Finite Group Databasebeta

← C32×#2672 #11769721

Subgroups — C32×#2672 #11769721

Order 1152.

1854 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#124C211yesmaximal, characteristic, complemented
2C2×C32×#123C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C32×#121C211yesmaximal, characteristic
5C32×#399C211yesmaximal, characteristic, complemented
6C32×#396C211yesmaximal, characteristic, complemented
7C32×#395C211yesmaximal, characteristic, complemented
8C32×#394C211yesmaximal, characteristic, complemented
9C32×#394C211yesmaximal, characteristic, complemented
10C32×#394C211yesmaximal, characteristic, complemented
11C32×#389C211yesmaximal, characteristic, complemented
12C32×#388C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic, complemented
14C32×#385C211yesmaximal, characteristic, complemented
15C32×#380C211yesmaximal, characteristic, complemented
16C3×#2672C314yesmaximal, direct product factor
17C22×C32×Q8C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic
22C23×C32×C4C2211yescharacteristic
23C32×#124—24no—
24C32×#123—24no—
25C32×C22⋊Q8—24no—
26C32×#121—24no—
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C4⋊C4C2211yescharacteristic
34C2×C32×C4⋊C4C2211yescharacteristic
35C2×C32×C4⋊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×#123C2×C314yescomplemented
58C2×C3×C22⋊Q8C2×C314yescomplemented
59C2×C3×#121C2×C314yes—
60C3×#399C2×C314yescomplemented
61C3×#396C2×C314yescomplemented
62C3×#395C2×C314yescomplemented
63C3×#394C2×C314yescomplemented
64C3×#394C2×C314yescomplemented
65C3×#394C2×C314yescomplemented
66C3×#389C2×C314yescomplemented
67C3×#388C2×C314yescomplemented
68C3×#386C2×C314yescomplemented
69C3×#385C2×C314yescomplemented
70C3×#380C2×C314yescomplemented
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C24×C32C2311yescharacteristic
74C2×C32×Q8—22no—
75C2×C32×Q8—22no—
76C2×C32×Q8—41no—
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4—22no—
80C2×C32×D4—22no—
81C2×C32×D4—22no—
82C2×C32×D4—22no—
83C2×C32×D4—41no—
84C2×C32×D4—41no—
85C2×C32×D4—41no—
86C22×C32×C4—22no—
87C22×C32×C4—22no—
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—41no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
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
104C32×C4⋊C4—22no—
105C32×C4⋊C4—22no—
106C32×C4⋊C4—22no—
107C32×C4⋊C4—22no—
108C32×C4⋊C4—22no—
109C32×C4⋊C4—22no—
110C32×C4⋊C4—22no—
111C32×C4⋊C4—41no—
112C32×C4⋊C4—41no—
113C32×C22⋊C4—22no—
114C32×C22⋊C4—22no—
115C32×C22⋊C4—22no—
116C32×C22⋊C4—22no—
117C32×C22⋊C4—22no—
118C32×C22⋊C4—22no—
119C32×C22⋊C4—22no—
120C32×C22⋊C4—41no—
121C32×C22⋊C4—41no—
122C32×C22⋊C4—41no—
123C32×C22⋊C4—41no—
124C32×C22⋊C4D414yes—
125C32×C22⋊C4D414yescomplemented
126C32×C42—22no—
127#2672C3211yescharacteristic, direct product factor, Sylow
128C22×C3×Q8C22×C314yes—
129C22×C3×D4C22×C314yes—
130C22×C3×D4C22×C314yes—
131C22×C3×D4C22×C314yes—
132C23×C3×C4C22×C314yes—
133C23×C3×C4C22×C314yes—
134C3×#124—216no—
135C3×#123—216no—
136C3×C22⋊Q8—216no—
137C3×#121—216no—
138C2×C3×C4⋊C4C22×C314yes—
139C2×C3×C4⋊C4C22×C314yes—
140C2×C3×C4⋊C4C22×C314yes—
141C2×C3×C4⋊C4C22×C314yes—
142C2×C3×C4⋊C4C22×C314yes—
