Finite Group Databasebeta

← #10702005

Subgroups — #10702005

Order 768.

1278 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#950C211yesmaximal, characteristic
2C2×C3×#410C211yesmaximal, characteristic, complemented
3C2×#5236C211yesmaximal, characteristic, complemented
4C2×#5006C211yesmaximal, characteristic, complemented
5C2×#5005C211yesmaximal, characteristic, complemented
6#71580C211yesmaximal, characteristic, complemented
7#71579C211yesmaximal, characteristic, complemented
8#11026—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C22×#235C2211yescharacteristic
11C2×C3×#117C2211yescharacteristic
12C2×C3×#117C2211yescharacteristic
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
23C2×#926C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic
26C3×#410—22no—
27C3×#410—22no—
28C2×C3×#99—22no—
29#5236—22no—
30#5236—22no—
31C2×#837—22no—
32#5006—22no—
33#5006—22no—
34#5005—22no—
35#5005—22no—
36C2×#806—22no—
37C2×#805—22no—
38#4529—22no—
39#4524—22no—
40C22×#135—31no—
41C2×#421—31no—
42C2×#421—31no—
43C2×#410—31no—
44C2×#410D311yescharacteristic, complemented
45#1735—31no—
46#1729—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×C4C2311yescharacteristic
64C22×#67—21no—
65C2×#235—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×#235D412yes—
76C2×#235D412yes—
77C22×D12C2×C411yescharacteristic
78C22×C4×D3—21no—
79C22×Dic6C2×C411yescharacteristic
80C3×#117—21no—
81C3×#117—21no—
82C3×#117—21no—
83C3×#117—21no—
84C3×#117—21no—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117D412yes—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4D412yes—
92C2×C3×C42—21no—
93C2×C3×C42—21no—
94C2×#217—21no—
95#950—28no—
96#950—28no—
97#950—28no—
98#950—28no—
99C2×#216—22no—
100C2×#216—22no—
101C2×#216—22no—
102C2×#215—22no—
103C2×#215—22no—
104C2×#215—22no—
105C2×#214—22no—
106C2×#214—22no—
107C2×#214—22no—
108C2×#213—22no—
109C2×#213—22no—
110C2×#213—22no—
111#926—21no—
112#926—21no—
113#926—21no—
114#926D412yes—
115C2×C4⋊Dic3—21no—
116C2×C4×Dic3—21no—
117C2×#208—21no—
118C2×#208—21no—
119C2×#208—21no—
120C2×#208—21no—
121C2×#208—21no—
122C2×#208D412yes—
123C22×C3⋊C8—21no—
124C22×C3⋊C8—21no—
125C22×C3⋊C8—21no—
126C22×C3⋊C8—21no—
127C22×C3⋊C8—21no—
128C22×C3⋊C8C2×C411yescharacteristic
129C22×C3⋊C8C2×C411yescharacteristic
130C22×C3⋊C8D412yes—
131C22×C3⋊C8D412yes—
132C3×#99—28no—
133#837—28no—
134#806—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—
149C23×C8—31no—
150C2×#117—31no—
151C2×#117C2×D311yescharacteristic
152C2×#117C2×D311yescharacteristic
153#421—62no—
154#421—62no—
155#421—62no—
156#421—62no—
157C2×#104—62no—
158C2×#104—62no—
159#410—22no—
160#410—22no—
161#410—62no—
162#410—62no—
163C2×#99—22no—
164C2×#99—62no—
165#340—62no—
166#336—62no—
167C24×C3—21no—
168C24×C3C2×D411yescharacteristic
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—21no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—41no—
209C22×C3×C4—41no—
210C22×C3×C4—41no—
211C22×C3×C4—41no—
212C22×C3×C4—41no—
213C22×C3×C4C22×C411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
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×C4#4111yescharacteristic
224C22×C3×C4#4111yescharacteristic
225C22×C3×C4#4111yescharacteristic
226C22×C3×C4#4111yescharacteristic
227C2×#67—22no—
228C2×#67—22no—
229C2×#67—41no—
230C2×#67—41no—
231C2×#67—41no—
232C2×#67—41no—
233C22×Dic3—21no—
234C22×Dic3—41no—
235#235—22no—
236#235—22no—
237#235—22no—
238#235—22no—
239#235—22no—
240#235—22no—
