Finite Group Databasebeta

← #10800197

Subgroups — #10800197

Order 768.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5538C211yesmaximal, characteristic
2C2×#4840C211yesmaximal, characteristic, complemented
3C2×#4689C211yesmaximal, characteristic, complemented
4C3×#1954C211yesmaximal, characteristic, complemented
5#71615C211yesmaximal, characteristic, complemented
6#70473C211yesmaximal, characteristic, complemented
7#69958C211yesmaximal, characteristic, complemented
8#69958C211yesmaximal, characteristic, complemented
9#69957C211yesmaximal, characteristic, complemented
10#69957C211yesmaximal, characteristic, complemented
11#69907C211yesmaximal, characteristic, complemented
12#69907C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14Dic3×C22⋊C8C211yesmaximal, characteristic, complemented
15#69788C211yesmaximal, characteristic, complemented
16#21381—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#939C411yescharacteristic
19C2×#935C411yescharacteristic
20C2×C4×#67C2211yescharacteristic
21C2×C4×#67C2211yescharacteristic
22C2×#926C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26#5538—24no—
27#5538—24no—
28C2×#898C411yescharacteristic
29C2×#889C411yescharacteristic
30C2×#886C411yescharacteristic
31C2×#885C411yescharacteristic
32C2×#879C411yescharacteristic
33C2×#878C411yescharacteristic
34C2×#872C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C4×C8C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×#815C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51C2×C8×Dic3C2211yescharacteristic
52C2×C4⋊(C3⋊C8)C2211yescharacteristic
53C2×#803C2211yescharacteristic
54#4840—24no—
55#4689—24no—
56#4550C2211yescharacteristic
57#4550C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#529—31no—
65C2×#433—31no—
66C2×#405—31no—
67#1985—31no—
68#1984—31no—
69#1955—31no—
70#1954D311yescharacteristic, complemented
71#1870—31no—
72#1870—31no—
73#1869—31no—
74#1869—31no—
75#1750—31no—
76#1750—31no—
77#1749—31no—
78C4×C22⋊C8—31no—
79C22×C3×D4C2×C411yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67C2×C411yescharacteristic
83C22×#67C2×C411yescharacteristic
84C23×Dic3C2×C411yescharacteristic
85C23×Dic3C2×C411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6C2×C411yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C2×C3×C4⋊C4C2×C411yescharacteristic
95C2×C3×C22⋊C4C2×C411yescharacteristic
96C2×C3×C22⋊C4C2×C411yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×#217C2×C411yescharacteristic
99C2×#217C2×C411yescharacteristic
100C2×#217C2×C411yescharacteristic
101C2×#217C2×C411yescharacteristic
102#939—24no—
103#935—24no—
104C4×#67—22no—
105C4×#67—22no—
106C4×#67—22no—
107C4×#67—22no—
108C2×(C2×D3)⋊C4C2×C411yescharacteristic
109C2×(C2×D3)⋊C4C2×C411yescharacteristic
110C2×(C2×D3)⋊C4C2×C411yescharacteristic
111C2×(C2×D3)⋊C4C2×C411yescharacteristic
112#926—22no—
113#926—22no—
114C2×C4⋊Dic3C2×C411yescharacteristic
115C2×C4⋊Dic3C2×C411yescharacteristic
116C2×C4⋊Dic3C2×C411yescharacteristic
117C2×Dic3⋊C4C2×C411yescharacteristic
118C2×Dic3⋊C4C2×C411yescharacteristic
119C2×Dic3⋊C4C2×C411yescharacteristic
120C2×Dic3⋊C4C2×C411yescharacteristic
121C2×Dic3⋊C4C2×C411yescharacteristic
122C2×Dic3⋊C4C2×C411yescharacteristic
123C2×C4×Dic3—22no—
