Finite Group Databasebeta

← #10815958

Subgroups — #10815958

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3002C211yesmaximal, characteristic
2C22×#837C211yesmaximal, characteristic, complemented
3#84075C211yesmaximal, characteristic, complemented
4C2×#5196C211yesmaximal, characteristic, complemented
5#82918C211yesmaximal, characteristic, complemented
6#72087C211yesmaximal, characteristic, complemented
7#72087C211yesmaximal, characteristic, complemented
8#72084C211yesmaximal, characteristic, complemented
9#71711C211yesmaximal, characteristic, complemented
10#70292C211yesmaximal, characteristic, complemented
11#70291C211yesmaximal, characteristic, complemented
12#70289C211yesmaximal, characteristic, complemented
13#70287C211yesmaximal, characteristic, complemented
14#69954C211yesmaximal, characteristic, complemented
15Dic3×C22⋊C8C211yesmaximal, characteristic, complemented
16#22888—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×#135C2211yescharacteristic
19C2×C3×#135C2211yescharacteristic
20C3×#525C2211yescharacteristic
21C2×#948C2211yescharacteristic
22C2×#948C2211yescharacteristic
23C2×#948C2211yescharacteristic, complemented
24C22×C4×Dic3C2211yescharacteristic
25C22×#208C2211yescharacteristic
26C3×#452C411yescharacteristic, complemented
27C3×#452C411yescharacteristic, complemented
28C3×#451C411yescharacteristic, complemented
29C3×#450C411yescharacteristic, complemented
30C3×#449C411yescharacteristic, complemented
31C3×#449C411yescharacteristic, complemented
32C3×#448C411yescharacteristic, complemented
33C3×#447C411yescharacteristic, complemented
34C3×#416C2211yescharacteristic
35C3×#416C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#837—24no—
38C2×#837C2211yescharacteristic
39C2×#837C2211yescharacteristic
40C2×#837C2211yescharacteristic
41C2×#837C2211yescharacteristic
42C2×#837C2211yescharacteristic, complemented
43C2×#837C2211yescharacteristic, complemented
44#5234—21no—
45#5234—21no—
46#5234C2211yescharacteristic
47#5234C2211yescharacteristic
48#5234C2211yescharacteristic, complemented
49#5207—21no—
50#5207C2211yescharacteristic
51C2×#830—21no—
52C2×#830C2211yescharacteristic
53#5196—24no—
54C2×#819C2211yescharacteristic, complemented
55C2×#819C2211yescharacteristic, complemented
56C2×C8×Dic3C2211yescharacteristic, complemented
57C2×C8×Dic3C2211yescharacteristic, complemented
58#5012—21no—
59#5011—21no—
60#5011—21no—
61D4×C3⋊C8—21no—
62#4999C2211yescharacteristic, complemented
63#4997C2211yescharacteristic, complemented
64#4552C2211yescharacteristic, complemented
65#4552C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4550C2211yescharacteristic, complemented
68#4532C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#3002D311yescharacteristic
71C2×#443—31no—
72#2933—31no—
73C22×#104—31no—
74#2880—31no—
75#1974—31no—
76#1937—31no—
77#1929—31no—
78#1896—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1764—31no—
84C4×C22⋊C8—31no—
85C2×C3×#41—21no—
86C2×C3×#41—21no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C2×C3×#41C2×C411yescharacteristic
92C2×C3×#41C2×C411yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C2×C3×#41C2311yescharacteristic
95C2×C3×#41C2311yescharacteristic
96C22×C3×Q8C2×C411yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4C2×C411yescharacteristic
99C23×C3×C4—21no—
100C23×C3×C4C2311yescharacteristic
101C23×Dic3—21no—
102C3×#135—22no—
103C3×#135—22no—
104C3×#135—41no—
105C3×#135—41no—
106C2×C3×Q16C2×C411yescharacteristic, complemented
107C2×C3×Q16C2×C411yescharacteristic, complemented
108C2×C3×SD16C2×C411yescharacteristic, complemented
109C2×C3×SD16C2×C411yescharacteristic, complemented
110C2×C3×SD16C2×C411yescharacteristic, complemented
111C2×C3×SD16C2×C411yescharacteristic, complemented