143C2×C3×C4⋊C4C22×C314yes—
144C2×C3×C4⋊C4C22×C314yes—
145C2×C3×C4⋊C4C22×C314yes—
146C2×C3×C4⋊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×C22⋊C4C22×C314yes—
158C2×C3×C22⋊C4C22×C314yes—
159C2×C3×C22⋊C4C22×C314yes—
160C2×C3×C42C22×C314yes—
161C3×#95C22×C314yes—
162C3×#95C22×C314yes—
163C3×#95C22×C314yes—
164C3×#95C22×C314yes—
165C3×#95C22×C314yes—
166C3×#95C22×C314yes—
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×C32C2×D412yes—
187C23×C32C2×D412yes—
188C23×C32C2411yescharacteristic
189C32×Q8—44no—
190C32×D4—44no—
191C32×D4—44no—
192C32×D4—44no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
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—44no—
225C2×C32×C4—44no—
226C2×C32×C4C2×D412yes—
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2×D412yes—
229C2×C32×C4C2×D412yes—
230C2×C32×C4#4112yes—
231C2×#124C2×C3211yescharacteristic, complemented
232C2×#123C2×C3211yescharacteristic, complemented
233C2×C22⋊Q8C2×C3211yescharacteristic, complemented
234C2×#121C2×C3211yescharacteristic
235#399C2×C3211yescharacteristic, complemented
236#396C2×C3211yescharacteristic, complemented
237#395C2×C3211yescharacteristic, complemented
238#394C2×C3211yescharacteristic, complemented
239#394C2×C3211yescharacteristic, complemented
240#394C2×C3211yescharacteristic, complemented
241#389C2×C3211yescharacteristic, complemented
242#388C2×C3211yescharacteristic, complemented
243#386C2×C3211yescharacteristic, complemented
244#385C2×C3211yescharacteristic, complemented
245#380C2×C3211yescharacteristic, complemented
246C24×C3C23×C314yes—
247C24×C3C23×C314yes—
248C24×C3C23×C314yes—
249C2×C3×Q8—28no—
250C2×C3×Q8—28no—
251C2×C3×Q8—44no—
252C2×C3×D4—28no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—44no—
261C22×C3×C4—28no—
262C22×C3×C4—28no—
263C22×C3×C4—28no—
264C22×C3×C4—28no—
265C22×C3×C4—44no—
266C22×C3×C4—44no—
267C22×C3×C4C23×C314yes—
268C22×C3×C4C23×C314yes—
269C22×C3×C4C23×C314yes—
270C22×C3×C4C23×C314yes—
271C22×C3×C4C23×C314yes—
272C22×C3×C4C23×C314yes—
273C22×C3×C4C23×C314yes—
274C22×C3×C4C23×C314yes—
275C22×C3×C4C23×C314yes—
276C22×C3×C4C23×C314yes—
277C22×C3×C4C23×C314yes—
278C22×C3×C4C23×C314yes—
279C3×C4⋊C4—28no—
280C3×C4⋊C4—28no—
281C3×C4⋊C4—28no—
282C3×C4⋊C4—28no—
283C3×C4⋊C4—28no—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—44no—
287C3×C4⋊C4—44no—
288C3×C22⋊C4—28no—
289C3×C22⋊C4—28no—
290C3×C22⋊C4—28no—
291C3×C22⋊C4—28no—
292C3×C22⋊C4—28no—
293C3×C22⋊C4—28no—
294C3×C22⋊C4—28no—
295C3×C22⋊C4—44no—
296C3×C22⋊C4—44no—
297C3×C22⋊C4—44no—
298C3×C22⋊C4—44no—
299C3×C22⋊C4C3×D4116yes—
300C3×C22⋊C4C3×D4116yescomplemented
301C3×C42—28no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—41no—
309C22×C32—41no—
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×C32C22×D411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C2×#4111yescharacteristic
326C22×C32H(5,𝔽2)11yescharacteristic
327C22×C32H(5,𝔽2)11yescharacteristic
328C22×C322−1+411yescharacteristic
329C22×C322−1+411yescharacteristic
330C32×C4—22no—
331C32×C4—22no—
332C32×C4—22no—
333C32×C4—22no—
334C32×C4—22no—
335C32×C4—41no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4—41no—
