Finite Group Databasebeta

← C3×#14398 #10633005

Subgroups — C3×#14398 #10633005

Order 768.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#387C211yesmaximal, characteristic, complemented
2C2×C3×#385C211yesmaximal, characteristic
3C2×C3×#380C211yesmaximal, characteristic
4C3×#1444C211yesmaximal, characteristic, complemented
5C3×#1443C211yesmaximal, characteristic, complemented
6C3×#1442C211yesmaximal, characteristic, complemented
7C3×#1441C211yesmaximal, characteristic, complemented
8C3×#1439C211yesmaximal, characteristic
9C3×#1439C211yesmaximal, characteristic
10C3×#1437C211yesmaximal, characteristic
11C3×#1437C211yesmaximal, characteristic
12C3×#1436C211yesmaximal, characteristic, complemented
13C3×#1436C211yesmaximal, characteristic, complemented
14C3×C4⋊#95C211yesmaximal, characteristic, complemented
15C3×C22⋊#95C211yesmaximal, characteristic
16#14398C311yesmaximal, characteristic, direct product factor, Sylow
17C24×C3×C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic
31C22×C3×C42C2211yescharacteristic
32C3×#387—24no—
33C3×#385C418yescomplemented
34C3×#380—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
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×#387C2×C311yescharacteristic, complemented
56C2×#385C2×C311yescharacteristic
57C2×#380C2×C311yescharacteristic
58#1444C2×C311yescharacteristic, complemented
59#1443C2×C311yescharacteristic, complemented
60#1442C2×C311yescharacteristic, complemented
61#1441C2×C311yescharacteristic, complemented
62#1439C2×C311yescharacteristic
63#1439C2×C311yescharacteristic
64#1437C2×C311yescharacteristic
65#1437C2×C311yescharacteristic
66#1436C2×C311yescharacteristic, complemented
67#1436C2×C311yescharacteristic, complemented
68C4⋊#95C2×C311yescharacteristic, complemented
69C22⋊#95C2×C311yescharacteristic
70C25×C3C2311yescharacteristic
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—41no—
74C23×C3×C4—41no—
75C23×C3×C4—41no—
76C23×C3×C4—41no—
77C23×C3×C4C2×C414yes—
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—22no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—41no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4—41no—
102C2×C3×C4⋊C4—41no—
103C2×C3×C4⋊C4—41no—
104C2×C3×C4⋊C4—41no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C4⋊C4—41no—
107C2×C3×C4⋊C4C2×C414yes—
108C2×C3×C4⋊C4C2×C414yes—
109C2×C3×C4⋊C4D414yes—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—41no—
118C2×C3×C22⋊C4—41no—
119C2×C3×C22⋊C4—41no—
120C2×C3×C22⋊C4—41no—
121C2×C3×C22⋊C4—41no—
122C2×C3×C22⋊C4—41no—
123C2×C3×C22⋊C4—41no—
124C2×C3×C22⋊C4—41no—
125C2×C3×C22⋊C4C2×C414yes—
126C2×C3×C22⋊C4C2×C414yes—
127C2×C3×C22⋊C4Q814yes—
128C2×C3×C42—22no—
129C2×C3×C42—22no—
130C2×C3×C42—41no—
131C2×C3×C42—41no—
132C2×C3×C42—41no—
133C2×C3×C42—41no—
134C3×#95—22no—
135C3×#95—22no—
136C3×#95—22no—
137C3×#95—22no—
138C3×#95—22no—
139C3×#95—22no—
140C3×#95—22no—
141C3×#95—22no—
142C3×#95—22no—
143C3×#95—41no—
144C3×#95—41no—
145C3×#95—41no—
146C3×#95—41no—
147C3×#95—41no—
148C3×#95—41no—
149C3×#95—41no—
150C3×#95—41no—
151C3×#95—41no—
152C3×#95C2×C414yes—
153C3×#95C2×C414yes—
154C24×C4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156C22×C4⋊C4C22×C311yescharacteristic
157C22×C4⋊C4C22×C311yescharacteristic
158C22×C4⋊C4C22×C311yescharacteristic
159C22×C4⋊C4C22×C311yescharacteristic
160C22×C4⋊C4C22×C311yescharacteristic
161C22×C22⋊C4C22×C311yescharacteristic