112C2×C3×D8C2×C411yescharacteristic, complemented
113C2×C3×D8C2×C411yescharacteristic, complemented
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×#123—21no—
117C3×C22⋊Q8C2×C411yescharacteristic
118C3×C22⋊Q8C2×C411yescharacteristic
119C3×#121C2×C411yescharacteristic
120C3×#121C2×C411yescharacteristic
121C3×#120—21no—
122C3×C4×D4—21no—
123C3×C4×D4—21no—
124C3×#117C2311yescharacteristic
125#948—22no—
126#948—22no—
127#948—22no—
128#948—41no—
129#948—41no—
130#948—41no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—41no—
134C2×C4×Dic3C2311yescharacteristic
135C2×C4×Dic3C2311yescharacteristic
136C2×#208—21no—
137C2×#208—21no—
138C2×#208—21no—
139C2×#208—21no—
140C2×#208—22no—
141C2×#208—41no—
142C2×#208C2311yescharacteristic
143C2×#208C2311yescharacteristic
144C2×#208C2311yescharacteristic
145C2×#208C2311yescharacteristic
146C22×C3⋊C8—21no—
147C22×C3⋊C8—21no—
148C22×C3⋊C8—21no—
149C22×C3⋊C8—21no—
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C3×#103C2×C411yescharacteristic, complemented
153C3×#103C2×C411yescharacteristic, complemented
154C3×#103C2×C411yescharacteristic, complemented
155C3×#103C2×C411yescharacteristic, complemented
156C3×#102C2×C411yescharacteristic, complemented
157C3×#102C2×C411yescharacteristic, complemented
158C3×#102C2×C411yescharacteristic, complemented
159C3×#102C2×C411yescharacteristic, complemented
160C3×C22⋊C8C2×C411yescharacteristic
161C3×C22⋊C8C2×C411yescharacteristic
162C3×C22⋊C8C2×C411yescharacteristic
163C3×C22⋊C8C2×C411yescharacteristic
164#837—22no—
165#837—22no—
166#837—22no—
167#837—22no—
168#837—41no—
169#837D414yescomplemented
170#830—21no—
171#830—21no—
172#830—21no—
173#830—21no—
174#830—21no—
175#830—21no—
176#830—21no—
177#830—21no—
178#830D411yescharacteristic
179#830D411yescharacteristic
180#830D411yescharacteristic
181#830D411yescharacteristic
182#819—22no—
183#819—41no—
184C8×Dic3—22no—
185C8×Dic3—41no—
186C4⋊(C3⋊C8)—21no—
187C4⋊(C3⋊C8)—21no—
188#803—21no—
189C4×C3⋊C8—21no—
190C22×#41C2×D311yescharacteristic
191C2×#135C2×D311yescharacteristic
192C2×#135C2×D311yescharacteristic
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16—31no—
197#525C2×D311yescharacteristic
198C22×C42—31no—
199#452Dic311yescharacteristic, complemented
200#452Dic311yescharacteristic, complemented
201#451Dic311yescharacteristic, complemented
202#450Dic311yescharacteristic, complemented
203#449Dic311yescharacteristic, complemented
204#449Dic311yescharacteristic, complemented
205#448Dic311yescharacteristic, complemented
206#447Dic311yescharacteristic, complemented
207#443—64no—
208#436—61no—
209#435—61no—
210#435—61no—
211C8×D4—61no—
212C2×#108—31no—
213C2×#108—31no—
214#424—31no—
215C2×#104—31no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—64no—
222#416C2×D311yescharacteristic
223#416C2×D311yescharacteristic
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—61no—
233C2×C22⋊C8C2×D311yescharacteristic
234#405—31no—
235C2×C4×C8—31no—
236C2×C4×C8—31no—
237#341—31no—
238#341—31no—
239#339—31no—
240#339—31no—
241#336—31no—
242#336—31no—
243C24×C3—21no—
244C24×C3#4111yescharacteristic
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—22no—
248C3×#41—22no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—21no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—42no—
258C3×#41—42no—
259C3×#41—41no—
260C3×#41—41no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41C2×D412yes—
264C3×#41#4112yes—
265C2×C3×Q8—21no—
266C2×C3×Q8—22no—
267C2×C3×Q8—41no—
268C2×C3×Q8C22×C411yescharacteristic
269C2×C3×Q8C22×C411yescharacteristic
270C2×C3×Q8C22×C411yescharacteristic
271C2×C3×D4—21no—
272C2×C3×D4—22no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—41no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4C22×C411yescharacteristic
284C2×C3×D4C22×C411yescharacteristic