241#235—22no—
242#235—22no—
243#235—41no—
244#235—41no—
245#235—41no—
246#235—41no—
247#235—41no—
248#235—41no—
249#235—41no—
250#235—41no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12C22⋊C412yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—41no—
260C2×C4×D3—41no—
261C2×C4×D3—41no—
262C2×C4×D3—41no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6C22⋊C412yes—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—41no—
271C3×C4⋊C4—41no—
272C3×C4⋊C4—41no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—41no—
277C3×C42—22no—
278C3×C42—41no—
279C3×C42—41no—
280C3×C42—41no—
281#217—22no—
282#217—41no—
283#216—28no—
284#215—28no—
285#214—28no—
286#213—28no—
287C4⋊Dic3—22no—
288C4⋊Dic3—41no—
289C4×Dic3—22no—
290C4×Dic3—41no—
291#208—22no—
292#208—22no—
293#208—41no—
294#208—41no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8—22no—
303C2×C3⋊C8—22no—
304C2×C3⋊C8—41no—
305C2×C3⋊C8—41no—
306C2×C3⋊C8C22⋊C412yes—
307C2×C3⋊C8C22⋊C412yes—
308C2×#41—21no—
309C2×#41—21no—
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—32no—
319C2×#41—32no—
320C2×#41—61no—
321C2×#41—61no—
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×#41D1212yes—
331C2×#41#6712yes—
332C22×Q8—31no—
333C22×Q8C4×D311yescharacteristic
334C22×D4—21no—
335C22×D4—31no—
336C22×D4—61no—
337C22×D4C4×D311yescharacteristic
338C23×C4—21no—
339C23×C4—61no—
340C23×C4C22×D311yescharacteristic
341#135—68no—
342#135—68no—
343#135—68no—
344#135—68no—
345C2×Q16—62no—
346C2×Q16—62no—
347C2×Q16—62no—
348C2×SD16—62no—
349C2×SD16—62no—
350C2×SD16—62no—
351C2×SD16—62no—
352C2×SD16—62no—
353C2×SD16—62no—
354C2×D8—62no—
355C2×D8—62no—
356C2×D8—62no—
357C2×M16—32no—
358C2×M16—61no—
359C2×M16—61no—
360C2×M16—61no—
361C2×M16—61no—
362C2×M16—61no—
363C22×C8—31no—
364C22×C8—31no—
365C22×C8—32no—
366C22×C8—32no—
367C22×C8—61no—
368C22×C8—61no—
369C22×C8—61no—
370C22×C8—61no—
371C22×C8—61no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—32no—
380#117—61no—
381#117—61no—
382#117—61no—
383#117#6712yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—61no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4#6712yes—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—61no—
393#104—68no—
394#104—68no—
395#99—28no—
396#99—68no—
397C23×C3—22no—
398C23×C3—42no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—82no—
402C23×C3C4×D411yescharacteristic
403C23×C3#12011yescharacteristic
404C23×C3#12011yescharacteristic
405C23×C3#12111yescharacteristic
406C23×C3#12111yescharacteristic
407C23×C3#12111yescharacteristic
408C23×C3#12711yescharacteristic
409C22×D3—22no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—82no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—42no—
420C3×D4—42no—
421C3×D4—42no—
422C3×D4—42no—
423C3×D4—41no—
424C3×D4—41no—
425C2×C3×C4—22no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—44no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—82no—
436C2×C3×C4C2×C22⋊C411yescharacteristic
437C2×C3×C4C2×C22⋊C411yescharacteristic
438C2×C3×C4C2×C22⋊C411yescharacteristic
439C2×C3×C4C4×D411yescharacteristic
440C2×C3×C4C4×D411yescharacteristic
441C2×C3×C4C4×D411yescharacteristic
442C2×C3×C4#12011yescharacteristic
443C2×C3×C4#12011yescharacteristic
444C2×C3×C4#12011yescharacteristic
445C2×C3×C4#12011yescharacteristic
446C2×C3×C4#12011yescharacteristic
447C2×C3×C4#12011yescharacteristic
448C2×C3×C4#12111yescharacteristic
449C2×C3×C4#12111yescharacteristic
450C2×C3×C4#12111yescharacteristic
