Finite Group Databasebeta

← C32×#2676 #11769725

Subgroups — C32×#2676 #11769725

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic, complemented
2C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C32×#121C211yesmaximal, characteristic, complemented
4C2×C32×#121C211yesmaximal, characteristic, complemented
5C32×#396C211yesmaximal, characteristic, complemented
6C32×#394C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8C32×#393C211yesmaximal, characteristic, complemented
9C32×#392C211yesmaximal, characteristic, complemented
10C32×#392C211yesmaximal, characteristic, complemented
11C32×#390C211yesmaximal, characteristic, complemented
12C32×#387C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic, complemented
14C32×#386C211yesmaximal, characteristic, complemented
15C32×#385C211yesmaximal, characteristic, complemented
16C3×#2676C314yesmaximal, direct product factor
17C22×C32×Q8C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic
23C22×C32×D4C2211yescharacteristic
24C23×C32×C4C2211yescharacteristic
25C23×C32×C4C2211yescharacteristic
26C32×#124—24no—
27C32×C22⋊Q8—24no—
28C32×#121—24no—
29C32×#121—24no—
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C32×C4⋊C4C2211yescharacteristic
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×C32×C22⋊C4C2211yescharacteristic
37C2×C32×C22⋊C4C2211yescharacteristic
38C2×C32×C22⋊C4C2211yescharacteristic
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×C32×C22⋊C4C2211yescharacteristic
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×C32×C22⋊C4C2211yescharacteristic
44C2×C32×C22⋊C4C2211yescharacteristic
45C2×C32×C22⋊C4C2211yescharacteristic
46C2×C32×C22⋊C4C2211yescharacteristic
47C2×C32×C22⋊C4C2211yescharacteristic
48C2×C32×C22⋊C4C2211yescharacteristic
49C2×C32×C42C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C32×#95C2211yescharacteristic
53C32×#95C2211yescharacteristic
54C32×#95C2211yescharacteristic
55C32×#95C2211yescharacteristic
56C2×C3×#124C2×C314yescomplemented
57C2×C3×C22⋊Q8C2×C314yescomplemented
58C2×C3×#121C2×C314yescomplemented
59C2×C3×#121C2×C314yescomplemented
60C3×#396C2×C314yescomplemented
61C3×#394C2×C314yescomplemented
62C3×#394C2×C314yescomplemented
63C3×#393C2×C314yescomplemented
64C3×#392C2×C314yescomplemented
65C3×#392C2×C314yescomplemented
66C3×#390C2×C314yescomplemented
67C3×#387C2×C314yescomplemented
68C3×#386C2×C314yescomplemented
69C3×#386C2×C314yescomplemented
70C3×#385C2×C314yescomplemented
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C24×C32C2311yescharacteristic
74C24×C32C2311yescharacteristic
75C2×C32×Q8—22no—
76C2×C32×Q8—22no—
77C2×C32×Q8—41no—
78C2×C32×D4—22no—
79C2×C32×D4—22no—
80C2×C32×D4—22no—
81C2×C32×D4—22no—
82C2×C32×D4—22no—
83C2×C32×D4—22no—
84C2×C32×D4—22no—
85C2×C32×D4—22no—
86C2×C32×D4—22no—
87C2×C32×D4—22no—
88C2×C32×D4—41no—
89C2×C32×D4—41no—
90C2×C32×D4—41no—
91C2×C32×D4—41no—
92C2×C32×D4—41no—
93C2×C32×D4—41no—
94C2×C32×D4—41no—
95C2×C32×D4—41no—
96C22×C32×C4—22no—
97C22×C32×C4—22no—
98C22×C32×C4—22no—
99C22×C32×C4—41no—
100C22×C32×C4—41no—
101C22×C32×C4—41no—
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C32×C4⋊C4—22no—
114C32×C4⋊C4—22no—
115C32×C4⋊C4—22no—
116C32×C4⋊C4—41no—
117C32×C4⋊C4D414yescomplemented
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4—22no—
121C32×C22⋊C4—22no—
122C32×C22⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—41no—
127C32×C22⋊C4—41no—
128C32×C22⋊C4—41no—
129C32×C22⋊C4—41no—
130C32×C22⋊C4—41no—
131C32×C22⋊C4D414yescomplemented