339C32×C4—41no—
340C32×C4—41no—
341C32×C4—41no—
342C22×Q8C22×C3211yescharacteristic
343C22×D4C22×C3211yescharacteristic
344C22×D4C22×C3211yescharacteristic
345C22×D4C22×C3211yescharacteristic
346C23×C4C22×C3211yescharacteristic
347C23×C4C22×C3211yescharacteristic
348#124—24no—
349#123—24no—
350C22⋊Q8—24no—
351#121—24no—
352C2×C4⋊C4C22×C3211yescharacteristic
353C2×C4⋊C4C22×C3211yescharacteristic
354C2×C4⋊C4C22×C3211yescharacteristic
355C2×C4⋊C4C22×C3211yescharacteristic
356C2×C4⋊C4C22×C3211yescharacteristic
357C2×C4⋊C4C22×C3211yescharacteristic
358C2×C4⋊C4C22×C3211yescharacteristic
359C2×C4⋊C4C22×C3211yescharacteristic
360C2×C4⋊C4C22×C3211yescharacteristic
361C2×C22⋊C4C22×C3211yescharacteristic
362C2×C22⋊C4C22×C3211yescharacteristic
363C2×C22⋊C4C22×C3211yescharacteristic
364C2×C22⋊C4C22×C3211yescharacteristic
365C2×C22⋊C4C22×C3211yescharacteristic
366C2×C22⋊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×C42C22×C3211yescharacteristic
375#95C22×C3211yescharacteristic
376#95C22×C3211yescharacteristic
377#95C22×C3211yescharacteristic
378#95C22×C3211yescharacteristic
379#95C22×C3211yescharacteristic
380#95C22×C3211yescharacteristic
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—24no—
387C23×C3—24no—
388C23×C3—24no—
389C23×C3—24no—
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×C3C2×C3×D418yes—
401C23×C3C2×C3×D418yes—
402C23×C3C24×C314yes—
403C3×Q8—416no—
404C3×D4—416no—
405C3×D4—416no—
406C3×D4—416no—
407C2×C3×C4—24no—
408C2×C3×C4—24no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—24no—
418C2×C3×C4—24no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
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—416no—
439C2×C3×C4—416no—
440C2×C3×C4C2×C3×D418yes—
441C2×C3×C4C2×C3×D418yes—
442C2×C3×C4C2×C3×D418yes—
443C2×C3×C4C2×C3×D418yes—
444C2×C3×C4C3×#4118yes—
445C2×C32—42no—
446C2×C32—42no—
447C2×C32—81no—
448C2×C32#53611yescharacteristic
449C2×C32#53711yescharacteristic
450C2×C32#54211yescharacteristic
451C2×C32D4211yescharacteristic
452C2×C32#54611yescharacteristic
453C2×C32#54711yescharacteristic
454C2×C32#56211yescharacteristic
455C24C23×C3211yescharacteristic
456C24C23×C3211yescharacteristic
457C24C23×C3211yescharacteristic
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—41no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4C23×C3211yescharacteristic
477C22×C4C23×C3211yescharacteristic
478C22×C4C23×C3211yescharacteristic
479C22×C4C23×C3211yescharacteristic
480C22×C4C23×C3211yescharacteristic
481C22×C4C23×C3211yescharacteristic
482C22×C4C23×C3211yescharacteristic
483C22×C4C23×C3211yescharacteristic
484C22×C4C23×C3211yescharacteristic
485C22×C4C23×C3211yescharacteristic
486C22×C4C23×C3211yescharacteristic
487C22×C4C23×C3211yescharacteristic
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4C32×D414yes—
509C22⋊C4C32×D414yescomplemented
510C42—22no—
511C22×C3—28no—
512C22×C3—28no—
513C22×C3—28no—
514C22×C3—28no—
515C22×C3—28no—
516C22×C3—28no—
517C22×C3—44no—
518C22×C3—44no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—44no—
532C22×C3C22×C3×D414yes—
533C22×C3C22×C3×D414yes—