451C2×C3×C4#12111yescharacteristic
452C2×C3×C4#12111yescharacteristic
453C2×C3×C4#12111yescharacteristic
454C2×C3×C4#12111yescharacteristic
455C2×C3×C4#12111yescharacteristic
456C2×C3×C4#12111yescharacteristic
457C2×C3×C4#12311yescharacteristic
458C2×C3×C4#12311yescharacteristic
459C2×C3×C4#12311yescharacteristic
460C2×C3×C4#12311yescharacteristic
461C2×C3×C4#12411yescharacteristic
462C2×C3×C4#12411yescharacteristic
463C2×C3×C4#12711yescharacteristic
464#67—42no—
465#67—42no—
466#67—42no—
467#67—42no—
468C2×Dic3—22no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—42no—
472C2×Dic3—82no—
473D12—22no—
474D12—22no—
475D12—41no—
476D12—41no—
477C4×D3—42no—
478C4×D3—42no—
479C4×D3—42no—
480C4×D3—42no—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3⋊C8—22no—
486C3⋊C8—22no—
487C3⋊C8—42no—
488C24—21no—
489C24—61no—
490C24C2×#6711yescharacteristic
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—62no—
508#41—62no—
509#41—62no—
510#41—62no—
511#41—62no—
512#41—62no—
513#41—62no—
514#41—62no—
515#41—121no—
516#41—121no—
517#41—121no—
518#41—121no—
519#41—121no—
520#41—121no—
521#41—121no—
522#41—121no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—32no—
529C2×Q8—61no—
530C2×Q8—61no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8(C2×D3)⋊C412yes—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—32no—
543C2×D4—41no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—62no—
548C2×D4—62no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—121no—
555C2×D4—121no—
556C2×D4—121no—
557C2×D4—121no—
558C2×D4(C2×D3)⋊C412yes—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—61no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—121no—
572C22×C4—121no—
573C22×C4—121no—
574C22×C4—121no—
575C22×C4—121no—
576C22×C4C2×C4×D311yescharacteristic
577C22×C4C2×D1211yescharacteristic
578C22×C4#23511yescharacteristic
579C22×C4#23511yescharacteristic
580C22×C4D3×D411yescharacteristic
581C22×C4D3×D411yescharacteristic
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D411yescharacteristic
584C22×C4D3×D411yescharacteristic
585C22×C4D3×D411yescharacteristic
586C22×C4#23711yescharacteristic
587C22×C4#23711yescharacteristic
588C22×C4C2×#6711yescharacteristic
589C22×C4C2×#6711yescharacteristic
590Q16—68no—
591SD16—68no—
592SD16—68no—
593D8—68no—
594M16—62no—
595M16—62no—
596M16—121no—
597M16—121no—
598C2×C8—32no—
599C2×C8—32no—
600C2×C8—61no—
601C2×C8—61no—
602C2×C8—62no—
603C2×C8—62no—
604C2×C8—61no—
605C2×C8—61no—
606C2×C8—62no—
607C2×C8—62no—
608C2×C8—62no—
609C2×C8—121no—
610C2×C8—121no—
611C4⋊C4—22no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—41no—
615C4⋊C4—62no—
616C4⋊C4—121no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—62no—
622C22⋊C4—121no—
623C42—22no—
624C42—41no—
625C42—41no—
626C42—41no—
627C42—62no—
628C42—121no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—42no—
637C22×C3—82no—
638C22×C3—82no—
639C22×C3—82no—
640C22×C3#38611yescharacteristic
641C22×C3#38611yescharacteristic
642C22×C3#39011yescharacteristic
643C22×C3#39211yescharacteristic
644C22×C3#39211yescharacteristic
645C22×C3#39211yescharacteristic
646C22×C3#39411yescharacteristic
647C2×D3—42no—
648C2×D3—82no—
649C2×D3—82no—
650C2×D3—82no—
651C3×C4—42no—
652C3×C4—82no—
653C3×C4—82no—
654C3×C4#37911yescharacteristic
655C3×C4#38611yescharacteristic
656C3×C4#38611yescharacteristic
657C3×C4#39011yescharacteristic
658C3×C4#39211yescharacteristic
659C3×C4#39411yescharacteristic
