264C2×C4×D3—41no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6C22⋊C412yes—
271C3×M16—22no—
272C3×M16—22no—
273C3×M16—41no—
274C3×M16—41no—
275C2×C3×C8—22no—
276C2×C3×C8—41no—
277C2×C3×C8—41no—
278C3×C42—22no—
279C3×C42—22no—
280C3×C42—41no—
281C3×C42—41no—
282#216—28no—
283#215—28no—
284#214—28no—
285#213—28no—
286#208—22no—
287#208—22no—
288#208—41no—
289#208—41no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C2×C3⋊C8—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8—22no—
296C2×C3⋊C8—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8—41no—
303C2×C3⋊C8—41no—
304C2×C3⋊C8—41no—
305C2×C3⋊C8—41no—
306C2×C3⋊C8—41no—
307C2×C3⋊C8—41no—
308C2×C3⋊C8C22⋊C412yes—
309C2×C3⋊C8C22⋊C412yes—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—32no—
321C2×#41—32no—
322C2×#41—61no—
323C2×#41—61no—
324C2×#41—61no—
325C2×#41—61no—
326C2×#41—61no—
327C2×#41—61no—
328C2×#41—61no—
329C2×#41—61no—
330C2×#41—61no—
331C2×#41—61no—
332C2×#41D1212yes—
333C2×#41#6712yes—
334C22×Q8—31no—
335C22×Q8C4×D311yescharacteristic
336C22×D4—21no—
337C22×D4—31no—
338C22×D4—61no—
339C22×D4C4×D311yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—61no—
343C23×C4C22×D311yescharacteristic
344#135—68no—
345#135—68no—
346#135—68no—
347#135—68no—
348C2×Q16—62no—
349C2×Q16—62no—
350C2×Q16—62no—
351C2×SD16—62no—
352C2×SD16—62no—
353C2×SD16—62no—
354C2×SD16—62no—
355C2×SD16—62no—
356C2×SD16—62no—
357C2×D8—62no—
358C2×D8—62no—
359C2×D8—62no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—32no—
366C2×M16—61no—
367C2×M16—61no—
368C2×M16—61no—
369C2×M16—61no—
370C2×M16—61no—
371C2×M16#6712yes—
372C22×C8—21no—
373C22×C8—31no—
374C22×C8—31no—
375C22×C8—32no—
376C22×C8—32no—
377C22×C8—32no—
378C22×C8—61no—
379C22×C8—61no—
380C22×C8—61no—
381C22×C8—61no—
382C22×C8—61no—
383C22×C8—61no—
384C22×C8—61no—
385C22×C8—61no—
386C22×C8—61no—
387C22×C8—61no—
388C22×C8—61no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42#6712yes—
395#104—28no—
396#104—68no—
397C22⋊C8—68no—
398C22⋊C8—68no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3C4×D411yescharacteristic
407C23×C3#12111yescharacteristic
408C23×C3#12111yescharacteristic
409C23×C3#12111yescharacteristic
410C23×C3#12311yescharacteristic
411C23×C3#12311yescharacteristic
412C23×C3#12411yescharacteristic
413C22×D3—22no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—42no—
417C22×D3—42no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—42no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—42no—
428C3×D4—41no—
429C3×D4—41no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—44no—
433C2×C3×C4—44no—
434C2×C3×C4—42no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—42no—
441C2×C3×C4—42no—
442C2×C3×C4C2×C22⋊C411yescharacteristic
443C2×C3×C4C2×C22⋊C411yescharacteristic
444C2×C3×C4C2×C22⋊C411yescharacteristic
445C2×C3×C4C4×D411yescharacteristic
446C2×C3×C4C4×D411yescharacteristic
447C2×C3×C4C4×D411yescharacteristic
448C2×C3×C4#12011yescharacteristic
449C2×C3×C4#12011yescharacteristic
450C2×C3×C4#12011yescharacteristic
451C2×C3×C4#12011yescharacteristic
452C2×C3×C4#12011yescharacteristic
453C2×C3×C4#12011yescharacteristic
454C2×C3×C4#12011yescharacteristic
455C2×C3×C4#12011yescharacteristic
456C2×C3×C4#12111yescharacteristic
457C2×C3×C4#12111yescharacteristic
458C2×C3×C4#12111yescharacteristic
459C2×C3×C4#12111yescharacteristic
460C2×C3×C4#12111yescharacteristic
461C2×C3×C4#12111yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4#12311yescharacteristic