534C22×C3C2×C3×#4114yes—
535C22×C3C3×H(5,𝔽2)14yes—
536C22×C3C3×H(5,𝔽2)14yes—
537C22×C3C3×2−1+414yes—
538C22×C3C3×2−1+414yes—
539C3×C4—28no—
540C3×C4—28no—
541C3×C4—28no—
542C3×C4—28no—
543C3×C4—28no—
544C3×C4—44no—
545C3×C4—44no—
546C3×C4—44no—
547C3×C4—44no—
548C3×C4—44no—
549C3×C4—44no—
550C3×C4—44no—
551C32#267211yescharacteristic, direct product factor, Sylow
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23C2×C32×D412yes—
572C23C2×C32×D412yes—
573C23C24×C3211yescharacteristic
574Q8—44no—
575D4—44no—
576D4—44no—
577D4—44no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4C2×C32×D412yes—
612C2×C4C2×C32×D412yes—
613C2×C4C2×C32×D412yes—
614C2×C4C2×C32×D412yes—
615C2×C4C32×#4112yes—
616C2×C3—48no—
617C2×C3—48no—
618C2×C3—84no—
619C2×C3C3×#53614yes—
620C2×C3C3×#53714yes—
621C2×C3C3×#54214yes—
622C2×C3C3×D4214yes—
623C2×C3C3×#54614yes—
624C2×C3C3×#54714yes—
625C2×C3C3×#56214yes—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C22×C32×D411yescharacteristic
648C22C22×C32×D411yescharacteristic
649C22C2×C32×#4111yescharacteristic
650C22C32×H(5,𝔽2)11yescharacteristic
651C22C32×H(5,𝔽2)11yescharacteristic
652C22C32×2−1+411yescharacteristic
653C22C32×2−1+411yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C3C3×#267214yesdirect product factor
667C2—42no—
668C2—42no—
669C2—81no—
670C2C32×#53611yescharacteristic
671C2C32×#53711yescharacteristic
672C2C32×#54211yescharacteristic
673C2C32×D4211yescharacteristic
674C2C32×#54611yescharacteristic
675C2C32×#54711yescharacteristic
676C2C32×#56211yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
prime radicalC2×C32×#121C2
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×#123C2semidirect
3. C2×C32×C22⋊Q8C2semidirect
5. C32×#399C2semidirect
6. C32×#396C2semidirect
7. C32×#395C2semidirect
8. C32×#394C2semidirect
9. C32×#394C2semidirect
10. C32×#394C2semidirect
11. C32×#389C2semidirect
12. C32×#388C2semidirect
13. C32×#386C2semidirect
14. C32×#385C2semidirect
15. C32×#380C2semidirect
16. C3×#2672C3direct (N × H)
56. C2×C3×#124C2×C3semidirect
57. C2×C3×#123C2×C3semidirect
58. C2×C3×C22⋊Q8C2×C3semidirect
60. C3×#399C2×C3semidirect
61. C3×#396C2×C3semidirect
62. C3×#395C2×C3semidirect
63. C3×#394C2×C3semidirect
64. C3×#394C2×C3semidirect
65. C3×#394C2×C3semidirect
66. C3×#389C2×C3semidirect
67. C3×#388C2×C3semidirect
68. C3×#386C2×C3semidirect
69. C3×#385C2×C3semidirect
70. C3×#380C2×C3semidirect
125. C32×C22⋊C4D4semidirect
127. #2672C32direct (N × H)
231. C2×#124C2×C32semidirect
232. C2×#123C2×C32semidirect
233. C2×C22⋊Q8C2×C32semidirect
235. #399C2×C32semidirect
236. #396C2×C32semidirect
237. #395C2×C32semidirect
238. #394C2×C32semidirect
239. #394C2×C32semidirect
240. #394C2×C32semidirect
241. #389C2×C32semidirect
242. #388C2×C32semidirect
243. #386C2×C32semidirect
244. #385C2×C32semidirect
245. #380C2×C32semidirect
300. C3×C22⋊C4C3×D4semidirect
509. C22⋊C4C32×D4semidirect
551. C32#2672direct (N × H)
666. C3C3×#2672direct (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×#1232
C2×C32×C22⋊Q82
C2×C32×#1212
C32×#3992
C32×#3962
C32×#3952
C32×#3942
C32×#3892
C32×#3882
C32×#3862
C32×#3852
C32×#3802
C3×#26723