285C2×C3×D4C22×C411yescharacteristic
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4C22×C411yescharacteristic
299C22×C3×C4C22×C411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4#4111yescharacteristic
303C22×C3×C4C2411yescharacteristic
304C22×Dic3—21no—
305C22×Dic3—24no—
306C22×Dic3—21no—
307C22×Dic3—42no—
308C22×Dic3—42no—
309C3×Q16—22no—
310C3×Q16—41no—
311C3×SD16—22no—
312C3×SD16—22no—
313C3×SD16—41no—
314C3×SD16—41no—
315C3×D8—22no—
316C3×D8—41no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8C22×C411yescharacteristic
322C2×C3×C8C22×C411yescharacteristic
323C2×C3×C8C22×C411yescharacteristic
324C2×C3×C8C22×C411yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4C22×C411yescharacteristic
328C3×C4⋊C4C22×C411yescharacteristic
329C3×C22⋊C4—21no—
330C3×C22⋊C4—21no—
331C3×C22⋊C4—21no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—21no—
334C3×C42—21no—
335C4×Dic3—21no—
336C4×Dic3—21no—
337C4×Dic3—21no—
338C4×Dic3—42no—
339C4×Dic3C2×D412yes—
340#208—21no—
341#208—21no—
342#208—21no—
343#208—21no—
344#208—21no—
345#208—21no—
346#208—21no—
347#208—42no—
348#208—42no—
349#208—42no—
350#208—42no—
351#208C2×D412yes—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—42no—
361C2×C3⋊C8—42no—
362C2×C3⋊C8—42no—
363C2×C3⋊C8—42no—
364C2×C3⋊C8C2×D411yescharacteristic
365C2×C3⋊C8C2×D411yescharacteristic
366C2×C3⋊C8C2×D411yescharacteristic
367C2×C3⋊C8C2×D411yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—22no—
371C2×#41—22no—
372C2×#41—41no—
373C2×#41—41no—
374C2×#41C2×Dic311yescharacteristic
375C2×#41C2×Dic311yescharacteristic
376C2×#41C22×D311yescharacteristic
377C2×#41C22×D311yescharacteristic
378C2×#41C22×D311yescharacteristic
379C22×Q8C2×Dic311yescharacteristic
380C22×D4—21no—
381C22×D4C2×Dic311yescharacteristic
382C23×C4—21no—
383C23×C4—61no—
384C23×C4C22×D311yescharacteristic
385#135—22no—
386#135—22no—
387#135—41no—
388#135—41no—
389C2×Q16C2×Dic311yescharacteristic, complemented
390C2×Q16C2×Dic311yescharacteristic, complemented
391C2×SD16C2×Dic311yescharacteristic, complemented
392C2×SD16C2×Dic311yescharacteristic, complemented
393C2×SD16C2×Dic311yescharacteristic, complemented
394C2×SD16C2×Dic311yescharacteristic, complemented
395C2×D8C2×Dic311yescharacteristic, complemented
396C2×D8C2×Dic311yescharacteristic, complemented
397#131—62no—
398#131—62no—
399#131—62no—
400#131—121no—
401#131—121no—
402#131—121no—
403C2×M16—31no—
404C2×M16—31no—
405C2×M16—31no—
406C2×M16—31no—
407C2×M16—61no—
408C2×M16—61no—
409C2×M16—61no—
410C2×M16—61no—
411C2×M16—62no—
412C2×M16—121no—
413C22×C8—31no—
414C22×C8—31no—
415C22×C8—61no—
416C22×C8—61no—
417C22×C8—61no—
418C22×C8—61no—
419C22×C8C22×D311yescharacteristic
420C22×C8C22×D311yescharacteristic
421#123—21no—
422C22⋊Q8C2×Dic311yescharacteristic
423C22⋊Q8C2×Dic311yescharacteristic
424#121C2×Dic311yescharacteristic
425#121C2×Dic311yescharacteristic
426#120—21no—
427C4×D4—21no—
428C4×D4—21no—
429#117C22×D311yescharacteristic
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—62no—
433C2×C42—61no—
434C2×C42—121no—
435#108—62no—
436#108—121no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439#104—34no—
440#104—62no—
441#104—62no—
442#104—62no—
443#104—62no—
444#104—121no—
445#103C2×Dic311yescharacteristic, complemented
446#103C2×Dic311yescharacteristic, complemented
447#103C2×Dic311yescharacteristic, complemented
448#103C2×Dic311yescharacteristic, complemented
449#102C2×Dic311yescharacteristic, complemented
450#102C2×Dic311yescharacteristic, complemented
451#102C2×Dic311yescharacteristic, complemented
452#102C2×Dic311yescharacteristic, complemented
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—61no—
458C22⋊C8—61no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8C2×Dic311yescharacteristic