162C22×C22⋊C4C22×C311yescharacteristic
163C22×C22⋊C4C22×C311yescharacteristic
164C22×C22⋊C4C22×C311yescharacteristic
165C22×C22⋊C4C22×C311yescharacteristic
166C22×C22⋊C4C22×C311yescharacteristic
167C22×C42C22×C311yescharacteristic
168C22×C42C22×C311yescharacteristic
169#387—24no—
170#385C3×C418yescomplemented
171#380—24no—
172C2×#95C22×C311yescharacteristic
173C2×#95C22×C311yescharacteristic
174C2×#95C22×C311yescharacteristic
175C2×#95C22×C311yescharacteristic
176C2×#95C22×C311yescharacteristic
177C2×#95C22×C311yescharacteristic
178C2×#95C22×C311yescharacteristic
179C2×#95C22×C311yescharacteristic
180C2×#95C22×C311yescharacteristic
181C2×#95C22×C311yescharacteristic
182C2×#95C22×C311yescharacteristic
183C2×#95C22×C311yescharacteristic
184C2×#95C22×C311yescharacteristic
185C2×#95C22×C311yescharacteristic
186C2×#95C22×C311yescharacteristic
187C2×#95C22×C311yescharacteristic
188C2×#95C22×C311yescharacteristic
189C2×#95C22×C311yescharacteristic
190C2×#95C22×C311yescharacteristic
191C2×#95C22×C311yescharacteristic
192C24×C3—21no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3C22×C412yes—
205C24×C3C2×Q812yes—
206C24×C3#4112yes—
207C24×C3C2411yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
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×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—28no—
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—44no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4C22×C412yes—
300C22×C3×C4C22×C412yes—
301C22×C3×C4C22×C412yes—
302C22×C3×C4C22×C412yes—
303C22×C3×C4C22×C412yes—
304C22×C3×C4C22×C412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×Q812yes—
309C22×C3×C4C2×Q812yes—
310C22×C3×C4#4112yes—
311C22×C3×C4#4112yes—
312C22×C3×C4#4112yes—
313C3×C4⋊C4—28no—
314C3×C4⋊C4—44no—
315C3×C4⋊C4—44no—
316C3×C4⋊C4—44no—
317C3×C4⋊C4—44no—
318C3×C4⋊C4—44no—
319C3×C22⋊C4—28no—
320C3×C22⋊C4—44no—
321C3×C22⋊C4—44no—
322C3×C22⋊C4—44no—
323C3×C22⋊C4—44no—
324C3×C22⋊C4—44no—
325C3×C42—44no—
326C3×C42—44no—
327C25C23×C311yescharacteristic
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—41no—
331C23×C4—41no—
332C23×C4—41no—
333C23×C4—41no—
334C23×C4C2×C3×C414yes—
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C23×C4C23×C311yescharacteristic
338C23×C4C23×C311yescharacteristic
339C23×C4C23×C311yescharacteristic
340C23×C4C23×C311yescharacteristic
341C23×C4C23×C311yescharacteristic
342C23×C4C23×C311yescharacteristic
343C23×C4C23×C311yescharacteristic
344C23×C4C23×C311yescharacteristic
345C23×C4C23×C311yescharacteristic
346C23×C4C23×C311yescharacteristic
347C23×C4C23×C311yescharacteristic
348C23×C4C23×C311yescharacteristic
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4C2×C3×C414yes—
365C2×C4⋊C4C2×C3×C414yes—
366C2×C4⋊C4C3×D414yes—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4C2×C3×C414yes—
383C2×C22⋊C4C2×C3×C414yes—
384C2×C22⋊C4C3×Q814yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—41no—
388C2×C42—41no—
389C2×C42—41no—
390C2×C42—41no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
398#95—22no—
399#95—22no—
400#95—41no—
401#95—41no—
402#95—41no—
403#95—41no—
404#95—41no—
405#95—41no—
406#95—41no—
407#95—41no—
408#95—41no—
409#95C2×C3×C414yes—
410#95C2×C3×C414yes—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3C4×Q814yes—
446C23×C3C23×C411yescharacteristic
447C23×C3C22×D411yescharacteristic
448C23×C3C22×Q811yescharacteristic
