Finite Group Databasebeta

← C2×C3×#2692 #10670719

Subgroups — C2×C3×#2692 #10670719

Order 768.

3046 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C3×#2692C2116yesmaximal, direct product factor
4C2×C3×#399C211yesmaximal, characteristic, complemented
5C2×C3×#398C211yesmaximal, characteristic, complemented
6C2×C3×#396C211yesmaximal, characteristic, complemented
7C2×C3×#395C211yesmaximal, characteristic, complemented
8C2×C3×#393C211yesmaximal, characteristic, complemented
9C2×C3×#393C211yesmaximal, characteristic, complemented
10C2×C3×#391C211yesmaximal, characteristic, complemented
11C2×C3×#390C211yesmaximal, characteristic
12C2×C3×#387C211yesmaximal, characteristic, complemented
13C2×C3×#386C211yesmaximal, characteristic
14C2×C3×#386C211yesmaximal, characteristic
15C2×C3×#385C211yesmaximal, characteristic, complemented
16C2×C3×#380C211yesmaximal, characteristic, complemented
17C2×#2692C311yesmaximal, characteristic, direct product factor, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C23×C3×D4C2211yescharacteristic
21C24×C3×C4C2211yescharacteristic
22C24×C3×C4C2211yescharacteristic
23C2×C3×C22⋊Q8—28no—
24C2×C3×C22⋊Q8—28no—
25C2×C3×C22⋊Q8C2218yescomplemented
26C2×C3×C22⋊Q8C2218yescomplemented
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×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4C2211yescharacteristic
37C22×C3×C22⋊C4C2211yescharacteristic
38C22×C3×C22⋊C4C2211yescharacteristic
39C22×C3×C22⋊C4C2211yescharacteristic
40C22×C3×C22⋊C4C2211yescharacteristic
41C22×C3×C22⋊C4C2211yescharacteristic
42C22×C3×C22⋊C4C2211yescharacteristic
43C22×C3×C22⋊C4C2211yescharacteristic
44C22×C3×C22⋊C4C2211yescharacteristic
45C22×C3×C22⋊C4C2211yescharacteristic
46C22×C3×C42C2211yescharacteristic
47C3×#399C2218yescomplemented
48C3×#398C2218yescomplemented
49C3×#396C2218yescomplemented
50C3×#395C2218yescomplemented
51C3×#393C2218yescomplemented
52C3×#393C2218yescomplemented
53C3×#391C2218yescomplemented
54C3×#390C2218yes—
55C3×#387C2218yescomplemented
56C3×#386C2218yes—
57C3×#386C2218yes—
58C3×#385C2218yescomplemented
59C3×#380C2218yescomplemented
60C2×C3×#95C2211yescharacteristic
61C2×C3×#95C2211yescharacteristic
62C2×C3×#95C2211yescharacteristic
63C2×C3×#95C2211yescharacteristic
64C2×C3×#95C2211yescharacteristic
65C2×C3×#95C2211yescharacteristic
66C2×C3×#95C2211yescharacteristic
67C2×C3×#95C2211yescharacteristic
68C2×C3×#95C2211yescharacteristic
69C2×C3×#95C2211yescharacteristic
70C22×C22⋊Q8C2×C311yescharacteristic, complemented
71C22×C22⋊Q8C2×C311yescharacteristic, complemented
72#2692C2×C3116yesdirect product factor
73C2×#399C2×C311yescharacteristic, complemented
74C2×#398C2×C311yescharacteristic, complemented
75C2×#396C2×C311yescharacteristic, complemented
76C2×#395C2×C311yescharacteristic, complemented
77C2×#393C2×C311yescharacteristic, complemented
78C2×#393C2×C311yescharacteristic, complemented
79C2×#391C2×C311yescharacteristic, complemented
80C2×#390C2×C311yescharacteristic
81C2×#387C2×C311yescharacteristic, complemented
82C2×#386C2×C311yescharacteristic
83C2×#386C2×C311yescharacteristic
84C2×#385C2×C311yescharacteristic, complemented
85C2×#380C2×C311yescharacteristic, complemented
86C25×C3C2311yescharacteristic
87C25×C3C2311yescharacteristic