124C2×C4×Dic3—22no—
125C2×C4×Dic3C2×C411yescharacteristic
126C2×C4×Dic3C2×C411yescharacteristic
127C2×C4×Dic3C2311yescharacteristic
128C2×C4×Dic3C2311yescharacteristic
129C2×C4×Dic3C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×ΓL(1,𝔽25)—22no—
135C2×ΓL(1,𝔽25)—22no—
136C2×ΓL(1,𝔽25)—22no—
137C2×D3×C8—22no—
138C2×D3×C8—22no—
139C2×D3×C8—22no—
140#898—24no—
141#889—24no—
142#886—24no—
143#885—24no—
144#879—24no—
145#878—24no—
146#872D414yes—
147#872D414yes—
148C4×Dic6—22no—
149C4×Dic6—22no—
150C3×C4⋊C8—22no—
151C3×C22⋊C8—22no—
152C3×C22⋊C8—22no—
153C3×C22⋊C8—22no—
154C3×C22⋊C8—22no—
155C3×C4×C8—22no—
156#830—22no—
157#830—22no—
158#830—22no—
159#830—22no—
160(C2×D3)⋊C8—22no—
161(C2×D3)⋊C8—22no—
162#815—22no—
163#815—22no—
164C8×Dic3—22no—
165C8×Dic3—22no—
166C4⋊(C3⋊C8)—22no—
167#803—22no—
168C22×M16—31no—
169C23×C8—31no—
170#529—64no—
171#529—64no—
172C2×#126—31no—
173C2×#126—31no—
174C2×#125—31no—
175C2×#124—31no—
176C2×#123—31no—
177C2×#123—31no—
178C2×C22⋊Q8—31no—
179C2×#121—31no—
180C2×C4×Q8—31no—
181C2×C4×D4—31no—
182C2×C4×D4—31no—
183C2×C4×D4C2×D311yescharacteristic
184C2×#117—31no—
185C2×#117—31no—
186C22×C42—31no—
187#433—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8C2×D311yescharacteristic
190C2×C22⋊C8—31no—
191C2×C22⋊C8—31no—
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×C22⋊C8C2×D311yescharacteristic
198C2×C22⋊C8C2×D311yescharacteristic
199C2×C22⋊C8C2×D311yescharacteristic
200#405—64no—
201C2×#97—31no—
202C2×#97—31no—
203C2×#97—31no—
204C2×C4×C8—31no—
205C2×C4×C8—31no—
206C2×C4×C8C2×D311yescharacteristic
207#336—31no—
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212#336—31no—
213#336—31no—
214#336—31no—
215C24×C3C22×C411yescharacteristic
216C24×C3C22×C411yescharacteristic
217C23×D3C22×C411yescharacteristic
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—41no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4C22×C411yescharacteristic
234C22×C3×C4C22×C411yescharacteristic
235C22×C3×C4C22×C411yescharacteristic
236C22×C3×C4C22×C411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—22no—
239C2×#67—22no—
240C2×#67—22no—
241C2×#67—22no—
242C2×#67—41no—
243C2×#67—41no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—41no—
249C22×Dic3—41no—
250C22×Dic3C22×C411yescharacteristic
251C22×Dic3C22×C411yescharacteristic
252C22×Dic3C22×C411yescharacteristic
253C22×Dic3C22×C411yescharacteristic
254C22×Dic3C22×C411yescharacteristic
255C22×Dic3C22×C411yescharacteristic
256C22×Dic3C22×C411yescharacteristic
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3C2×D412yes—
262C2×C4×D3C2×D412yes—
263C2×Dic6—22no—
264C2×Dic6—22no—
265C2×Dic6—41no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8#4112yes—
277C2×C3×C8#4112yes—
278C3×C4⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C42C2×D412yes—
282C3×C42C2×D412yes—
283#217—22no—
284#217—22no—
285#217—22no—
286#217—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4C22⋊C414yes—
290(C2×D3)⋊C4C22⋊C414yes—
291C4⋊Dic3—22no—
292C4⋊Dic3—22no—
293C4⋊Dic3—22no—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296Dic3⋊C4—22no—
297Dic3⋊C4—22no—
298Dic3⋊C4C22⋊C414yes—
299Dic3⋊C4C22⋊C414yes—
300C4×Dic3—21no—
301C4×Dic3—21no—
302C4×Dic3—21no—
303C4×Dic3—21no—
304C4×Dic3—22no—
