Finite Group Databasebeta

← #10800206

Subgroups — #10800206

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×C3×#529C211yesmaximal, characteristic
2C2×#5000C211yesmaximal, characteristic, complemented
3C2×#4997C211yesmaximal, characteristic, complemented
4#71635C211yesmaximal, characteristic, complemented
5#71634C211yesmaximal, characteristic, complemented
6#71615C211yesmaximal, characteristic, complemented
7#71614C211yesmaximal, characteristic, complemented
8#71611C211yesmaximal, characteristic, complemented
9#71611C211yesmaximal, characteristic, complemented
10#71610C211yesmaximal, characteristic, complemented
11#71610C211yesmaximal, characteristic, complemented
12#71582C211yesmaximal, characteristic, complemented
13#71582C211yesmaximal, characteristic, complemented
14#71529C211yesmaximal, characteristic, complemented
15C4×#830C211yesmaximal, characteristic, complemented
16#21381—31nomaximal, Sylow
17C3×#529—24no—
18C3×#529—24no—
19C2×C3×#126C411yescharacteristic
20C2×C3×#126C411yescharacteristic
21C2×C3×#125C411yescharacteristic
22C2×C3×#124C411yescharacteristic
23C2×C3×#123C411yescharacteristic
24C2×C3×#123C411yescharacteristic
25C2×C3×C22⋊Q8C411yescharacteristic
26C2×C3×#121C411yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117C2211yescharacteristic
32C2×C3×#117C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C22×#208C2211yescharacteristic
35C23×C3⋊C8C2211yescharacteristic
36C2×#830C2211yescharacteristic
37C2×#830C2211yescharacteristic
38C2×#830C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5000—24no—
47#4997—24no—
48C2×C4⋊(C3⋊C8)C2211yescharacteristic
49C2×C4⋊(C3⋊C8)C2211yescharacteristic
50C2×#803C2211yescharacteristic
51C2×#803C2211yescharacteristic
52C2×#803C2211yescharacteristic
53C2×C4×C3⋊C8C2211yescharacteristic
54C2×C4×C3⋊C8C2211yescharacteristic
55C2×C4×C3⋊C8C2211yescharacteristic
56#4524C2211yescharacteristic
57#4524C2211yescharacteristic
58#4524C2211yescharacteristic
59#4524C2211yescharacteristic
60#4524C2211yescharacteristic
61#4524C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529D311yescharacteristic
65C2×#433—31no—
66C2×#405—31no—
67#1985—31no—
68#1984—31no—
69#1955—31no—
70#1954—31no—
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×Q8C2×C411yescharacteristic
80C22×C3×D4C2×C411yescharacteristic
81C22×C3×D4C2×C411yescharacteristic
82C22×C3×D4C2×C411yescharacteristic
83C23×C3×C4C2×C411yescharacteristic
84C23×C3×C4C2×C411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C3×#126—24no—
89C3×#126—24no—
90C3×#125—24no—
91C3×#124—24no—
92C3×#123—24no—
93C3×#123—24no—
94C3×C22⋊Q8—24no—
95C3×#121—24no—
96C3×C4×Q8—22no—
97C3×C4×Q8—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×#117—22no—
105C3×#117—22no—
106C3×#117D414yes—
107C3×#117D414yes—
108C2×C3×C4⋊C4C2×C411yescharacteristic
109C2×C3×C4⋊C4C2×C411yescharacteristic
110C2×C3×C4⋊C4C2×C411yescharacteristic
111C2×C3×C4⋊C4C2×C411yescharacteristic
112C2×C3×C4⋊C4C2×C411yescharacteristic
113C2×C3×C4⋊C4C2×C411yescharacteristic
114C2×C3×C4⋊C4C2×C411yescharacteristic
115C2×C3×C4⋊C4C2×C411yescharacteristic
116C2×C3×C4⋊C4C2×C411yescharacteristic
117C2×C3×C4⋊C4C2×C411yescharacteristic
118C2×C3×C22⋊C4C2×C411yescharacteristic
119C2×C3×C22⋊C4C2×C411yescharacteristic
120C2×C3×C22⋊C4C2×C411yescharacteristic