88C22×C3×Q8—24no—
89C22×C3×Q8—24no—
90C22×C3×Q8—24no—
91C22×C3×Q8—42no—
92C22×C3×Q8—42no—
93C22×C3×Q8—42no—
94C22×C3×Q8C2314yes—
95C22×C3×Q8C2314yes—
96C22×C3×D4—42no—
97C22×C3×D4—42no—
98C22×C3×D4Q818yescomplemented
99C22×C3×D4C2314yes—
100C23×C3×C4—24no—
101C23×C3×C4—24no—
102C23×C3×C4—24no—
103C23×C3×C4—42no—
104C23×C3×C4—42no—
105C23×C3×C4—42no—
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2314yes—
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C23×C3×C4C2311yescharacteristic
118C23×C3×C4C2311yescharacteristic
119C23×C3×C4C2311yescharacteristic
120C23×C3×C4C2314yes—
121C3×C22⋊Q8—232no—
122C3×C22⋊Q8—232no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4—24no—
126C2×C3×C4⋊C4—24no—
127C2×C3×C4⋊C4—42no—
128C2×C3×C4⋊C4—42no—
129C2×C3×C4⋊C4—42no—
130C2×C3×C4⋊C4—42no—
131C2×C3×C4⋊C4D418yescomplemented
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2314yes—
136C2×C3×C4⋊C4C2314yes—
137C2×C3×C4⋊C4C2314yes—
138C2×C3×C4⋊C4C2314yes—
139C2×C3×C4⋊C4C2314yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C22⋊C4—24no—
142C2×C3×C22⋊C4—24no—
143C2×C3×C22⋊C4—24no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—24no—
146C2×C3×C22⋊C4—42no—
147C2×C3×C22⋊C4—42no—
148C2×C3×C22⋊C4—42no—
149C2×C3×C22⋊C4—42no—
150C2×C3×C22⋊C4—42no—
151C2×C3×C22⋊C4C2314yes—
152C2×C3×C22⋊C4C2314yes—
153C2×C3×C22⋊C4C2314yes—
154C2×C3×C22⋊C4C2314yes—
155C2×C3×C22⋊C4C2314yes—
156C2×C3×C22⋊C4C2314yes—
157C2×C3×C22⋊C4C2314yes—
158C2×C3×C22⋊C4C2314yes—
159C2×C3×C22⋊C4C2314yes—
160C2×C3×C22⋊C4C2314yes—
161C2×C3×C42—42no—
162C2×C3×C42C2314yes—
163C3×#95C2314yes—
164C3×#95C2314yes—
165C3×#95C2314yes—
166C3×#95C2314yes—
167C3×#95C2314yes—
168C3×#95C2314yes—
169C3×#95C2314yes—
170C3×#95C2314yes—
171C3×#95C2314yes—
172C3×#95C2314yes—
173C23×Q8C22×C311yescharacteristic
174C23×Q8C22×C311yescharacteristic
175C23×D4C22×C311yescharacteristic
176C24×C4C22×C311yescharacteristic
177C24×C4C22×C311yescharacteristic
178C2×C22⋊Q8—28no—
179C2×C22⋊Q8—28no—
180C2×C22⋊Q8C22×C318yescomplemented
181C2×C22⋊Q8C22×C318yescomplemented
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184C22×C4⋊C4C22×C311yescharacteristic
185C22×C4⋊C4C22×C311yescharacteristic
186C22×C4⋊C4C22×C311yescharacteristic
187C22×C4⋊C4C22×C311yescharacteristic
188C22×C4⋊C4C22×C311yescharacteristic
189C22×C4⋊C4C22×C311yescharacteristic
190C22×C4⋊C4C22×C311yescharacteristic
191C22×C22⋊C4C22×C311yescharacteristic
192C22×C22⋊C4C22×C311yescharacteristic
193C22×C22⋊C4C22×C311yescharacteristic
194C22×C22⋊C4C22×C311yescharacteristic
195C22×C22⋊C4C22×C311yescharacteristic
196C22×C22⋊C4C22×C311yescharacteristic
197C22×C22⋊C4C22×C311yescharacteristic
198C22×C22⋊C4C22×C311yescharacteristic
199C22×C22⋊C4C22×C311yescharacteristic
200C22×C22⋊C4C22×C311yescharacteristic
201C22×C42C22×C311yescharacteristic
202#399C22×C318yescomplemented
203#398C22×C318yescomplemented
204#396C22×C318yescomplemented
205#395C22×C318yescomplemented
206#393C22×C318yescomplemented
207#393C22×C318yescomplemented
208#391C22×C318yescomplemented
209#390C22×C318yes—
210#387C22×C318yescomplemented
211#386C22×C318yes—
212#386C22×C318yes—
213#385C22×C318yescomplemented
214#380C22×C318yescomplemented
215C2×#95C22×C311yescharacteristic
216C2×#95C22×C311yescharacteristic