305C4×Dic3—22no—
306C4×Dic3C2×D412yes—
307C4×Dic3C2×D412yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8#4112yes—
319C2×C3⋊C8#4112yes—
320ΓL(1,𝔽25)—28no—
321D3×C8—28no—
322C22×Q8—31no—
323C22×D4—31no—
324C22×D4—31no—
325C22×D4C4×D311yescharacteristic
326C23×C4—31no—
327C23×C4—31no—
328C23×C4—31no—
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C2×M16—62no—
332C2×M16—62no—
333C2×M16—62no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—62no—
339C22×C8—62no—
340C22×C8—62no—
341C22×C8C22×D311yescharacteristic
342C22×C8C22×D311yescharacteristic
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345#126—64no—
346#126—64no—
347#125—64no—
348#124—64no—
349#123—64no—
350#123—64no—
351C22⋊Q8—64no—
352#121—64no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4—62no—
360C4×D4—62no—
361#117—34no—
362#117—34no—
363#117—62no—
364#117—62no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4C4×D311yescharacteristic
375C2×C22⋊C4—31no—
376C2×C22⋊C4—31no—
377C2×C22⋊C4—31no—
378C2×C22⋊C4—31no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4C4×D311yescharacteristic
384C2×C22⋊C4C4×D311yescharacteristic
385C2×C42—31no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—62no—
391C2×C42—62no—
392C2×C42C22×D311yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—62no—
395C22⋊C8—22no—
396C22⋊C8—22no—
397C22⋊C8—22no—
398C22⋊C8—22no—
399C22⋊C8—62no—
400C22⋊C8—62no—
401C22⋊C8—62no—
402C22⋊C8—62no—
403C22⋊C8—62no—
404C22⋊C8—62no—
405#97—62no—
406#97—62no—
407#97—62no—
408C4×C8—22no—
409C4×C8—62no—
410C4×C8—62no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3#13112yes—
425C23×C3C23×C411yescharacteristic
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—21no—
431C22×D3—21no—
432C22×D3C2×C22⋊C412yes—
433C3×D4—44no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4C2×C22⋊C412yes—
453C2×C3×C4C2×C22⋊C412yes—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460#67—44no—
461#67—44no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—44no—
480C2×Dic3—44no—
481C2×Dic3C2×C22⋊C412yes—
482C2×Dic3C2×C22⋊C412yes—
483C2×Dic3C2×C22⋊C412yes—
484C2×Dic3#13112yes—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—22no—
488C4×D3—22no—
489Dic6—44no—
490C3×C8—22no—
491C3×C8—22no—
492C3×C8—41no—
493C3×C8—41no—
494C3⋊C8—22no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C3⋊C8—41no—
498C24—31no—
499C24C2×C4×D311yescharacteristic
500C24C2×C4×D311yescharacteristic
501C2×Q8—62no—
502C2×Q8—62no—
503C2×Q8—121no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—41no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—121no—
512C2×D4—121no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—62no—
542C22×C4—121no—
543C22×C4—121no—
544C22×C4C2×C4×D311yescharacteristic
545C22×C4C2×C4×D311yescharacteristic
546C22×C4C2×C4×D311yescharacteristic
547C22×C4C2×C4×D311yescharacteristic
548C22×C4C23×D311yescharacteristic
549M16—68no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—32no—
561C2×C8—32no—
562C2×C8—68no—
563C2×C8—61no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8#23712yes—
574C2×C8#23712yes—
575C4⋊C4—22no—
576C4⋊C4—34no—
577C4⋊C4—34no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—34no—
588C22⋊C4—34no—
589C22⋊C4—62no—
590C22⋊C4—62no—