121C2×C3×C22⋊C4C2×C411yescharacteristic
122C2×C3×C22⋊C4C2×C411yescharacteristic
123C2×C3×C22⋊C4C2×C411yescharacteristic
124C2×C3×C22⋊C4C2×C411yescharacteristic
125C2×C3×C22⋊C4C2×C411yescharacteristic
126C2×C3×C22⋊C4C2×C411yescharacteristic
127C2×C3×C22⋊C4C2×C411yescharacteristic
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42C2×C411yescharacteristic
131C2×C3×C42C2×C411yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×#208—22no—
137C2×#208—22no—
138C2×#208—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—22no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150#830—22no—
151#830—22no—
152#830—22no—
153#830—22no—
154#830—22no—
155#830—22no—
156#830—22no—
157#830—22no—
158#830—22no—
159#830—22no—
160C4⋊(C3⋊C8)—22no—
161C4⋊(C3⋊C8)—22no—
162#803—22no—
163#803—22no—
164#803—22no—
165C4×C3⋊C8—22no—
166C4×C3⋊C8—22no—
167C4×C3⋊C8—22no—
168C22×M16—31no—
169C23×C8—31no—
170#529—24no—
171#529—24no—
172C2×#126Dic311yescharacteristic
173C2×#126Dic311yescharacteristic
174C2×#125Dic311yescharacteristic
175C2×#124Dic311yescharacteristic
176C2×#123Dic311yescharacteristic
177C2×#123Dic311yescharacteristic
178C2×C22⋊Q8Dic311yescharacteristic
179C2×#121Dic311yescharacteristic
180C2×C4×Q8C2×D311yescharacteristic
181C2×C4×D4C2×D311yescharacteristic
182C2×C4×D4C2×D311yescharacteristic
183C2×C4×D4C2×D311yescharacteristic
184C2×#117C2×D311yescharacteristic
185C2×#117C2×D311yescharacteristic
186C22×C42C2×D311yescharacteristic
187#433—64no—
188C2×C4⋊C8—31no—
189C2×C4⋊C8—31no—
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⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C22⋊C8—31no—
199C2×C22⋊C8—31no—
200#405—64no—
201C2×#97—31no—
202C2×#97—31no—
203C2×#97—31no—
204C2×C4×C8—31no—
205C2×C4×C8—31no—
206C2×C4×C8—31no—
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
217C24×C3C22×C411yescharacteristic
218C2×C3×Q8—22no—
219C2×C3×Q8—22no—
220C2×C3×Q8—41no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—41no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C22×C411yescharacteristic
258C22×C3×C4C22×C411yescharacteristic
259C22×C3×C4C22×C411yescharacteristic
260C22×C3×C4C22×C411yescharacteristic
261C22×C3×C4C22×C411yescharacteristic
262C22×C3×C4C22×C411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2×D412yes—
265C22×C3×C4C2411yescharacteristic
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—22no—
274C3×C4⋊C4C22⋊C414yes—
275C3×C4⋊C4C22⋊C414yes—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—22no—
284C3×C22⋊C4C22⋊C414yes—
285C3×C22⋊C4C22⋊C414yes—
286C3×C42—22no—
287C3×C42—22no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294C3×C42C2×D412yes—
295C3×C42C2×D412yes—
296#208—28no—
297C2×C3⋊C8—28no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
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—
320C2×C3⋊C8#4112yes—
321C2×C3⋊C8#4112yes—
322C22×Q8C2×Dic311yescharacteristic
323C22×D4C2×Dic311yescharacteristic
324C22×D4C2×Dic311yescharacteristic
325C22×D4C2×Dic311yescharacteristic
326C23×C4C2×Dic311yescharacteristic
327C23×C4C2×Dic311yescharacteristic
328C23×C4C22×D311yescharacteristic
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—31no—
339C22×C8—31no—
340C22×C8—31no—
341C22×C8—31no—
342C22×C8—62no—
343C22×C8—62no—
344C22×C8—62no—
345#126—24no—
346#126—24no—
