Finite Group Databasebeta

← C3×#15318 #10633925

Subgroups — C3×#15318 #10633925

Order 768.

1722 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Q8C211yesmaximal, characteristic
2C2×C3×#398C211yesmaximal, characteristic
3C2×C3×#395C211yesmaximal, characteristic
4C2×C3×#395C211yesmaximal, characteristic
5C2×C3×#391C211yesmaximal, characteristic
6C2×C3×#389C211yesmaximal, characteristic
7C3×#1446C211yesmaximal, characteristic
8C3×#1444C211yesmaximal, characteristic
9C3×#1444C211yesmaximal, characteristic
10C3×#1442C211yesmaximal, characteristic
11C3×#1441C211yesmaximal, characteristic
12C3×#1441C211yesmaximal, characteristic
13C3×#1436C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic
15C3×#1436C211yesmaximal, characteristic
16#15318C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×C4⋊Q8—24no—
20C2×C3×C4⋊Q8—24no—
21C2×C3×C4⋊Q8—24no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C42C2211yescharacteristic
34C22×C3×C42C2211yescharacteristic
35C3×#398—24no—
36C3×#395—24no—
37C3×#395—24no—
38C3×#391—24no—
39C3×#389—24no—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×C3×#95C2211yescharacteristic
55C2×C3×#95C2211yescharacteristic
56C2×C3×#95C2211yescharacteristic
57C2×C3×#95C2211yescharacteristic
58C2×C3×#95C2211yescharacteristic
59C2×C3×#95C2211yescharacteristic
60C22×C4⋊Q8C2×C311yescharacteristic
61C2×#398C2×C311yescharacteristic
62C2×#395C2×C311yescharacteristic
63C2×#395C2×C311yescharacteristic
64C2×#391C2×C311yescharacteristic
65C2×#389C2×C311yescharacteristic
66#1446C2×C311yescharacteristic
67#1444C2×C311yescharacteristic
68#1444C2×C311yescharacteristic
69#1442C2×C311yescharacteristic
70#1441C2×C311yescharacteristic
71#1441C2×C311yescharacteristic
72#1436C2×C311yescharacteristic
73#1436C2×C311yescharacteristic
74#1436C2×C311yescharacteristic
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8—41no—
87C22×C3×Q8—41no—
88C22×C3×Q8D414yes—
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C3×C4⋊Q8—232no—
105C2×C3×C4⋊C4—22no—
106C2×C3×C4⋊C4—22no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—22no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—22no—
130C2×C3×C4⋊C4—41no—
131C2×C3×C4⋊C4—41no—
132C2×C3×C4⋊C4—41no—
133C2×C3×C4⋊C4—41no—
134C2×C3×C4⋊C4—41no—
135C2×C3×C4⋊C4D414yes—
136C2×C3×C4⋊C4D414yes—
137C2×C3×C4⋊C4Q814yescomplemented
138C2×C3×C42—22no—
139C2×C3×C42—22no—
140C2×C3×C42—22no—
141C2×C3×C42—22no—
142C2×C3×C42—22no—
143C2×C3×C42—41no—
144C3×#95—22no—
145C3×#95—22no—
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—22no—
149C3×#95—22no—
150C3×#95—22no—
151C3×#95—22no—
152C3×#95—22no—
153C3×#95—22no—
154C3×#95—22no—
155C3×#95—22no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—41no—
160C3×#95—41no—
161C3×#95D414yes—
162C3×#95Q814yescomplemented
163C3×#95Q814yescomplemented
164C23×Q8C22×C311yescharacteristic
165C23×Q8C22×C311yescharacteristic
166C2×C4⋊Q8—24no—
167C2×C4⋊Q8—24no—
168C2×C4⋊Q8—24no—
169C22×C4⋊C4C22×C311yescharacteristic
170C22×C4⋊C4C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172C22×C4⋊C4C22×C311yescharacteristic
173C22×C4⋊C4C22×C311yescharacteristic
174C22×C4⋊C4C22×C311yescharacteristic
175C22×C4⋊C4C22×C311yescharacteristic
