Finite Group Databasebeta

← C32×#2714 #11769763

Subgroups — C32×#2714 #11769763

Order 1152.

1794 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C32×#397C211yesmaximal, characteristic, complemented
4C32×#394C211yesmaximal, characteristic, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6C32×#392C211yesmaximal, characteristic, complemented
7C32×#392C211yesmaximal, characteristic, complemented
8C32×#392C211yesmaximal, characteristic, complemented
9C32×#390C211yesmaximal, characteristic, complemented
10C32×#390C211yesmaximal, characteristic, complemented
11C32×#390C211yesmaximal, characteristic, complemented
12C32×#388C211yesmaximal, characteristic, complemented
13C32×#387C211yesmaximal, characteristic, complemented
14C32×#386C211yesmaximal, characteristic, complemented
15C32×#385C211yesmaximal, characteristic, complemented
16C3×#2714C314yesmaximal, direct product factor
17C22×C32×D4C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic
23C23×C32×C4C2211yescharacteristic
24C32×#126—24no—
25C32×#121—24no—
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C22⋊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×C42C2211yescharacteristic
47C2×C32×C42C2211yescharacteristic
48C32×#95C2211yescharacteristic
49C32×#95C2211yescharacteristic
50C32×#95C2211yescharacteristic
51C32×#95C2211yescharacteristic
52C32×#95C2211yescharacteristic
53C32×#95C2211yescharacteristic
54C2×C3×#126C2×C314yescomplemented
55C2×C3×#121C2×C314yescomplemented
56C3×#397C2×C314yescomplemented
57C3×#394C2×C314yescomplemented
58C3×#394C2×C314yescomplemented
59C3×#392C2×C314yescomplemented
60C3×#392C2×C314yescomplemented
61C3×#392C2×C314yescomplemented
62C3×#390C2×C314yescomplemented
63C3×#390C2×C314yescomplemented
64C3×#390C2×C314yescomplemented
65C3×#388C2×C314yescomplemented
66C3×#387C2×C314yescomplemented
67C3×#386C2×C314yescomplemented
68C3×#385C2×C314yescomplemented
69C24×C32C2311yescharacteristic
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—22no—
76C2×C32×D4—22no—
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4—22no—
80C2×C32×D4—41no—
81C2×C32×D4—41no—
82C2×C32×D4—41no—
83C2×C32×D4—41no—
84C2×C32×D4—41no—
85C2×C32×D4—41no—
86C2×C32×D4—41no—
87C2×C32×D4—41no—
88C2×C32×D4—41no—
89C2×C32×D4—41no—
90C2×C32×D4—41no—
91C22×C32×C4—22no—
92C22×C32×C4—41no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C32×C4⋊C4—22no—
106C32×C4⋊C4—22no—
107C32×C4⋊C4—41no—
108C32×C4⋊C4—41no—
109C32×C4⋊C4D414yescomplemented
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—22no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4—22no—
116C32×C22⋊C4—22no—
117C32×C22⋊C4—41no—
118C32×C22⋊C4—41no—
119C32×C22⋊C4—41no—
120C32×C22⋊C4—41no—
121C32×C22⋊C4—41no—
122C32×C22⋊C4—41no—
123C32×C22⋊C4—41no—
124C32×C22⋊C4—41no—
125C32×C42—22no—
126C32×C42—41no—
127#2714C3211yescharacteristic, direct product factor, Sylow
128C22×C3×D4C22×C314yes—
129C22×C3×D4C22×C314yes—
130C22×C3×D4C22×C314yes—
131C22×C3×D4C22×C314yes—
132C22×C3×D4C22×C314yes—
133C22×C3×D4C22×C314yes—
134C23×C3×C4C22×C314yes—
135C3×#126—216no—
136C3×#121—216no—
137C2×C3×C4⋊C4C22×C314yes—
138C2×C3×C4⋊C4C22×C314yes—
139C2×C3×C4⋊C4C22×C314yes—
140C2×C3×C4⋊C4C22×C314yes—
141C2×C3×C4⋊C4C22×C314yes—
142C2×C3×C22⋊C4C22×C314yes—
143C2×C3×C22⋊C4C22×C314yes—