466C2×C3×C4#12311yescharacteristic
467C2×C3×C4#12411yescharacteristic
468C2×C3×C4#12711yescharacteristic
469C2×C3×C4#12711yescharacteristic
470#67—42no—
471#67—42no—
472#67—42no—
473#67—42no—
474C2×Dic3—22no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477D12—22no—
478D12—22no—
479D12—41no—
480D12—41no—
481C4×D3—42no—
482C4×D3—42no—
483C4×D3—42no—
484C4×D3—42no—
485Dic6—22no—
486Dic6—22no—
487Dic6—41no—
488Dic6—41no—
489C3×C8—42no—
490C3⋊C8—22no—
491C3⋊C8—22no—
492C3⋊C8—42no—
493C3⋊C8—42no—
494C24—21no—
495C24—61no—
496C24#23711yescharacteristic
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—62no—
514#41—62no—
515#41—62no—
516#41—62no—
517#41—62no—
518#41—62no—
519#41—62no—
520#41—62no—
521#41—121no—
522#41—121no—
523#41—121no—
524#41—121no—
525#41—121no—
526#41—121no—
527#41—121no—
528#41—121no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—32no—
535C2×Q8—61no—
536C2×Q8—61no—
537C2×Q8—61no—
538C2×Q8—61no—
539C2×Q8—61no—
540C2×Q8(C2×D3)⋊C412yes—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—32no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—62no—
554C2×D4—62no—
555C2×D4—61no—
556C2×D4—61no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—121no—
561C2×D4—121no—
562C2×D4—121no—
563C2×D4—121no—
564C2×D4(C2×D3)⋊C412yes—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—42no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—61no—
578C22×C4—62no—
579C22×C4—62no—
580C22×C4—121no—
581C22×C4—121no—
582C22×C4—121no—
583C22×C4—121no—
584C22×C4C2×C4×D311yescharacteristic
585C22×C4C2×D1211yescharacteristic
586C22×C4#23511yescharacteristic
587C22×C4#23511yescharacteristic
588C22×C4D3×D411yescharacteristic
589C22×C4D3×D411yescharacteristic
590C22×C4D3×D411yescharacteristic
591C22×C4D3×D411yescharacteristic
592C22×C4D3×D411yescharacteristic
593C22×C4D3×D411yescharacteristic
594C22×C4#23711yescharacteristic
595C22×C4C2×#6711yescharacteristic
596C22×C4C2×#6711yescharacteristic
597C22×C4C2×#6711yescharacteristic
598Q16—68no—
599SD16—68no—
600SD16—68no—
601D8—68no—
602M16—22no—
603M16—22no—
604M16—41no—
605M16—41no—
606M16—62no—
607M16—62no—
608M16—121no—
609M16—121no—
610C2×C8—22no—
611C2×C8—32no—
612C2×C8—32no—
613C2×C8—41no—
614C2×C8—41no—
615C2×C8—61no—
616C2×C8—61no—
617C2×C8—62no—
618C2×C8—62no—
619C2×C8—61no—
620C2×C8—61no—
621C2×C8—62no—
622C2×C8—62no—
623C2×C8—62no—
624C2×C8—62no—
625C2×C8—62no—
626C2×C8—62no—
627C2×C8—121no—
628C2×C8—121no—
629C2×C8—121no—
630C2×C8—121no—
631C2×C8—121no—
632C2×C8—121no—
633C42—22no—
634C42—22no—
635C42—41no—
636C42—41no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—44no—
646C22×C3—42no—
647C22×C3—82no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3#38611yescharacteristic
651C22×C3#38611yescharacteristic
652C22×C3#39011yescharacteristic
653C22×C3#39211yescharacteristic
654C22×C3#39411yescharacteristic
655C22×C3#39411yescharacteristic
656C22×C3#39411yescharacteristic
657C22×C3#44312yes—
658C22×C3#44412yes—
659C2×D3—44no—
660C2×D3—42no—
661C2×D3—82no—
662C2×D3—81no—
663C2×D3—81no—
664C3×C4—44no—
665C3×C4—42no—
666C3×C4#37911yescharacteristic
667C3×C4#38611yescharacteristic
668C3×C4#38611yescharacteristic
669C3×C4#39011yescharacteristic
670C3×C4#39211yescharacteristic
671C3×C4#39211yescharacteristic
672C3×C4#39211yescharacteristic
673C3×C4#39411yescharacteristic
674Dic3—42no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—62no—
683C23—121no—
684C23—121no—
685C23—122no—
686C23—122no—