132C32×C42—22no—
133#2676C3211yescharacteristic, direct product factor, Sylow
134C22×C3×Q8C22×C314yes—
135C22×C3×D4C22×C314yes—
136C22×C3×D4C22×C314yes—
137C22×C3×D4C22×C314yes—
138C22×C3×D4C22×C314yes—
139C22×C3×D4C22×C314yes—
140C22×C3×D4C22×C314yes—
141C23×C3×C4C22×C314yes—
142C23×C3×C4C22×C314yes—
143C3×#124—216no—
144C3×C22⋊Q8—216no—
145C3×#121—216no—
146C3×#121—216no—
147C2×C3×C4⋊C4C22×C314yes—
148C2×C3×C4⋊C4C22×C314yes—
149C2×C3×C4⋊C4C22×C314yes—
150C2×C3×C4⋊C4C22×C314yes—
151C2×C3×C4⋊C4C22×C314yes—
152C2×C3×C22⋊C4C22×C314yes—
153C2×C3×C22⋊C4C22×C314yes—
154C2×C3×C22⋊C4C22×C314yes—
155C2×C3×C22⋊C4C22×C314yes—
156C2×C3×C22⋊C4C22×C314yes—
157C2×C3×C22⋊C4C22×C314yes—
158C2×C3×C22⋊C4C22×C314yes—
159C2×C3×C22⋊C4C22×C314yes—
160C2×C3×C22⋊C4C22×C314yes—
161C2×C3×C22⋊C4C22×C314yes—
162C2×C3×C22⋊C4C22×C314yes—
163C2×C3×C22⋊C4C22×C314yes—
164C2×C3×C22⋊C4C22×C314yes—
165C2×C3×C22⋊C4C22×C314yes—
166C2×C3×C42C22×C314yes—
167C3×#95C22×C314yes—
168C3×#95C22×C314yes—
169C3×#95C22×C314yes—
170C3×#95C22×C314yes—
171C3×#95C22×C314yes—
172C3×#95C22×C314yes—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32C2×D412yes—
200C23×C32#4112yes—
201C23×C32C2411yescharacteristic
202C32×Q8—44no—
203C32×D4—44no—
204C32×D4—44no—
205C32×D4—44no—
206C32×D4—44no—
207C32×D4—44no—
208C32×D4—44no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—44no—
238C2×C32×C4—44no—
239C2×C32×C4C2×D412yes—
240C2×C32×C4C2×D412yes—
241C2×C32×C4C2×D412yes—
242C2×C32×C4C2×D412yes—
243C2×C32×C4C2×D412yes—
244C2×#124C2×C3211yescharacteristic, complemented
245C2×C22⋊Q8C2×C3211yescharacteristic, complemented
246C2×#121C2×C3211yescharacteristic, complemented
247C2×#121C2×C3211yescharacteristic, complemented
248#396C2×C3211yescharacteristic, complemented
249#394C2×C3211yescharacteristic, complemented
250#394C2×C3211yescharacteristic, complemented
251#393C2×C3211yescharacteristic, complemented
252#392C2×C3211yescharacteristic, complemented
253#392C2×C3211yescharacteristic, complemented
254#390C2×C3211yescharacteristic, complemented
255#387C2×C3211yescharacteristic, complemented
256#386C2×C3211yescharacteristic, complemented
257#386C2×C3211yescharacteristic, complemented
258#385C2×C3211yescharacteristic, complemented
259C24×C3C23×C314yes—
260C24×C3C23×C314yes—
261C24×C3C23×C314yes—
262C24×C3C23×C314yes—
263C2×C3×Q8—28no—
264C2×C3×Q8—28no—
265C2×C3×Q8—44no—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—28no—
273C2×C3×D4—28no—
274C2×C3×D4—28no—
275C2×C3×D4—28no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C22×C3×C4—28no—
285C22×C3×C4—28no—
286C22×C3×C4—28no—
287C22×C3×C4—44no—
288C22×C3×C4—44no—
289C22×C3×C4—44no—
290C22×C3×C4C23×C314yes—
291C22×C3×C4C23×C314yes—
292C22×C3×C4C23×C314yes—
293C22×C3×C4C23×C314yes—
294C22×C3×C4C23×C314yes—
295C22×C3×C4C23×C314yes—
296C22×C3×C4C23×C314yes—
297C22×C3×C4C23×C314yes—
298C22×C3×C4C23×C314yes—
299C22×C3×C4C23×C314yes—
300C22×C3×C4C23×C314yes—
301C3×C4⋊C4—28no—
302C3×C4⋊C4—28no—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—44no—
305C3×C4⋊C4C3×D4116yescomplemented
306C3×C22⋊C4—28no—
307C3×C22⋊C4—28no—
308C3×C22⋊C4—28no—
309C3×C22⋊C4—28no—
310C3×C22⋊C4—28no—
311C3×C22⋊C4—28no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—44no—
315C3×C22⋊C4—44no—
316C3×C22⋊C4—44no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4C3×D4116yescomplemented
320C3×C42—28no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—41no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32—41no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32C22×D411yescharacteristic
