Finite Group Databasebeta

← C32×#2472 #11769521

Subgroups — C32×#2472 #11769521

Order 1152.

2358 conjugacy classes of subgroups.

The subgroup lattice has 753 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×#120C211yesmaximal, characteristic
4C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
5C32×#397C211yesmaximal, characteristic, complemented
6C32×#394C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8C32×#393C211yesmaximal, characteristic, complemented
9C32×#390C211yesmaximal, characteristic, complemented
10C32×#388C211yesmaximal, characteristic, complemented
11C32×#388C211yesmaximal, characteristic, complemented
12C32×#386C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic, complemented
14C32×#379C211yesmaximal, characteristic, complemented
15C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
16C3×#2472C314yesmaximal, direct product factor
17C25×C32C2211yescharacteristic
18C22×C32×Q8C2211yescharacteristic, complemented
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C23×C32×C4C2211yescharacteristic
23C23×C32×C4C2211yescharacteristic
24C32×#124—24no—
25C32×C22⋊Q8—24no—
26C32×#120—24no—
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×C32×C4⋊C4C2211yescharacteristic, complemented
30C2×C32×C22⋊C4—24no—
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, complemented
45C2×C32×C22⋊C4C2211yescharacteristic, complemented
46C2×C32×C22⋊C4C2211yescharacteristic, complemented
47C2×C32×C22⋊C4C2211yescharacteristic, complemented
48C2×C32×C42C2211yescharacteristic, complemented
49C2×C32×C42C2211yescharacteristic, complemented
50C32×#95C2211yescharacteristic, complemented
51C32×#95C2211yescharacteristic, complemented
52C32×#95C2211yescharacteristic, complemented
53C32×#95C2211yescharacteristic, complemented
54C32×#95C2211yescharacteristic, complemented
55C32×#95C2211yescharacteristic, complemented
56C2×C3×#124C2×C314yescomplemented
57C2×C3×C22⋊Q8C2×C314yescomplemented
58C2×C3×#120C2×C314yes—
59C22×C3×C22⋊C4C2×C314yescomplemented
60C3×#397C2×C314yescomplemented
61C3×#394C2×C314yescomplemented
62C3×#394C2×C314yescomplemented
63C3×#393C2×C314yescomplemented
64C3×#390C2×C314yescomplemented
65C3×#388C2×C314yescomplemented
66C3×#388C2×C314yescomplemented
67C3×#386C2×C314yescomplemented
68C3×#386C2×C314yescomplemented
69C3×#379C2×C314yescomplemented
70C3×C4×C22⋊C4C2×C314yescomplemented
71C24×C32—22no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—22no—
75C24×C32—22no—
76C24×C32—41no—
77C24×C32—41no—
78C24×C32C2311yescharacteristic
79C24×C32C2311yescharacteristic
80C24×C32C2311yescharacteristic
81C24×C32C2311yescharacteristic
82C2×C32×Q8—22no—
83C2×C32×Q8—22no—
84C2×C32×Q8—41no—
85C2×C32×D4—22no—
86C2×C32×D4—22no—
87C2×C32×D4—22no—
88C2×C32×D4—22no—
89C2×C32×D4—22no—
90C2×C32×D4—22no—
91C2×C32×D4—22no—
92C2×C32×D4—41no—
93C2×C32×D4—41no—
94C22×C32×C4—22no—
95C22×C32×C4—22no—
96C22×C32×C4—22no—
97C22×C32×C4—22no—
98C22×C32×C4—41no—
99C22×C32×C4—41no—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
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
111C32×C4⋊C4—22no—
112C32×C4⋊C4—22no—
113C32×C4⋊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—22no—
121C32×C22⋊C4—22no—
122C32×C22⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—41no—
126C32×C22⋊C4—41no—
127C32×C22⋊C4—41no—
128C32×C22⋊C4—41no—
129C32×C22⋊C4D414yes—
130C32×C22⋊C4D414yescomplemented
131C32×C42—22no—
132C32×C42—41no—
133#2472C3211yescharacteristic, direct product factor, Sylow
134C25×C3C22×C314yes—
135C22×C3×Q8C22×C314yescomplemented
136C22×C3×D4C22×C314yes—
137C22×C3×D4C22×C314yes—
138C22×C3×D4C22×C314yes—
139C23×C3×C4C22×C314yes—
140C23×C3×C4C22×C314yes—
141C3×#124—216no—
142C3×C22⋊Q8—216no—
143C3×#120—216no—
144C2×C3×C4⋊C4C22×C314yescomplemented
145C2×C3×C4⋊C4C22×C314yescomplemented