347#125—24no—
348#124—24no—
349#123—24no—
350#123—24no—
351C22⋊Q8—24no—
352#121—24no—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361#117—22no—
362#117—22no—
363#117#6714yes—
364#117#6714yes—
365C2×C4⋊C4C2×Dic311yescharacteristic
366C2×C4⋊C4C2×Dic311yescharacteristic
367C2×C4⋊C4C2×Dic311yescharacteristic
368C2×C4⋊C4C2×Dic311yescharacteristic
369C2×C4⋊C4C2×Dic311yescharacteristic
370C2×C4⋊C4C2×Dic311yescharacteristic
371C2×C4⋊C4C2×Dic311yescharacteristic
372C2×C4⋊C4C2×Dic311yescharacteristic
373C2×C4⋊C4C2×Dic311yescharacteristic
374C2×C4⋊C4C2×Dic311yescharacteristic
375C2×C22⋊C4C2×Dic311yescharacteristic
376C2×C22⋊C4C2×Dic311yescharacteristic
377C2×C22⋊C4C2×Dic311yescharacteristic
378C2×C22⋊C4C2×Dic311yescharacteristic
379C2×C22⋊C4C2×Dic311yescharacteristic
380C2×C22⋊C4C2×Dic311yescharacteristic
381C2×C22⋊C4C2×Dic311yescharacteristic
382C2×C22⋊C4C2×Dic311yescharacteristic
383C2×C22⋊C4C2×Dic311yescharacteristic
384C2×C22⋊C4C2×Dic311yescharacteristic
385C2×C42—22no—
386C2×C42—22no—
387C2×C42C2×Dic311yescharacteristic
388C2×C42C2×Dic311yescharacteristic
389C2×C42C22×D311yescharacteristic
390C2×C42C22×D311yescharacteristic
391C2×C42C22×D311yescharacteristic
392C2×C42C22×D311yescharacteristic
393C4⋊C8—62no—
394C4⋊C8—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397C22⋊C8—62no—
398C22⋊C8—62no—
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—62no—
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—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3C2×C22⋊C412yes—
431C23×C3#13112yes—
432C23×C3C23×C411yescharacteristic
433C3×Q8—44no—
434C3×D4—44no—
435C3×D4—44no—
436C3×D4—44no—
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—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—44no—
469C2×C3×C4—44no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4C2×C22⋊C412yes—
479C2×C3×C4C2×C22⋊C412yes—
480C2×C3×C4C2×C22⋊C412yes—
481C2×C3×C4C2×C22⋊C412yes—
482C2×C3×C4C2×C22⋊C412yes—
483C2×C3×C4#13112yes—
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4C2×#4111yescharacteristic
488C2×C3×C4C2×#4111yescharacteristic
489C2×C3×C4C2×#4111yescharacteristic
490C3⋊C8—22no—
491C3⋊C8—22no—
492C3⋊C8—22no—
493C3⋊C8—22no—
494C3⋊C8—41no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C3⋊C8—41no—
498C24C22×Dic311yescharacteristic
499C24C22×Dic311yescharacteristic
500C24C22×Dic311yescharacteristic
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—41no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4C22×Dic311yescharacteristic
536C22×C4C22×Dic311yescharacteristic
537C22×C4C22×Dic311yescharacteristic
538C22×C4C22×Dic311yescharacteristic
539C22×C4C22×Dic311yescharacteristic
540C22×C4C22×Dic311yescharacteristic
541C22×C4C22×Dic311yescharacteristic
542C22×C4C22×Dic311yescharacteristic
543C22×C4C22×Dic311yescharacteristic
544C22×C4C22×Dic311yescharacteristic
545C22×C4C22×Dic311yescharacteristic
546C22×C4C2×#6712yes—
547C22×C4C2×#6712yes—
548C22×C4C23×D311yescharacteristic
549M16—68no—
550C2×C8—32no—
551C2×C8—32no—
552C2×C8—32no—
553C2×C8—32no—
554C2×C8—68no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
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—61no—
574C2×C8—61no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4#21714yes—