176C22×C4⋊C4C22×C311yescharacteristic
177C22×C4⋊C4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C22×C4⋊C4C22×C311yescharacteristic
180C22×C42C22×C311yescharacteristic
181C22×C42C22×C311yescharacteristic
182#398—24no—
183#395—24no—
184#395—24no—
185#391—24no—
186#389—24no—
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C2×#95C22×C311yescharacteristic
193C2×#95C22×C311yescharacteristic
194C2×#95C22×C311yescharacteristic
195C2×#95C22×C311yescharacteristic
196C2×#95C22×C311yescharacteristic
197C2×#95C22×C311yescharacteristic
198C2×#95C22×C311yescharacteristic
199C2×#95C22×C311yescharacteristic
200C2×#95C22×C311yescharacteristic
201C2×#95C22×C311yescharacteristic
202C2×#95C22×C311yescharacteristic
203C2×#95C22×C311yescharacteristic
204C2×#95C22×C311yescharacteristic
205C2×#95C22×C311yescharacteristic
206C2×#95C22×C311yescharacteristic
207C24×C3C2411yescharacteristic
208C2×C3×Q8—28no—
209C2×C3×Q8—28no—
210C2×C3×Q8—28no—
211C2×C3×Q8—44no—
212C2×C3×Q8—44no—
213C2×C3×Q8—44no—
214C2×C3×Q8—44no—
215C2×C3×Q8—44no—
216C2×C3×Q8—44no—
217C2×C3×Q8—44no—
218C2×C3×Q8—44no—
219C2×C3×Q8—44no—
220C2×C3×Q8—44no—
221C2×C3×Q8—44no—
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×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
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—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
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—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D412yes—
315C22×C3×C4C2×D412yes—
316C22×C3×C4C2×Q812yes—
317C22×C3×C4C2×Q812yes—
318C22×C3×C4C2×Q812yes—
319C22×C3×C4C2×Q812yes—
320C22×C3×C4C2×Q812yes—
321C22×C3×C4C2×Q812yes—
322C22×C3×C4C2×Q812yes—
323C22×C3×C4C2×Q812yes—
324C22×C3×C4C2×Q812yes—
325C22×C3×C4#4112yes—
326C22×C3×C4#4112yes—
327C3×C4⋊C4—28no—
328C3×C4⋊C4—28no—
329C3×C4⋊C4—28no—
330C3×C4⋊C4—28no—
331C3×C4⋊C4—28no—
332C3×C4⋊C4—44no—
333C3×C4⋊C4—44no—
334C3×C4⋊C4—44no—
335C3×C4⋊C4—44no—
336C3×C4⋊C4—44no—
337C3×C4⋊C4—44no—
338C3×C42—28no—
339C3×C42—44no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8—22no—
347C22×Q8—22no—
348C22×Q8—22no—
349C22×Q8—41no—
350C22×Q8—41no—
351C22×Q8—41no—
352C22×Q8—41no—
353C22×Q8C3×D414yes—
354C23×C4C23×C311yescharacteristic
355C23×C4C23×C311yescharacteristic
356C23×C4C23×C311yescharacteristic
357C23×C4C23×C311yescharacteristic
358C23×C4C23×C311yescharacteristic
359C23×C4C23×C311yescharacteristic
360C23×C4C23×C311yescharacteristic
361C23×C4C23×C311yescharacteristic
362C23×C4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C311yescharacteristic
369C4⋊Q8—232no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4C3×D414yes—
401C2×C4⋊C4C3×D414yes—
402C2×C4⋊C4C3×Q814yescomplemented
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—41no—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—41no—
425#95—41no—
426#95C3×D414yes—
427#95C3×Q814yescomplemented
428#95C3×Q814yescomplemented
429C23×C3C22×D411yescharacteristic
430C23×C3C22×D411yescharacteristic
431C23×C3C22×D411yescharacteristic
432C23×C3C22×D411yescharacteristic
433C23×C3C22×Q811yescharacteristic
434C23×C3C22×Q811yescharacteristic
435C23×C3C22×Q811yescharacteristic
436C23×C3C2×#4111yescharacteristic