144C2×C3×C22⋊C4C22×C314yes—
145C2×C3×C22⋊C4C22×C314yes—
146C2×C3×C22⋊C4C22×C314yes—
147C2×C3×C22⋊C4C22×C314yes—
148C2×C3×C22⋊C4C22×C314yes—
149C2×C3×C22⋊C4C22×C314yes—
150C2×C3×C22⋊C4C22×C314yes—
151C2×C3×C22⋊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×C42C22×C314yes—
158C2×C3×C42C22×C314yes—
159C3×#95C22×C314yes—
160C3×#95C22×C314yes—
161C3×#95C22×C314yes—
162C3×#95C22×C314yes—
163C3×#95C22×C314yes—
164C3×#95C22×C314yes—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
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#4112yes—
193C23×C32C2411yescharacteristic
194C32×D4—44no—
195C32×D4—44no—
196C32×D4—44no—
197C32×D4—44no—
198C32×D4—44no—
199C32×D4—44no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
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—44no—
230C2×C32×C4C2×D412yes—
231C2×C32×C4C2×D412yes—
232C2×C32×C4C2×D412yes—
233C2×C32×C4#4112yes—
234C2×#126C2×C3211yescharacteristic, complemented
235C2×#121C2×C3211yescharacteristic, complemented
236#397C2×C3211yescharacteristic, complemented
237#394C2×C3211yescharacteristic, complemented
238#394C2×C3211yescharacteristic, complemented
239#392C2×C3211yescharacteristic, complemented
240#392C2×C3211yescharacteristic, complemented
241#392C2×C3211yescharacteristic, complemented
242#390C2×C3211yescharacteristic, complemented
243#390C2×C3211yescharacteristic, complemented
244#390C2×C3211yescharacteristic, complemented
245#388C2×C3211yescharacteristic, complemented
246#387C2×C3211yescharacteristic, complemented
247#386C2×C3211yescharacteristic, complemented
248#385C2×C3211yescharacteristic, complemented
249C24×C3C23×C314yes—
250C24×C3C23×C314yes—
251C24×C3C23×C314yes—
252C24×C3C23×C314yes—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—28no—
259C2×C3×D4—28no—
260C2×C3×D4—44no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4—44no—
264C2×C3×D4—44no—
265C2×C3×D4—44no—
266C2×C3×D4—44no—
267C2×C3×D4—44no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C22×C3×C4—28no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4C23×C314yes—
275C22×C3×C4C23×C314yes—
276C22×C3×C4C23×C314yes—
277C22×C3×C4C23×C314yes—
278C22×C3×C4C23×C314yes—
279C22×C3×C4C23×C314yes—
280C22×C3×C4C23×C314yes—
281C22×C3×C4C23×C314yes—
282C22×C3×C4C23×C314yes—
283C22×C3×C4C23×C314yes—
284C22×C3×C4C23×C314yes—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—28no—
287C3×C4⋊C4—44no—
288C3×C4⋊C4—44no—
289C3×C4⋊C4C3×D4116yescomplemented
290C3×C22⋊C4—28no—
291C3×C22⋊C4—28no—
292C3×C22⋊C4—28no—
293C3×C22⋊C4—28no—
294C3×C22⋊C4—28no—
295C3×C22⋊C4—28no—
296C3×C22⋊C4—28no—
297C3×C22⋊C4—44no—
298C3×C22⋊C4—44no—
299C3×C22⋊C4—44no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—44no—
302C3×C22⋊C4—44no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C42—28no—
306C3×C42—44no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—41no—
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×C32C22×D411yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32H(5,𝔽2)11yescharacteristic
339C22×C32H(5,𝔽2)11yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C22×C32H(5,𝔽2)11yescharacteristic
342C32×C4—22no—
343C32×C4—22no—
344C32×C4—22no—
345C32×C4—22no—
346C32×C4—41no—
347C32×C4—41no—
348C32×C4—41no—
349C32×C4—41no—
350C32×C4—41no—
351C32×C4—41no—
352C32×C4—41no—