217C2×#95C22×C311yescharacteristic
218C2×#95C22×C311yescharacteristic
219C2×#95C22×C311yescharacteristic
220C2×#95C22×C311yescharacteristic
221C2×#95C22×C311yescharacteristic
222C2×#95C22×C311yescharacteristic
223C2×#95C22×C311yescharacteristic
224C2×#95C22×C311yescharacteristic
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—22no—
230C24×C3—22no—
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3C2×Q814yes—
238C24×C3C2×Q814yes—
239C24×C3C2412yes—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
242C2×C3×Q8—28no—
243C2×C3×Q8—28no—
244C2×C3×Q8—28no—
245C2×C3×Q8—44no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—416no—
249C2×C3×Q8—416no—
250C2×C3×D4—416no—
251C2×C3×D4—44no—
252C2×C3×D4—44no—
253C2×C3×D4C2×Q8116yescomplemented
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—28no—
289C22×C3×C4—28no—
290C22×C3×C4—28no—
291C22×C3×C4—44no—
292C22×C3×C4—44no—
293C22×C3×C4—44no—
294C22×C3×C4—416no—
295C22×C3×C4—416no—
296C22×C3×C4C2×D414yes—
297C22×C3×C4C2×D414yes—
298C22×C3×C4C2×D414yes—
299C22×C3×C4C2×Q814yes—
300C22×C3×C4#4114yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C22×C3×C4C2412yes—
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2412yes—
308C22×C3×C4C2412yes—
309C22×C3×C4C2412yes—
310C22×C3×C4C2412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2412yes—
313C22×C3×C4C2412yes—
314C3×C4⋊C4—28no—
315C3×C4⋊C4—28no—
316C3×C4⋊C4—28no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—44no—
319C3×C4⋊C4—44no—
320C3×C4⋊C4—44no—
321C3×C4⋊C4—44no—
322C3×C4⋊C4C2×D4116yescomplemented
323C3×C22⋊C4—28no—
324C3×C22⋊C4—28no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—28no—
328C3×C22⋊C4—44no—
329C3×C22⋊C4—44no—
330C3×C22⋊C4—44no—
331C3×C22⋊C4—44no—
332C3×C22⋊C4—44no—
333C3×C42—44no—
334C25C23×C311yescharacteristic
335C25C23×C311yescharacteristic
336C22×Q8—24no—
337C22×Q8—24no—
338C22×Q8—24no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×Q8C23×C314yes—
343C22×Q8C23×C314yes—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4C3×Q818yescomplemented
347C22×D4C23×C314yes—
348C23×C4—24no—
349C23×C4—24no—
350C23×C4—24no—
351C23×C4—42no—
352C23×C4—42no—
353C23×C4—42no—
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×C314yes—
363C23×C4C23×C311yescharacteristic
364C23×C4C23×C311yescharacteristic
365C23×C4C23×C311yescharacteristic
366C23×C4C23×C311yescharacteristic
367C23×C4C23×C311yescharacteristic
368C23×C4C23×C314yes—
369C22⋊Q8—232no—
370C22⋊Q8—232no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4C3×D418yescomplemented
380C2×C4⋊C4C23×C314yes—
381C2×C4⋊C4C23×C314yes—
382C2×C4⋊C4C23×C314yes—
383C2×C4⋊C4C23×C314yes—
384C2×C4⋊C4C23×C314yes—
385C2×C4⋊C4C23×C314yes—
386C2×C4⋊C4C23×C314yes—
387C2×C4⋊C4C23×C314yes—
388C2×C4⋊C4C23×C314yes—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4C23×C314yes—
400C2×C22⋊C4C23×C314yes—
401C2×C22⋊C4C23×C314yes—
402C2×C22⋊C4C23×C314yes—
403C2×C22⋊C4C23×C314yes—
404C2×C22⋊C4C23×C314yes—
405C2×C22⋊C4C23×C314yes—
406C2×C22⋊C4C23×C314yes—
407C2×C22⋊C4C23×C314yes—
408C2×C22⋊C4C23×C314yes—
409C2×C42—42no—
410C2×C42C23×C314yes—
411#95C23×C314yes—
412#95C23×C314yes—
413#95C23×C314yes—
414#95C23×C314yes—
415#95C23×C314yes—
416#95C23×C314yes—
417#95C23×C314yes—