437C23×C3C2×#4111yescharacteristic
438C23×C3H(5,𝔽2)11yescharacteristic
439C23×C3H(5,𝔽2)11yescharacteristic
440C23×C32−1+411yescharacteristic
441C23×C32−1+411yescharacteristic
442C23×C32−1+411yescharacteristic
443C23×C32−1+411yescharacteristic
444C3×Q8—416no—
445C3×Q8—416no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4#12014yes—
547C2×C3×C4#12114yes—
548C2×C3×C4C22⋊Q814yes—
549C2×C3×C4C4⋊Q814yes—
550C2×C3×C4C4⋊Q814yescomplemented
551C24C24×C311yescharacteristic
552C2×Q8—28no—
553C2×Q8—28no—
554C2×Q8—28no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×Q8—44no—
565C2×Q8—44no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
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—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4C2×C3×D412yes—
649C22×C4C2×C3×D412yes—
650C22×C4C2×C3×D412yes—
651C22×C4C2×C3×D412yes—
652C22×C4C2×C3×D412yes—
653C22×C4C2×C3×D412yes—
654C22×C4C2×C3×D412yes—
655C22×C4C2×C3×D412yes—
656C22×C4C2×C3×D412yes—
657C22×C4C2×C3×D412yes—
658C22×C4C2×C3×D412yes—
659C22×C4C2×C3×D412yes—
660C22×C4C2×C3×Q812yes—
661C22×C4C2×C3×Q812yes—
662C22×C4C2×C3×Q812yes—
663C22×C4C2×C3×Q812yes—
664C22×C4C2×C3×Q812yes—
665C22×C4C2×C3×Q812yes—
666C22×C4C2×C3×Q812yes—
667C22×C4C2×C3×Q812yes—
668C22×C4C2×C3×Q812yes—
669C22×C4C3×#4112yes—
670C22×C4C3×#4112yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—28no—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—44no—
682C42—28no—
683C42—44no—
684C22×C3C2×#12011yescharacteristic
685C22×C3C2×#12111yescharacteristic
686C22×C3C2×C22⋊Q811yescharacteristic
687C22×C3C2×C4⋊Q811yescharacteristic
688C22×C3C2×C4⋊Q811yescharacteristic
689C22×C3#53311yescharacteristic
690C22×C3#53411yescharacteristic
691C22×C3#53611yescharacteristic
692C22×C3#53611yescharacteristic
693C22×C3#53611yescharacteristic
694C22×C3#54111yescharacteristic
695C22×C3#54211yescharacteristic
696C22×C3#54411yescharacteristic
697C22×C3#54411yescharacteristic
698C22×C3#54411yescharacteristic
699C22×C3D4211yescharacteristic
700C22×C3D4211yescharacteristic
701C22×C3#54611yescharacteristic
702C22×C3#54611yescharacteristic
703C22×C3#54711yescharacteristic
704C22×C3#54811yescharacteristic
705C22×C3#54811yescharacteristic
706C22×C3D4×Q811yescharacteristic
707C22×C3D4×Q811yescharacteristic
708C22×C3D4×Q811yescharacteristic
709C22×C3D4×Q811yescharacteristic
710C22×C3D4×Q811yescharacteristic
711C22×C3D4×Q811yescharacteristic
712C22×C3D4×Q811yescharacteristic
713C22×C3#55411yescharacteristic
714C22×C3#55711yescharacteristic
715C22×C3#55711yescharacteristic
716C22×C3Q8211yescharacteristic
717C22×C3#56311yescharacteristic
718C22×C3#56311yescharacteristic
719C3×C4—24no—
720C3×C4—24no—
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—24no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—81no—
733C3×C4—81no—
734C23C22×C3×D411yescharacteristic
735C23C22×C3×D411yescharacteristic
736C23C22×C3×D411yescharacteristic
737C23C22×C3×D411yescharacteristic
738C23C22×C3×Q811yescharacteristic
739C23C22×C3×Q811yescharacteristic
740C23C22×C3×Q811yescharacteristic
741C23C2×C3×#4111yescharacteristic
742C23C2×C3×#4111yescharacteristic
743C23C3×H(5,𝔽2)11yescharacteristic
744C23C3×H(5,𝔽2)11yescharacteristic
745C23C3×2−1+411yescharacteristic