353C22×D4C22×C3211yescharacteristic
354C22×D4C22×C3211yescharacteristic
355C22×D4C22×C3211yescharacteristic
356C22×D4C22×C3211yescharacteristic
357C22×D4C22×C3211yescharacteristic
358C22×D4C22×C3211yescharacteristic
359C23×C4C22×C3211yescharacteristic
360#126—24no—
361#121—24no—
362C2×C4⋊C4C22×C3211yescharacteristic
363C2×C4⋊C4C22×C3211yescharacteristic
364C2×C4⋊C4C22×C3211yescharacteristic
365C2×C4⋊C4C22×C3211yescharacteristic
366C2×C4⋊C4C22×C3211yescharacteristic
367C2×C22⋊C4C22×C3211yescharacteristic
368C2×C22⋊C4C22×C3211yescharacteristic
369C2×C22⋊C4C22×C3211yescharacteristic
370C2×C22⋊C4C22×C3211yescharacteristic
371C2×C22⋊C4C22×C3211yescharacteristic
372C2×C22⋊C4C22×C3211yescharacteristic
373C2×C22⋊C4C22×C3211yescharacteristic
374C2×C22⋊C4C22×C3211yescharacteristic
375C2×C22⋊C4C22×C3211yescharacteristic
376C2×C22⋊C4C22×C3211yescharacteristic
377C2×C22⋊C4C22×C3211yescharacteristic
378C2×C22⋊C4C22×C3211yescharacteristic
379C2×C22⋊C4C22×C3211yescharacteristic
380C2×C22⋊C4C22×C3211yescharacteristic
381C2×C22⋊C4C22×C3211yescharacteristic
382C2×C42C22×C3211yescharacteristic
383C2×C42C22×C3211yescharacteristic
384#95C22×C3211yescharacteristic
385#95C22×C3211yescharacteristic
386#95C22×C3211yescharacteristic
387#95C22×C3211yescharacteristic
388#95C22×C3211yescharacteristic
389#95C22×C3211yescharacteristic
390C23×C3—24no—
391C23×C3—24no—
392C23×C3—24no—
393C23×C3—24no—
394C23×C3—24no—
395C23×C3—24no—
396C23×C3—24no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—24no—
404C23×C3—24no—
405C23×C3—24no—
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×C3C3×#4118yes—
418C23×C3C24×C314yes—
419C3×D4—416no—
420C3×D4—416no—
421C3×D4—416no—
422C3×D4—416no—
423C3×D4—416no—
424C3×D4—416no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—24no—
433C2×C3×C4—24no—
434C2×C3×C4—24no—
435C2×C3×C4—24no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
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—416no—
455C2×C3×C4C2×C3×D418yes—
456C2×C3×C4C2×C3×D418yes—
457C2×C3×C4C2×C3×D418yes—
458C2×C3×C4C3×#4118yes—
459C2×C32—42no—
460C2×C32—81no—
461C2×C32—81no—
462C2×C32—81no—
463C2×C32#53511yescharacteristic
464C2×C32#53811yescharacteristic
465C2×C32#53811yescharacteristic
466C2×C32#54611yescharacteristic
467C2×C32#55011yescharacteristic
468C2×C32#55311yescharacteristic
469C2×C32#56011yescharacteristic
470C24C23×C3211yescharacteristic
471C24C23×C3211yescharacteristic
472C24C23×C3211yescharacteristic
473C24C23×C3211yescharacteristic
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4—41no—
491C2×D4—41no—
492C22×C4—22no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4C23×C3211yescharacteristic
496C22×C4C23×C3211yescharacteristic
497C22×C4C23×C3211yescharacteristic
498C22×C4C23×C3211yescharacteristic
499C22×C4C23×C3211yescharacteristic
500C22×C4C23×C3211yescharacteristic
501C22×C4C23×C3211yescharacteristic
502C22×C4C23×C3211yescharacteristic
503C22×C4C23×C3211yescharacteristic
504C22×C4C23×C3211yescharacteristic
505C22×C4C23×C3211yescharacteristic
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4C32×D414yescomplemented
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—22no—
527C42—41no—
528C22×C3—28no—
529C22×C3—28no—
530C22×C3—28no—
531C22×C3—44no—