449C23×C3C2×#4111yescharacteristic
450C23×C3C2×#4111yescharacteristic
451C23×C3C2×#4111yescharacteristic
452C23×C3C2×#4111yescharacteristic
453C23×C3H(5,𝔽2)11yescharacteristic
454C23×C3H(5,𝔽2)11yescharacteristic
455C23×C3H(5,𝔽2)11yescharacteristic
456C23×C3H(5,𝔽2)11yescharacteristic
457C23×C3H(5,𝔽2)11yescharacteristic
458C23×C3H(5,𝔽2)11yescharacteristic
459C23×C32−1+411yescharacteristic
460C23×C32−1+411yescharacteristic
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—416no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
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—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4#11714yes—
559C2×C3×C4C4×D414yes—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24C22×C3×C412yes—
573C24C2×C3×Q812yes—
574C24C3×#4112yes—
575C24C24×C311yescharacteristic
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—28no—
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×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4C22×C3×C412yes—
668C22×C4C22×C3×C412yes—
669C22×C4C22×C3×C412yes—
670C22×C4C22×C3×C412yes—
671C22×C4C22×C3×C412yes—
672C22×C4C22×C3×C412yes—
673C22×C4C2×C3×D412yes—
674C22×C4C2×C3×D412yes—
675C22×C4C2×C3×D412yes—
676C22×C4C2×C3×Q812yes—
677C22×C4C2×C3×Q812yes—
678C22×C4C3×#4112yes—
679C22×C4C3×#4112yes—
680C22×C4C3×#4112yes—
681C4⋊C4—28no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C22⋊C4—28no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C42—44no—
694C42—44no—
695C22×C3—24no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3C2×#11711yescharacteristic
711C22×C3C2×C4×D411yescharacteristic
712C22×C3C2×C4×Q811yescharacteristic
713C22×C3#51811yescharacteristic
714C22×C3#51811yescharacteristic
715C22×C3#52011yescharacteristic
716C22×C3#52011yescharacteristic
717C22×C3#53411yescharacteristic
718C22×C3#53511yescharacteristic
719C22×C3#53811yescharacteristic
720C22×C3#53811yescharacteristic
721C22×C3#53811yescharacteristic
722C22×C3#53811yescharacteristic
723C22×C3#53811yescharacteristic
724C22×C3#53911yescharacteristic
725C22×C3#53911yescharacteristic
726C22×C3#53911yescharacteristic
727C22×C3#54311yescharacteristic
728C22×C3#54411yescharacteristic
729C22×C3#54611yescharacteristic
730C22×C3#54711yescharacteristic
731C22×C3D4×Q811yescharacteristic
732C22×C3#55011yescharacteristic
733C22×C3#55211yescharacteristic
734C22×C3#55311yescharacteristic
735C22×C3#55311yescharacteristic
736C22×C3#55411yescharacteristic
737C22×C3#55411yescharacteristic
738C22×C3#55411yescharacteristic
739C22×C3#55511yescharacteristic
740C22×C3#55611yescharacteristic
741C22×C3#56011yescharacteristic
742C22×C3#56211yescharacteristic
743C22×C3#56211yescharacteristic
744C22×C3#56311yescharacteristic
745C3×C4—24no—
746C3×C4—24no—
747C3×C4—42no—
748C3×C4—42no—
749C3×C4—42no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—42no—
753C3×C4—42no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—81no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23C3×C4×Q814yes—
794C23C23×C3×C411yescharacteristic
795C23C22×C3×D411yescharacteristic
796C23C22×C3×Q811yescharacteristic
797C23C2×C3×#4111yescharacteristic
798C23C2×C3×#4111yescharacteristic
799C23C2×C3×#4111yescharacteristic
800C23C2×C3×#4111yescharacteristic
801C23C3×H(5,𝔽2)11yescharacteristic
802C23C3×H(5,𝔽2)11yescharacteristic
803C23C3×H(5,𝔽2)11yescharacteristic
804C23C3×H(5,𝔽2)11yescharacteristic
805C23C3×H(5,𝔽2)11yescharacteristic