660C3×C4#39411yescharacteristic
661C3×C4#39411yescharacteristic
662Dic3—42no—
663Dic3—82no—
664C23—22no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—62no—
669C23—82no—
670C23—121no—
671C23—121no—
672C23—242no—
673C23C4×#6711yescharacteristic
674C23#93011yescharacteristic
675C23#93711yescharacteristic
676C23#93811yescharacteristic
677C23#93911yescharacteristic
678C23#94011yescharacteristic
679C23#95311yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—62no—
685Q8—62no—
686Q8—121no—
687Q8—121no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—41no—
695D4—41no—
696D4—62no—
697D4—62no—
698D4—122no—
699D4—122no—
700D4—122no—
701D4—122no—
702D4—121no—
703D4—121no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—62no—
715C2×C4—82no—
716C2×C4—121no—
717C2×C4—121no—
718C2×C4—122no—
719C2×C4—122no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—242no—
724C2×C4D3×C22⋊C411yescharacteristic
725C2×C4D3×C22⋊C411yescharacteristic
726C2×C4#67⋊C411yescharacteristic
727C2×C4#67⋊C411yescharacteristic
728C2×C4#88211yescharacteristic
729C2×C4#88211yescharacteristic
730C2×C4#88211yescharacteristic
731C2×C4#88311yescharacteristic
732C2×C4#88311yescharacteristic
733C2×C4#88411yescharacteristic
734C2×C4#88411yescharacteristic
735C2×C4#88411yescharacteristic
736C2×C4#88411yescharacteristic
737C2×C4#88511yescharacteristic
738C2×C4#88511yescharacteristic
739C2×C4#88611yescharacteristic
740C2×C4C2×(C2×D3)⋊C411yescharacteristic
741C2×C4C4×#6711yescharacteristic
742C2×C4#92911yescharacteristic
743C2×C4#93011yescharacteristic
744C2×C4#93711yescharacteristic
745C2×C4#93711yescharacteristic
746C2×C4#93711yescharacteristic
747C2×C4#93811yescharacteristic
748C2×C4#93911yescharacteristic
749C2×C4#93911yescharacteristic
750C2×C4#93911yescharacteristic
751C2×C4#94011yescharacteristic
752C8—62no—
753C8—62no—
754C8—122no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—82no—
762C2×C3#143811yescharacteristic
763C2×C3#197612yes—
764D3—82no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—122no—
777C22—242no—
778C22—242no—
779C22—242no—
780C22#495611yescharacteristic
781C22#495711yescharacteristic
782C22#496011yescharacteristic
783C22#496111yescharacteristic
784C22#521311yescharacteristic
785C22#522311yescharacteristic
786C22#522311yescharacteristic
787C4—42no—
788C4—82no—
789C4—82no—
790C4—122no—
791C4—242no—
792C4#495511yescharacteristic
793C4#495611yescharacteristic
794C4#495711yescharacteristic
795C4#495811yescharacteristic
796C4#495911yescharacteristic
797C4#495911yescharacteristic
798C4#496011yescharacteristic
799C4#496111yescharacteristic
800C3#1102611yescharacteristic, complemented, Sylow
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—82no—
808C2—242no—
809C2#7004212yes—
810C2#7155011yescharacteristic
subgroupG/H
centerC2×C4#884
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#410C2
socleC22×C3#390
prime radicalC22×#950C2
cosocleC23×C3×C4C23
hypercenterC2×#410D3
hypocenterC3#11026
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×C3×#410C2semidirect
3. C2×#5236C2semidirect
4. C2×#5006C2semidirect
5. C2×#5005C2semidirect
6. #71580C2semidirect
7. #71579C2semidirect
19. C22×#216C4semidirect
20. C22×#215C4semidirect
21. C22×#214C4semidirect
22. C22×#213C4semidirect
44. C2×#410D3semidirect
800. C3#11026semidirect

Maximal subgroups

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

subgroupindex
C22×#9502
C2×C3×#4102
C2×#52362
C2×#50062
C2×#50052
#715802
#715792
#110263