418#95C23×C314yes—
419#95C23×C314yes—
420#95C23×C314yes—
421C23×C3—28no—
422C23×C3—28no—
423C23×C3—28no—
424C23×C3—28no—
425C23×C3—28no—
426C23×C3—28no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3—44no—
442C23×C3—44no—
443C23×C3—44no—
444C23×C3—44no—
445C23×C3—44no—
446C23×C3—44no—
447C23×C3C22×D412yes—
448C23×C3C22×Q814yes—
449C23×C3C22×Q814yes—
450C23×C3C22×Q812yes—
451C23×C3C2×#4112yes—
452C23×C3H(5,𝔽2)12yes—
453C23×C3H(5,𝔽2)12yes—
454C23×C3H(5,𝔽2)12yes—
455C23×C32−1+412yes—
456C23×C3C2511yescharacteristic
457C3×Q8—416no—
458C3×Q8—416no—
459C3×D4—416no—
460C2×C3×C4—28no—
461C2×C3×C4—28no—
462C2×C3×C4—28no—
463C2×C3×C4—28no—
464C2×C3×C4—28no—
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—416no—
500C2×C3×C4—416no—
501C2×C3×C4—44no—
502C2×C3×C4—44no—
503C2×C3×C4—44no—
504C2×C3×C4—44no—
505C2×C3×C4—44no—
506C2×C3×C4—44no—
507C2×C3×C4—44no—
508C2×C3×C4—44no—
509C2×C3×C4C22×D414yes—
510C2×C3×C4C22×D414yes—
511C2×C3×C4C22×D414yes—
512C2×C3×C4C22×Q814yes—
513C2×C3×C4C2×#4114yes—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×C3×Q814yes—
527C24C2×C3×Q814yes—
528C24C24×C312yes—
529C24C24×C312yes—
530C24C24×C311yescharacteristic
531C2×Q8—28no—
532C2×Q8—28no—
533C2×Q8—28no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—44no—
537C2×Q8—416no—
538C2×Q8—416no—
539C2×D4—416no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4C2×C3×Q8116yescomplemented
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4C2×C3×D414yes—
586C22×C4C2×C3×D414yes—
587C22×C4C2×C3×D414yes—
588C22×C4C2×C3×Q814yes—
589C22×C4C3×#4114yes—
590C22×C4C24×C312yes—
591C22×C4C24×C312yes—
592C22×C4C24×C312yes—
593C22×C4C24×C312yes—
594C22×C4C24×C312yes—
595C22×C4C24×C312yes—
596C22×C4C24×C312yes—
597C22×C4C24×C312yes—
598C22×C4C24×C312yes—
599C22×C4C24×C312yes—
600C22×C4C24×C312yes—
601C22×C4C24×C312yes—
602C22×C4C24×C312yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4C2×C3×D4116yescomplemented
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C42—44no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—416no—
634C22×C3—416no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3#53514yes—
640C22×C3#54214yes—
641C22×C3#54314yes—
642C22×C3#54614yes—
643C22×C3D4×Q814yes—
644C22×C3#55414yes—
645C22×C3#56214yes—
646C22×C3C23×D411yescharacteristic
647C22×C3C23×Q811yescharacteristic
648C22×C3C22×#4111yescharacteristic
649C22×C3C2×H(5,𝔽2)11yescharacteristic
650C22×C3C2×H(5,𝔽2)11yescharacteristic
651C22×C3C2×H(5,𝔽2)11yescharacteristic
652C22×C3C2×2−1+411yescharacteristic
653C3×C4—24no—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—24no—
657C3×C4—24no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—42no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23C22×C3×D412yes—
693C23C22×C3×Q814yes—
694C23C22×C3×Q814yes—
695C23C22×C3×Q812yes—
696C23C2×C3×#4112yes—
697C23C3×H(5,𝔽2)12yes—
698C23C3×H(5,𝔽2)12yes—
699C23C3×H(5,𝔽2)12yes—
700C23C3×2−1+412yes—
701C23C25×C311yescharacteristic
702Q8—416no—
703Q8—416no—
704D4—416no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—416no—
745C2×C4—416no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4C22×C3×D414yes—
755C2×C4C22×C3×D414yes—
756C2×C4C22×C3×D414yes—
757C2×C4C22×C3×Q814yes—
758C2×C4C2×C3×#4114yes—
759C2×C3—44no—