746C23C3×2−1+411yescharacteristic
747C23C3×2−1+411yescharacteristic
748C23C3×2−1+411yescharacteristic
749Q8—416no—
750Q8—416no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4C3×#12014yes—
852C2×C4C3×#12114yes—
853C2×C4C3×C22⋊Q814yes—
854C2×C4C3×C4⋊Q814yes—
855C2×C4C3×C4⋊Q814yescomplemented
856C2×C3#240911yescharacteristic
857C2×C3#241011yescharacteristic
858C2×C3#242911yescharacteristic
859C2×C3#243411yescharacteristic
860C2×C3#244011yescharacteristic
861C2×C3#245111yescharacteristic
862C2×C3#254611yescharacteristic
863C2×C3#255011yescharacteristic
864C2×C3#255111yescharacteristic
865C2×C3#267411yescharacteristic
866C2×C3#267711yescharacteristic
867C2×C3#271311yescharacteristic
868C2×C3#271311yescharacteristic
869C2×C3#272911yescharacteristic
870C2×C3#273411yescharacteristic
871C22C2×C3×#12011yescharacteristic
872C22C2×C3×#12111yescharacteristic
873C22C2×C3×C22⋊Q811yescharacteristic
874C22C2×C3×C4⋊Q811yescharacteristic
875C22C2×C3×C4⋊Q811yescharacteristic
876C22C3×#53311yescharacteristic
877C22C3×#53411yescharacteristic
878C22C3×#53611yescharacteristic
879C22C3×#53611yescharacteristic
880C22C3×#53611yescharacteristic
881C22C3×#54111yescharacteristic
882C22C3×#54211yescharacteristic
883C22C3×#54411yescharacteristic
884C22C3×#54411yescharacteristic
885C22C3×#54411yescharacteristic
886C22C3×D4211yescharacteristic
887C22C3×D4211yescharacteristic
888C22C3×#54611yescharacteristic
889C22C3×#54611yescharacteristic
890C22C3×#54711yescharacteristic
891C22C3×#54811yescharacteristic
892C22C3×#54811yescharacteristic
893C22C3×D4×Q811yescharacteristic
894C22C3×D4×Q811yescharacteristic
895C22C3×D4×Q811yescharacteristic
896C22C3×D4×Q811yescharacteristic
897C22C3×D4×Q811yescharacteristic
898C22C3×D4×Q811yescharacteristic
899C22C3×D4×Q811yescharacteristic
900C22C3×#55411yescharacteristic
901C22C3×#55711yescharacteristic
902C22C3×#55711yescharacteristic
903C22C3×Q8211yescharacteristic
904C22C3×#56311yescharacteristic
905C22C3×#56311yescharacteristic
906C4—24no—
907C4—24no—
908C4—24no—
909C4—24no—
910C4—24no—
911C4—42no—
912C4—42no—
913C4—42no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—81no—
920C4—81no—
921C3#1531811yescharacteristic, direct product factor, Sylow
922C2C3×#240911yescharacteristic
923C2C3×#241011yescharacteristic
924C2C3×#242911yescharacteristic
925C2C3×#243411yescharacteristic
926C2C3×#244011yescharacteristic
927C2C3×#245111yescharacteristic
928C2C3×#254611yescharacteristic
929C2C3×#255011yescharacteristic
930C2C3×#255111yescharacteristic
931C2C3×#267411yescharacteristic
932C2C3×#267711yescharacteristic
933C2C3×#271311yescharacteristic
934C2C3×#271311yescharacteristic
935C2C3×#272911yescharacteristic
936C2C3×#273411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
16. #15318C3direct (N × H)
137. C2×C3×C4⋊C4Q8semidirect
162. C3×#95Q8semidirect
163. C3×#95Q8semidirect
402. C2×C4⋊C4C3×Q8semidirect
427. #95C3×Q8semidirect
428. #95C3×Q8semidirect
550. C2×C3×C4C4⋊Q8semidirect
855. C2×C4C3×C4⋊Q8semidirect
921. C3#15318direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Q82
C2×C3×#3982
C2×C3×#3952
C2×C3×#3912
C2×C3×#3892
C3×#14462
C3×#14442
C3×#14422
C3×#14412
C3×#14362
#153183