532C22×C3—44no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—44no—
549C22×C3—44no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3C22×C3×D414yes—
557C22×C3C2×C3×#4114yes—
558C22×C3C2×C3×#4114yes—
559C22×C3C3×H(5,𝔽2)14yes—
560C22×C3C3×H(5,𝔽2)14yes—
561C22×C3C3×H(5,𝔽2)14yes—
562C22×C3C3×H(5,𝔽2)14yes—
563C3×C4—28no—
564C3×C4—28no—
565C3×C4—28no—
566C3×C4—28no—
567C3×C4—44no—
568C3×C4—44no—
569C3×C4—44no—
570C3×C4—44no—
571C3×C4—44no—
572C3×C4—44no—
573C3×C4—44no—
574C32#271411yescharacteristic, direct product factor, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23C32×#4112yes—
603C23C24×C3211yescharacteristic
604D4—44no—
605D4—44no—
606D4—44no—
607D4—44no—
608D4—44no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—44no—
640C2×C4C2×C32×D412yes—
641C2×C4C2×C32×D412yes—
642C2×C4C2×C32×D412yes—
643C2×C4C32×#4112yes—
644C2×C3—48no—
645C2×C3—84no—
646C2×C3—84no—
647C2×C3—84no—
648C2×C3C3×#53514yes—
649C2×C3C3×#53814yes—
650C2×C3C3×#53814yes—
651C2×C3C3×#54614yes—
652C2×C3C3×#55014yes—
653C2×C3C3×#55314yes—
654C2×C3C3×#56014yes—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22C22×C32×D411yescharacteristic
684C22C2×C32×#4111yescharacteristic
685C22C2×C32×#4111yescharacteristic
686C22C32×H(5,𝔽2)11yescharacteristic
687C22C32×H(5,𝔽2)11yescharacteristic
688C22C32×H(5,𝔽2)11yescharacteristic
689C22C32×H(5,𝔽2)11yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C3C3×#271414yesdirect product factor
702C2—42no—
703C2—81no—
704C2—81no—
705C2—81no—
706C2C32×#53511yescharacteristic
707C2C32×#53811yescharacteristic
708C2C32×#53811yescharacteristic
709C2C32×#54611yescharacteristic
710C2C32×#55011yescharacteristic
711C2C32×#55311yescharacteristic
712C2C32×#56011yescharacteristic
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×#126C2semidirect
2. C2×C32×#121C2semidirect
3. C32×#397C2semidirect
4. C32×#394C2semidirect
5. C32×#394C2semidirect
6. C32×#392C2semidirect
7. C32×#392C2semidirect
8. C32×#392C2semidirect
9. C32×#390C2semidirect
10. C32×#390C2semidirect
11. C32×#390C2semidirect
12. C32×#388C2semidirect
13. C32×#387C2semidirect
14. C32×#386C2semidirect
15. C32×#385C2semidirect
16. C3×#2714C3direct (N × H)
54. C2×C3×#126C2×C3semidirect
55. C2×C3×#121C2×C3semidirect
56. C3×#397C2×C3semidirect
57. C3×#394C2×C3semidirect
58. C3×#394C2×C3semidirect
59. C3×#392C2×C3semidirect
60. C3×#392C2×C3semidirect
61. C3×#392C2×C3semidirect
62. C3×#390C2×C3semidirect
63. C3×#390C2×C3semidirect
64. C3×#390C2×C3semidirect
65. C3×#388C2×C3semidirect
66. C3×#387C2×C3semidirect
67. C3×#386C2×C3semidirect
68. C3×#385C2×C3semidirect
109. C32×C4⋊C4D4semidirect
127. #2714C32direct (N × H)
234. C2×#126C2×C32semidirect
235. C2×#121C2×C32semidirect
236. #397C2×C32semidirect
237. #394C2×C32semidirect
238. #394C2×C32semidirect
239. #392C2×C32semidirect
240. #392C2×C32semidirect
241. #392C2×C32semidirect
242. #390C2×C32semidirect
243. #390C2×C32semidirect
244. #390C2×C32semidirect
245. #388C2×C32semidirect
246. #387C2×C32semidirect
247. #386C2×C32semidirect
248. #385C2×C32semidirect
289. C3×C4⋊C4C3×D4semidirect
510. C4⋊C4C32×D4semidirect
574. C32#2714direct (N × H)
701. C3C3×#2714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1262
C2×C32×#1212
C32×#3972
C32×#3942
C32×#3922
C32×#3902
C32×#3882
C32×#3872
C32×#3862
C32×#3852
C3×#27143