806C23C3×H(5,𝔽2)11yescharacteristic
807C23C3×2−1+411yescharacteristic
808C23C3×2−1+411yescharacteristic
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—416no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4C3×#11714yes—
907C2×C4C3×C4×D414yes—
908C2×C3—44no—
909C2×C3#231811yescharacteristic
910C2×C3#232111yescharacteristic
911C2×C3#232911yescharacteristic
912C2×C3#234511yescharacteristic
913C2×C3#235411yescharacteristic
914C2×C3#236011yescharacteristic
915C2×C3#237611yescharacteristic
916C2×C3#270811yescharacteristic
917C2×C3#271411yescharacteristic
918C2×C3#272011yescharacteristic
919C2×C3#273211yescharacteristic
920C2×C3#278111yescharacteristic
921C2×C3#278411yescharacteristic
922C2×C3#278711yescharacteristic
923C2×C3#278811yescharacteristic
924C22—24no—
925C22—24no—
926C22—24no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22C2×C3×#11711yescharacteristic
940C22C2×C3×C4×D411yescharacteristic
941C22C2×C3×C4×Q811yescharacteristic
942C22C3×#51811yescharacteristic
943C22C3×#51811yescharacteristic
944C22C3×#52011yescharacteristic
945C22C3×#52011yescharacteristic
946C22C3×#53411yescharacteristic
947C22C3×#53511yescharacteristic
948C22C3×#53811yescharacteristic
949C22C3×#53811yescharacteristic
950C22C3×#53811yescharacteristic
951C22C3×#53811yescharacteristic
952C22C3×#53811yescharacteristic
953C22C3×#53911yescharacteristic
954C22C3×#53911yescharacteristic
955C22C3×#53911yescharacteristic
956C22C3×#54311yescharacteristic
957C22C3×#54411yescharacteristic
958C22C3×#54611yescharacteristic
959C22C3×#54711yescharacteristic
960C22C3×D4×Q811yescharacteristic
961C22C3×#55011yescharacteristic
962C22C3×#55211yescharacteristic
963C22C3×#55311yescharacteristic
964C22C3×#55311yescharacteristic
965C22C3×#55411yescharacteristic
966C22C3×#55411yescharacteristic
967C22C3×#55411yescharacteristic
968C22C3×#55511yescharacteristic
969C22C3×#55611yescharacteristic
970C22C3×#56011yescharacteristic
971C22C3×#56211yescharacteristic
972C22C3×#56211yescharacteristic
973C22C3×#56311yescharacteristic
974C4—24no—
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4—81no—
987C4—81no—
988C3#1439811yescharacteristic, direct product factor, Sylow
989C2—44no—
990C2C3×#231811yescharacteristic
991C2C3×#232111yescharacteristic
992C2C3×#232911yescharacteristic
993C2C3×#234511yescharacteristic
994C2C3×#235411yescharacteristic
995C2C3×#236011yescharacteristic
996C2C3×#237611yescharacteristic
997C2C3×#270811yescharacteristic
998C2C3×#271411yescharacteristic
999C2C3×#272011yescharacteristic
1000C2C3×#273211yescharacteristic
1001C2C3×#278111yescharacteristic
1002C2C3×#278411yescharacteristic
1003C2C3×#278711yescharacteristic
1004C2C3×#278811yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#387C2semidirect
4. C3×#1444C2semidirect
5. C3×#1443C2semidirect
6. C3×#1442C2semidirect
7. C3×#1441C2semidirect
12. C3×#1436C2semidirect
13. C3×#1436C2semidirect
14. C3×C4⋊#95C2semidirect
16. #14398C3direct (N × H)
33. C3×#385C4semidirect
55. C2×#387C2×C3semidirect
58. #1444C2×C3semidirect
59. #1443C2×C3semidirect
60. #1442C2×C3semidirect
61. #1441C2×C3semidirect
66. #1436C2×C3semidirect
67. #1436C2×C3semidirect
68. C4⋊#95C2×C3semidirect
170. #385C3×C4semidirect
988. C3#14398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×C3×#3852
C2×C3×#3802
C3×#14442
C3×#14432
C3×#14422
C3×#14412
C3×#14392
C3×#14372
C3×#14362
C3×C4⋊#952
C3×C22⋊#952
#143983