584C4⋊C4#21714yes—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4#21714yes—
594C22⋊C4#21714yes—
595C42—22no—
596C42—22no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42C2×#6712yes—
602C42C2×#6712yes—
603C42C2×#6712yes—
604C42C2×#6712yes—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
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×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3C22×C22⋊C411yescharacteristic
627C22×C3C4×#4111yescharacteristic
628C22×C3C4×#4111yescharacteristic
629C22×C3C2×#13111yescharacteristic
630C22×C3C2×#13111yescharacteristic
631C22×C3#56811yescharacteristic
632C22×C3#56811yescharacteristic
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4#52511yescharacteristic
645C3×C4#52511yescharacteristic
646C3×C4#53211yescharacteristic
647C3×C4#53211yescharacteristic
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—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23#94812yes—
668C23C2×#21712yes—
669C23C23×Dic311yescharacteristic
670Q8—44no—
671D4—44no—
672D4—44no—
673D4—44no—
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—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4#94812yes—
716C2×C4C2×#21712yes—
717C2×C4C2×#21712yes—
718C2×C4C2×#21712yes—
719C2×C4C2×#21712yes—
720C2×C4C2×#21712yes—
721C2×C4D3×#4111yescharacteristic
722C2×C4D3×#4111yescharacteristic
723C2×C4D3×#4111yescharacteristic
724C2×C4D3×#4111yescharacteristic
725C2×C4C22×#6711yescharacteristic
726C2×C4C22×#6711yescharacteristic
727C8—62no—
728C8—62no—
729C8—62no—
730C8—62no—
731C8—121no—
732C8—121no—
733C8—121no—
734C8—121no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—81no—
738C2×C3#229711yescharacteristic
739C2×C3#288011yescharacteristic
740C2×C3#288011yescharacteristic
741C2×C3#296611yescharacteristic
742C2×C3#296711yescharacteristic
743C2×C3#296811yescharacteristic
744C2×C3#296911yescharacteristic
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22C2×#94811yescharacteristic
767C22C2×#94811yescharacteristic
768C22#581911yescharacteristic
769C22#581911yescharacteristic
770C22Dic3×#4111yescharacteristic
771C22Dic3×#4111yescharacteristic
772C22C22×#21711yescharacteristic
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4#582811yescharacteristic
785C4#582811yescharacteristic
786C4#583211yescharacteristic
787C4#583211yescharacteristic
788C3#2138111yescharacteristic, complemented, Sylow
789C2—42no—
790C2—42no—
791C2—81no—
792C2#8312611yescharacteristic
793C2#8312711yescharacteristic
794C2#8312811yescharacteristic
795C2#8312911yescharacteristic
796C2#8407511yescharacteristic
797C2#8407511yescharacteristic
798C2#8408611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC2×C3×#529C2
prime radicalC2×C3×#121C4
cosocleC22×C3×C4C24
hypercenterC2×#529D3
hypocenterC3#21381
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. C2×#5000C2semidirect
3. C2×#4997C2semidirect
4. #71635C2semidirect
5. #71634C2semidirect
6. #71615C2semidirect
7. #71614C2semidirect
8. #71611C2semidirect
9. #71611C2semidirect
10. #71610C2semidirect
11. #71610C2semidirect
12. #71582C2semidirect
13. #71582C2semidirect
14. #71529C2semidirect
15. C4×#830C2semidirect
788. C3#21381semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×#50002
C2×#49972
#716352
#716342
#716152
#716142
#716112
#716102
#715822
#715292
C4×#8302
#213813