687C23#67⋊C411yescharacteristic
688C23#88311yescharacteristic
689C23#88511yescharacteristic
690C23#88611yescharacteristic
691C23#93811yescharacteristic
692C23#93911yescharacteristic
693C23#93911yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—62no—
699Q8—62no—
700Q8—121no—
701Q8—121no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—62no—
711D4—62no—
712D4—122no—
713D4—122no—
714D4—122no—
715D4—122no—
716D4—121no—
717D4—121no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—62no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—122no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4D3×C22⋊C411yescharacteristic
738C2×C4D3×C22⋊C411yescharacteristic
739C2×C4#67⋊C411yescharacteristic
740C2×C4#88211yescharacteristic
741C2×C4#88211yescharacteristic
742C2×C4#88211yescharacteristic
743C2×C4#88311yescharacteristic
744C2×C4#88411yescharacteristic
745C2×C4#88411yescharacteristic
746C2×C4#88411yescharacteristic
747C2×C4#88411yescharacteristic
748C2×C4#88511yescharacteristic
749C2×C4C2×(C2×D3)⋊C411yescharacteristic
750C2×C4C4×#6711yescharacteristic
751C2×C4C4×#6711yescharacteristic
752C2×C4#92911yescharacteristic
753C2×C4#93011yescharacteristic
754C2×C4#93011yescharacteristic
755C2×C4#93711yescharacteristic
756C2×C4#93711yescharacteristic
757C2×C4#93711yescharacteristic
758C2×C4#93711yescharacteristic
759C2×C4#93811yescharacteristic
760C2×C4#93911yescharacteristic
761C2×C4#93911yescharacteristic
762C2×C4#94011yescharacteristic
763C2×C4#94011yescharacteristic
764C2×C4#95311yescharacteristic
765C8—42no—
766C8—62no—
767C8—62no—
768C8—122no—
769C8—122no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—82no—
775C2×C3#143811yescharacteristic
776C2×C3#187612yes—
777C2×C3#187612yes—
778C2×C3#197411yescharacteristic
779C2×C3#197511yescharacteristic
780D3—82no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—42no—
790C22—44no—
791C22—81no—
792C22—81no—
793C22—82no—
794C22—122no—
795C22—124no—
796C22—241no—
797C22—241no—
798C22—242no—
799C22#482312yes—
800C22#482412yes—
801C22#495611yescharacteristic
802C22#495711yescharacteristic
803C22#495811yescharacteristic
804C22#495911yescharacteristic
805C22#496111yescharacteristic
806C22#496111yescharacteristic
807C22#522311yescharacteristic
808C4—44no—
809C4—42no—
810C4—122no—
811C4#495511yescharacteristic
812C4#495611yescharacteristic
813C4#495711yescharacteristic
814C4#495911yescharacteristic
815C4#496011yescharacteristic
816C4#496011yescharacteristic
817C4#521311yescharacteristic
818C4#522311yescharacteristic
819C3#1102511yescharacteristic, complemented, Sylow
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—82no—
825C2—242no—
826C2#7037311yescharacteristic
827C2#7037411yescharacteristic
828C2#7037712yes—
829C2#7039012yes—
830C2#7155011yescharacteristic
subgroupG/H
centerC22×C4D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#104C2
socleC23×C3C4×D4
prime radicalC22×#950C2
cosocleC23×C3×C4C23
hypercenterC22×#104D3
hypocenterC3#11025
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. C2×#5234C2semidirect
4. C2×#5129C2semidirect
5. C22×#805C2semidirect
6. C2×#4558C2semidirect
7. C2×#4524C2semidirect
19. C22×#216C4semidirect
20. C22×#215C4semidirect
21. C22×#214C4semidirect
22. C22×#213C4semidirect
42. C22×#104D3semidirect
819. C3#11025semidirect

Maximal subgroups

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

subgroupindex
C22×#9502
C22×C3×#1042
C2×#52342
C2×#51292
C22×#8052
C2×#45582
C2×#45242
#110253