466C22⋊C8C2×Dic311yescharacteristic
467C22⋊C8C2×Dic311yescharacteristic
468C22⋊C8C2×Dic311yescharacteristic
469#97—61no—
470C4×C8—61no—
471C4×C8—62no—
472C4×C8—121no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—22no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—41no—
480C23×C3—42no—
481C23×C3—42no—
482C23×C3—81no—
483C23×C3C4×D411yescharacteristic
484C23×C3C4×D411yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—42no—
492C3×Q8C4×D412yes—
493C3×D4—22no—
494C3×D4—22no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—42no—
501C3×D4—42no—
502C3×D4—42no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—42no—
508C3×D4—81no—
509C3×D4C4×D412yes—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4C4×D411yescharacteristic
535C2×C3×C4C4×D411yescharacteristic
536C2×C3×C4C23×C411yescharacteristic
537C2×C3×C4C22×D411yescharacteristic
538C2×C3×C4C22×D411yescharacteristic
539C2×C3×C4C2×#4111yescharacteristic
540C2×C3×C4H(5,𝔽2)11yescharacteristic
541C2×C3×C4H(5,𝔽2)11yescharacteristic
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—48no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—22no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—41no—
559C3⋊C8—41no—
560C3⋊C8—41no—
561C24—21no—
562C24#23711yescharacteristic
563#41—21no—
564#41—21no—
565#41—22no—
566#41—22no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—42no—
576#41—42no—
577#41—41no—
578#41—41no—
579#41—42no—
580#41—42no—
581#41D3×D412yes—
582#41#23712yes—
583C2×Q8—21no—
584C2×Q8—22no—
585C2×Q8—41no—
586C2×Q8C22×Dic311yescharacteristic
587C2×Q8C22×Dic311yescharacteristic
588C2×Q8C22×Dic311yescharacteristic
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4C22×Dic311yescharacteristic
602C2×D4C22×Dic311yescharacteristic
603C2×D4C22×Dic311yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—61no—
617C22×C4—64no—
618C22×C4—61no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4#23711yescharacteristic
624C22×C4C22×Dic311yescharacteristic
625C22×C4C22×Dic311yescharacteristic
626C22×C4C23×D311yescharacteristic
627Q16—22no—
628Q16—41no—
629SD16—22no—
630SD16—22no—
631SD16—41no—
632SD16—41no—
633D8—22no—
634D8—41no—
635M16—32no—
636M16—61no—
637M16—61no—
638M16—61no—
639M16—61no—
640M16—61no—
641M16—61no—
642M16—61no—
643M16—122no—
644M16—122no—
645M16—122no—
646M16—122no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C2×C8—122no—
664C2×C8—122no—
665C2×C8—122no—
666C2×C8—122no—
667C2×C8C22×Dic311yescharacteristic
668C2×C8C22×Dic311yescharacteristic
669C2×C8C22×Dic311yescharacteristic
670C2×C8C22×Dic311yescharacteristic
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4C22×Dic311yescharacteristic
674C4⋊C4C22×Dic311yescharacteristic
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C42—21no—
681C42—32no—
682C42—61no—
683C42—61no—
684C42—61no—
685C42—122no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—84no—
705C22×C3#44312yescomplemented
706C22×C3C2×C4×D411yescharacteristic
707C22×C3#54611yescharacteristic
708C22×C3#55111yescharacteristic
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—22no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4C2×C4×D411yescharacteristic
717C3×C4#51811yescharacteristic
718C3×C4D4211yescharacteristic
719C3×C4#54611yescharacteristic
720Dic3—24no—
721Dic3—42no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—81no—
732C23D4×Dic311yescharacteristic
733C23D4×Dic311yescharacteristic
734C23C2×#23711yescharacteristic
735Q8—21no—
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—42no—
741Q8D4×Dic312yes—
742D4—22no—
743D4—22no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—42no—
750D4—42no—
751D4—42no—
752D4—42no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—81no—