760C2×C3—44no—
761C2×C3#269218yesdirect product factor
762C2×C3C2×#53511yescharacteristic
763C2×C3C2×#54211yescharacteristic
764C2×C3C2×#54311yescharacteristic
765C2×C3C2×#54611yescharacteristic
766C2×C3C2×D4×Q811yescharacteristic
767C2×C3C2×#55411yescharacteristic
768C2×C3C2×#56211yescharacteristic
769C22—24no—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—416no—
783C22—42no—
784C22—42no—
785C22C3×#53514yes—
786C22C3×#54214yes—
787C22C3×#54314yes—
788C22C3×#54614yes—
789C22C3×D4×Q814yes—
790C22C3×#55414yes—
791C22C3×#56214yes—
792C22C23×C3×D411yescharacteristic
793C22C23×C3×Q811yescharacteristic
794C22C22×C3×#4111yescharacteristic
795C22C2×C3×H(5,𝔽2)11yescharacteristic
796C22C2×C3×H(5,𝔽2)11yescharacteristic
797C22C2×C3×H(5,𝔽2)11yescharacteristic
798C22C2×C3×2−1+411yescharacteristic
799C4—24no—
800C4—24no—
801C4—24no—
802C4—24no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C3C2×#269211yescharacteristic, direct product factor, Sylow
813C2—44no—
814C2—44no—
815C2C3×#269218yesdirect product factor
816C2C2×C3×#53511yescharacteristic
817C2C2×C3×#54211yescharacteristic
818C2C2×C3×#54311yescharacteristic
819C2C2×C3×#54611yescharacteristic
820C2C2×C3×D4×Q811yescharacteristic
821C2C2×C3×#55411yescharacteristic
822C2C2×C3×#56211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC23C25×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×C3×C22⋊Q8C2semidirect
3. C3×#2692C2direct (N × H)
4. C2×C3×#399C2semidirect
5. C2×C3×#398C2semidirect
6. C2×C3×#396C2semidirect
7. C2×C3×#395C2semidirect
8. C2×C3×#393C2semidirect
9. C2×C3×#393C2semidirect
10. C2×C3×#391C2semidirect
12. C2×C3×#387C2semidirect
15. C2×C3×#385C2semidirect
16. C2×C3×#380C2semidirect
17. C2×#2692C3direct (N × H)
25. C2×C3×C22⋊Q8C22semidirect
26. C2×C3×C22⋊Q8C22semidirect
47. C3×#399C22semidirect
48. C3×#398C22semidirect
49. C3×#396C22semidirect
50. C3×#395C22semidirect
51. C3×#393C22semidirect
52. C3×#393C22semidirect
53. C3×#391C22semidirect
55. C3×#387C22semidirect
58. C3×#385C22semidirect
59. C3×#380C22semidirect
70. C22×C22⋊Q8C2×C3semidirect
71. C22×C22⋊Q8C2×C3semidirect
72. #2692C2×C3direct (N × H)
73. C2×#399C2×C3semidirect
74. C2×#398C2×C3semidirect
75. C2×#396C2×C3semidirect
76. C2×#395C2×C3semidirect
77. C2×#393C2×C3semidirect
78. C2×#393C2×C3semidirect
79. C2×#391C2×C3semidirect
81. C2×#387C2×C3semidirect
84. C2×#385C2×C3semidirect
85. C2×#380C2×C3semidirect
98. C22×C3×D4Q8semidirect
131. C2×C3×C4⋊C4D4semidirect
180. C2×C22⋊Q8C22×C3semidirect
181. C2×C22⋊Q8C22×C3semidirect
202. #399C22×C3semidirect
203. #398C22×C3semidirect
204. #396C22×C3semidirect
205. #395C22×C3semidirect
206. #393C22×C3semidirect
207. #393C22×C3semidirect
208. #391C22×C3semidirect
210. #387C22×C3semidirect
213. #385C22×C3semidirect
214. #380C22×C3semidirect
253. C2×C3×D4C2×Q8semidirect
322. C3×C4⋊C4C2×D4semidirect
346. C22×D4C3×Q8semidirect
379. C2×C4⋊C4C3×D4semidirect
542. C2×D4C2×C3×Q8semidirect
611. C4⋊C4C2×C3×D4semidirect
761. C2×C3#2692direct (N × H)
812. C3C2×#2692direct (N × H)
815. C2C3×#2692direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C3×#26922
C2×C3×#3992
C2×C3×#3982
C2×C3×#3962
C2×C3×#3952
C2×C3×#3932
C2×C3×#3912
C2×C3×#3902
C2×C3×#3872
C2×C3×#3862
C2×C3×#3852
C2×C3×#3802
C2×#26923