350C22×C32C22×D411yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32H(5,𝔽2)11yescharacteristic
353C22×C32H(5,𝔽2)11yescharacteristic
354C22×C32H(5,𝔽2)11yescharacteristic
355C22×C322−1+411yescharacteristic
356C32×C4—22no—
357C32×C4—22no—
358C32×C4—22no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—41no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C22×Q8C22×C3211yescharacteristic
368C22×D4C22×C3211yescharacteristic
369C22×D4C22×C3211yescharacteristic
370C22×D4C22×C3211yescharacteristic
371C22×D4C22×C3211yescharacteristic
372C22×D4C22×C3211yescharacteristic
373C22×D4C22×C3211yescharacteristic
374C23×C4C22×C3211yescharacteristic
375C23×C4C22×C3211yescharacteristic
376#124—24no—
377C22⋊Q8—24no—
378#121—24no—
379#121—24no—
380C2×C4⋊C4C22×C3211yescharacteristic
381C2×C4⋊C4C22×C3211yescharacteristic
382C2×C4⋊C4C22×C3211yescharacteristic
383C2×C4⋊C4C22×C3211yescharacteristic
384C2×C4⋊C4C22×C3211yescharacteristic
385C2×C22⋊C4C22×C3211yescharacteristic
386C2×C22⋊C4C22×C3211yescharacteristic
387C2×C22⋊C4C22×C3211yescharacteristic
388C2×C22⋊C4C22×C3211yescharacteristic
389C2×C22⋊C4C22×C3211yescharacteristic
390C2×C22⋊C4C22×C3211yescharacteristic
391C2×C22⋊C4C22×C3211yescharacteristic
392C2×C22⋊C4C22×C3211yescharacteristic
393C2×C22⋊C4C22×C3211yescharacteristic
394C2×C22⋊C4C22×C3211yescharacteristic
395C2×C22⋊C4C22×C3211yescharacteristic
396C2×C22⋊C4C22×C3211yescharacteristic
397C2×C22⋊C4C22×C3211yescharacteristic
398C2×C22⋊C4C22×C3211yescharacteristic
399C2×C42C22×C3211yescharacteristic
400#95C22×C3211yescharacteristic
401#95C22×C3211yescharacteristic
402#95C22×C3211yescharacteristic
403#95C22×C3211yescharacteristic
404#95C22×C3211yescharacteristic
405#95C22×C3211yescharacteristic
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3C2×C3×D418yes—
433C23×C3C3×#4118yes—
434C23×C3C24×C314yes—
435C3×Q8—416no—
436C3×D4—416no—
437C3×D4—416no—
438C3×D4—416no—
439C3×D4—416no—
440C3×D4—416no—
441C3×D4—416no—
442C2×C3×C4—24no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—24no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—416no—
471C2×C3×C4—416no—
472C2×C3×C4C2×C3×D418yes—
473C2×C3×C4C2×C3×D418yes—
474C2×C3×C4C2×C3×D418yes—
475C2×C3×C4C2×C3×D418yes—
476C2×C3×C4C2×C3×D418yes—
477C2×C32—42no—
478C2×C32—42no—
479C2×C32—81no—
480C2×C32—81no—
481C2×C32#53511yescharacteristic
482C2×C32#53711yescharacteristic
483C2×C32#53811yescharacteristic
484C2×C32D4211yescharacteristic
485C2×C32#54611yescharacteristic
486C2×C32#54811yescharacteristic
487C2×C32#56211yescharacteristic
488C24C23×C3211yescharacteristic
489C24C23×C3211yescharacteristic
490C24C23×C3211yescharacteristic
491C24C23×C3211yescharacteristic
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—41no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—41no—
512C2×D4—41no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4C23×C3211yescharacteristic
520C22×C4C23×C3211yescharacteristic
521C22×C4C23×C3211yescharacteristic
522C22×C4C23×C3211yescharacteristic
523C22×C4C23×C3211yescharacteristic
524C22×C4C23×C3211yescharacteristic
525C22×C4C23×C3211yescharacteristic
526C22×C4C23×C3211yescharacteristic
527C22×C4C23×C3211yescharacteristic
528C22×C4C23×C3211yescharacteristic
529C22×C4C23×C3211yescharacteristic
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—41no—
534C4⋊C4C32×D414yescomplemented
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4C32×D414yescomplemented
549C42—22no—