758D4D4×Dic312yes—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—128no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4D4×Dic311yescharacteristic
791C2×C4D4×Dic311yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×#23711yescharacteristic
795C2×C4#100411yescharacteristic
796C2×C4#100411yescharacteristic
797C2×C4C23×Dic311yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—61no—
803C8—61no—
804C8—62no—
805C8—61no—
806C8—61no—
807C8—121no—
808C8—121no—
809C8—121no—
810C2×C3—21no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—41no—
814C2×C3—42no—
815C2×C3—81no—
816C2×C3—81no—
817C2×C3#235811yescharacteristic
818C2×C3C2×#44311yescharacteristic
819C2×C3#295611yescharacteristic
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—84no—
839C22#519612yescomplemented
840C22#558711yescharacteristic
841C22#559111yescharacteristic
842C22C2×D4×Dic311yescharacteristic
843C4—21no—
844C4—21no—
845C4—22no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—64no—
851C4—122no—
852C4#559011yescharacteristic
853C4#559111yescharacteristic
854C4C2×D4×Dic311yescharacteristic
855C4#579811yescharacteristic
856C3#2288811yescharacteristic, complemented, Sylow
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#8257911yescharacteristic
865C2C2×#519611yescharacteristic
866C2#8400011yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3002C2
socleC22×C3C2×C4×D4
cosocleC22×C3×C4C24
hypercenter#3002D3
hypocenterC3#22888
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
2. C22×#837C2semidirect
3. #84075C2semidirect
4. C2×#5196C2semidirect
5. #82918C2semidirect
6. #72087C2semidirect
7. #72087C2semidirect
8. #72084C2semidirect
9. #71711C2semidirect
10. #70292C2semidirect
11. #70291C2semidirect
12. #70289C2semidirect
13. #70287C2semidirect
14. #69954C2semidirect
15. Dic3×C22⋊C8C2semidirect
23. C2×#948C22semidirect
26. C3×#452C4semidirect
27. C3×#452C4semidirect
28. C3×#451C4semidirect
29. C3×#450C4semidirect
30. C3×#449C4semidirect
31. C3×#449C4semidirect
32. C3×#448C4semidirect
33. C3×#447C4semidirect
42. C2×#837C22semidirect
43. C2×#837C22semidirect
48. #5234C22semidirect
54. C2×#819C22semidirect
55. C2×#819C22semidirect
56. C2×C8×Dic3C22semidirect
57. C2×C8×Dic3C22semidirect
62. #4999C22semidirect
63. #4997C22semidirect
64. #4552C22semidirect
65. #4552C22semidirect
66. #4550C22semidirect
67. #4550C22semidirect
68. #4532C22semidirect
69. #4532C22semidirect
106. C2×C3×Q16C2×C4semidirect
107. C2×C3×Q16C2×C4semidirect
108. C2×C3×SD16C2×C4semidirect
109. C2×C3×SD16C2×C4semidirect
110. C2×C3×SD16C2×C4semidirect
111. C2×C3×SD16C2×C4semidirect
112. C2×C3×D8C2×C4semidirect
113. C2×C3×D8C2×C4semidirect
152. C3×#103C2×C4semidirect
153. C3×#103C2×C4semidirect
154. C3×#103C2×C4semidirect
155. C3×#103C2×C4semidirect
156. C3×#102C2×C4semidirect
157. C3×#102C2×C4semidirect
158. C3×#102C2×C4semidirect
159. C3×#102C2×C4semidirect
169. #837D4semidirect
199. #452Dic3semidirect
200. #452Dic3semidirect
201. #451Dic3semidirect
202. #450Dic3semidirect
203. #449Dic3semidirect
204. #449Dic3semidirect
205. #448Dic3semidirect
206. #447Dic3semidirect
389. C2×Q16C2×Dic3semidirect
390. C2×Q16C2×Dic3semidirect
391. C2×SD16C2×Dic3semidirect
392. C2×SD16C2×Dic3semidirect
393. C2×SD16C2×Dic3semidirect
394. C2×SD16C2×Dic3semidirect
395. C2×D8C2×Dic3semidirect
396. C2×D8C2×Dic3semidirect
445. #103C2×Dic3semidirect
446. #103C2×Dic3semidirect
447. #103C2×Dic3semidirect
448. #103C2×Dic3semidirect
449. #102C2×Dic3semidirect
450. #102C2×Dic3semidirect
451. #102C2×Dic3semidirect
452. #102C2×Dic3semidirect
705. C22×C3#443semidirect
839. C22#5196semidirect
856. C3#22888semidirect

Maximal subgroups

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

subgroupindex
C3×#30022
C22×#8372
#840752
C2×#51962
#829182
#720872
#720842
#717112
#702922
#702912
#702892
#702872
#699542
Dic3×C22⋊C82
#228883