591C22⋊C4—62no—
592C22⋊C4—62no—
593C22⋊C4—62no—
594C22⋊C4—62no—
595C42—32no—
596C42—32no—
597C42—62no—
598C42—62no—
599C42—61no—
600C42—61no—
601C42—61no—
602C42—61no—
603C42D3×D412yes—
604C42D3×D412yes—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3C22×C22⋊C411yescharacteristic
620C22×C3C4×#4111yescharacteristic
621C22×C3C4×#4111yescharacteristic
622C22×C3C2×#13111yescharacteristic
623C22×C3C2×#13111yescharacteristic
624C22×C3#56811yescharacteristic
625C22×C3#56811yescharacteristic
626C2×D3—22no—
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4#52511yescharacteristic
638C3×C4#52511yescharacteristic
639C3×C4#53211yescharacteristic
640C3×C4#53211yescharacteristic
641Dic3—22no—
642Dic3—22no—
643Dic3—22no—
644Dic3—22no—
645Dic3—41no—
646Dic3—41no—
647Dic3—41no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—32no—
662C23—61no—
663C23—61no—
664C23—61no—
665C23—61no—
666C23—61no—
667C23—61no—
668C23#90112yes—
669C23C22×C4×D311yescharacteristic
670Q8—124no—
671D4—44no—
672D4—124no—
673D4—124no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—124no—
718C2×C4—124no—
719C2×C4D3×C22⋊C412yes—
720C2×C4D3×C22⋊C412yes—
721C2×C4C2×D3×D411yescharacteristic
722C2×C4C2×D3×D411yescharacteristic
723C2×C4C2×#23711yescharacteristic
724C2×C4C2×#23711yescharacteristic
725C2×C4D3×#4111yescharacteristic
726C2×C4D3×#4111yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C8—62no—
732C8—62no—
733C8—121no—
734C8—121no—
735C2×C3—42no—
736C2×C3—81no—
737C2×C3#229711yescharacteristic
738C2×C3#288011yescharacteristic
739C2×C3#288011yescharacteristic
740C2×C3#296611yescharacteristic
741C2×C3#296711yescharacteristic
742C2×C3#296811yescharacteristic
743C2×C3#296911yescharacteristic
744D3—42no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22C2×D3×C22⋊C411yescharacteristic
767C22C4×#23711yescharacteristic
768C22C4×#23711yescharacteristic
769C22C2×#90111yescharacteristic
770C22#574511yescharacteristic
771C22D3×#13111yescharacteristic
772C22#575011yescharacteristic
773C4—22no—
774C4—22no—
775C4—41no—
776C4—41no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4#560611yescharacteristic
785C4#560611yescharacteristic
786C4#566811yescharacteristic
787C4#571611yescharacteristic
788C3#2138111yescharacteristic, complemented, Sylow
789C2—42no—
790C2—81no—
791C2—122no—
792C2#7629011yescharacteristic
793C2#7860011yescharacteristic
794C2#7866311yescharacteristic
795C2#7940011yescharacteristic
796C2#7940211yescharacteristic
797C2#7951911yescharacteristic
798C2#7952011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1954C2
prime radicalC2×#939C4
cosocleC22×C3×C4C24
hypercenter#1954D3
hypocenterC3#21381
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#4840C2semidirect
3. C2×#4689C2semidirect
4. C3×#1954C2semidirect
5. #71615C2semidirect
6. #70473C2semidirect
7. #69958C2semidirect
8. #69958C2semidirect
9. #69957C2semidirect
10. #69957C2semidirect
11. #69907C2semidirect
12. #69907C2semidirect
13. #69906C2semidirect
14. Dic3×C22⋊C8C2semidirect
15. #69788C2semidirect
70. #1954D3semidirect
788. C3#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#55382
C2×#48402
C2×#46892
C3×#19542
#716152
#704732
#699582
#699572
#699072
#699062
Dic3×C22⋊C82
#697882
#213813