550C22×C3—28no—
551C22×C3—28no—
552C22×C3—28no—
553C22×C3—28no—
554C22×C3—28no—
555C22×C3—28no—
556C22×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3C22×C3×D414yes—
579C22×C3C22×C3×D414yes—
580C22×C3C2×C3×#4114yes—
581C22×C3C3×H(5,𝔽2)14yes—
582C22×C3C3×H(5,𝔽2)14yes—
583C22×C3C3×H(5,𝔽2)14yes—
584C22×C3C3×2−1+414yes—
585C3×C4—28no—
586C3×C4—28no—
587C3×C4—28no—
588C3×C4—28no—
589C3×C4—28no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—44no—
593C3×C4—44no—
594C3×C4—44no—
595C3×C4—44no—
596C32#267611yescharacteristic, direct product factor, Sylow
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×C32×D412yes—
624C23C32×#4112yes—
625C23C24×C3211yescharacteristic
626Q8—44no—
627D4—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4C2×C32×D412yes—
664C2×C4C2×C32×D412yes—
665C2×C4C2×C32×D412yes—
666C2×C4C2×C32×D412yes—
667C2×C4C2×C32×D412yes—
668C2×C3—48no—
669C2×C3—48no—
670C2×C3—84no—
671C2×C3—84no—
672C2×C3C3×#53514yes—
673C2×C3C3×#53714yes—
674C2×C3C3×#53814yes—
675C2×C3C3×D4214yes—
676C2×C3C3×#54614yes—
677C2×C3C3×#54814yes—
678C2×C3C3×#56214yes—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C22×C32×D411yescharacteristic
708C22C22×C32×D411yescharacteristic
709C22C2×C32×#4111yescharacteristic
710C22C32×H(5,𝔽2)11yescharacteristic
711C22C32×H(5,𝔽2)11yescharacteristic
712C22C32×H(5,𝔽2)11yescharacteristic
713C22C32×2−1+411yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C3C3×#267614yesdirect product factor
726C2—42no—
727C2—42no—
728C2—81no—
729C2—81no—
730C2C32×#53511yescharacteristic
731C2C32×#53711yescharacteristic
732C2C32×#53811yescharacteristic
733C2C32×D4211yescharacteristic
734C2C32×#54611yescharacteristic
735C2C32×#54811yescharacteristic
736C2C32×#56211yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C32 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C32×#124C2semidirect
2. C2×C32×C22⋊Q8C2semidirect
3. C2×C32×#121C2semidirect
4. C2×C32×#121C2semidirect
5. C32×#396C2semidirect
6. C32×#394C2semidirect
7. C32×#394C2semidirect
8. C32×#393C2semidirect
9. C32×#392C2semidirect
10. C32×#392C2semidirect
11. C32×#390C2semidirect
12. C32×#387C2semidirect
13. C32×#386C2semidirect
14. C32×#386C2semidirect
15. C32×#385C2semidirect
16. C3×#2676C3direct (N × H)
56. C2×C3×#124C2×C3semidirect
57. C2×C3×C22⋊Q8C2×C3semidirect
58. C2×C3×#121C2×C3semidirect
59. C2×C3×#121C2×C3semidirect
60. C3×#396C2×C3semidirect
61. C3×#394C2×C3semidirect
62. C3×#394C2×C3semidirect
63. C3×#393C2×C3semidirect
64. C3×#392C2×C3semidirect
65. C3×#392C2×C3semidirect
66. C3×#390C2×C3semidirect
67. C3×#387C2×C3semidirect
68. C3×#386C2×C3semidirect
69. C3×#386C2×C3semidirect
70. C3×#385C2×C3semidirect
117. C32×C4⋊C4D4semidirect
131. C32×C22⋊C4D4semidirect
133. #2676C32direct (N × H)
244. C2×#124C2×C32semidirect
245. C2×C22⋊Q8C2×C32semidirect
246. C2×#121C2×C32semidirect
247. C2×#121C2×C32semidirect
248. #396C2×C32semidirect
249. #394C2×C32semidirect
250. #394C2×C32semidirect
251. #393C2×C32semidirect
252. #392C2×C32semidirect
253. #392C2×C32semidirect
254. #390C2×C32semidirect
255. #387C2×C32semidirect
256. #386C2×C32semidirect
257. #386C2×C32semidirect
258. #385C2×C32semidirect
305. C3×C4⋊C4C3×D4semidirect
319. C3×C22⋊C4C3×D4semidirect
534. C4⋊C4C32×D4semidirect
548. C22⋊C4C32×D4semidirect
596. C32#2676direct (N × H)
725. C3C3×#2676direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1242
C2×C32×C22⋊Q82
C2×C32×#1212
C32×#3962
C32×#3942
C32×#3932
C32×#3922
C32×#3902
C32×#3872
C32×#3862
C32×#3852
C3×#26763