146C2×C3×C4⋊C4C22×C314yescomplemented
147C2×C3×C22⋊C4—216no—
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×C22⋊C4C22×C314yes—
161C2×C3×C22⋊C4C22×C314yescomplemented
162C2×C3×C22⋊C4C22×C314yescomplemented
163C2×C3×C22⋊C4C22×C314yescomplemented
164C2×C3×C22⋊C4C22×C314yescomplemented
165C2×C3×C42C22×C314yescomplemented
166C2×C3×C42C22×C314yescomplemented
167C3×#95C22×C314yescomplemented
168C3×#95C22×C314yescomplemented
169C3×#95C22×C314yescomplemented
170C3×#95C22×C314yescomplemented
171C3×#95C22×C314yescomplemented
172C3×#95C22×C314yescomplemented
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—28no—
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—44no—
198C23×C32—44no—
199C23×C32—44no—
200C23×C32—44no—
201C23×C32—44no—
202C23×C32—44no—
203C23×C32C2×D412yes—
204C23×C32C2×D412yes—
205C23×C32#4112yes—
206C23×C32#4112yes—
207C23×C32#4112yes—
208C23×C32C2411yescharacteristic
209C32×Q8—44no—
210C32×D4—44no—
211C32×D4—44no—
212C32×D4—44no—
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—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—44no—
243C2×C32×C4—44no—
244C2×C32×C4C2×D412yes—
245C2×C32×C4C2×D412yes—
246C2×C32×C4C2×D412yes—
247C2×C32×C4C2×D412yes—
248C2×#124C2×C3211yescharacteristic, complemented
249C2×C22⋊Q8C2×C3211yescharacteristic, complemented
250C2×#120C2×C3211yescharacteristic
251C22×C22⋊C4C2×C3211yescharacteristic, complemented
252#397C2×C3211yescharacteristic, complemented
253#394C2×C3211yescharacteristic, complemented
254#394C2×C3211yescharacteristic, complemented
255#393C2×C3211yescharacteristic, complemented
256#390C2×C3211yescharacteristic, complemented
257#388C2×C3211yescharacteristic, complemented
258#388C2×C3211yescharacteristic, complemented
259#386C2×C3211yescharacteristic, complemented
260#386C2×C3211yescharacteristic, complemented
261#379C2×C3211yescharacteristic, complemented
262C4×C22⋊C4C2×C3211yescharacteristic, complemented
263C24×C3—28no—
264C24×C3—28no—
265C24×C3—28no—
266C24×C3—28no—
267C24×C3—28no—
268C24×C3—44no—
269C24×C3—44no—
270C24×C3C23×C314yes—
271C24×C3C23×C314yes—
272C24×C3C23×C314yes—
273C24×C3C23×C314yes—
274C2×C3×Q8—28no—
275C2×C3×Q8—28no—
276C2×C3×Q8—44no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—28no—
281C2×C3×D4—28no—
282C2×C3×D4—28no—
283C2×C3×D4—28no—
284C2×C3×D4—44no—
285C2×C3×D4—44no—
286C22×C3×C4—28no—
287C22×C3×C4—28no—
288C22×C3×C4—28no—
289C22×C3×C4—28no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
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—
301C22×C3×C4C23×C314yes—
302C22×C3×C4C23×C314yes—
303C3×C4⋊C4—28no—
304C3×C4⋊C4—28no—
305C3×C4⋊C4—28no—
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—28no—
315C3×C22⋊C4—28no—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—44no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C22⋊C4—44no—
321C3×C22⋊C4C3×D4116yes—
322C3×C22⋊C4C3×D4116yescomplemented
323C3×C42—28no—
324C3×C42—44no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—22no—
337C22×C32—416no—
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×C32—41no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32#12414yescomplemented
354C22×C32C22×D411yescharacteristic
355C22×C32C22×D411yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32H(5,𝔽2)11yescharacteristic
360C22×C32H(5,𝔽2)11yescharacteristic
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—22no—
364C32×C4—22no—
365C32×C4—41no—
366C32×C4—41no—
367C32×C4—41no—
368C32×C4—41no—
369C32×C4—41no—
370C32×C4—41no—
371C32×C4—41no—
372C25C22×C3211yescharacteristic
373C22×Q8C22×C3211yescharacteristic, complemented
374C22×D4C22×C3211yescharacteristic
375C22×D4C22×C3211yescharacteristic
376C22×D4C22×C3211yescharacteristic
377C23×C4C22×C3211yescharacteristic
378C23×C4C22×C3211yescharacteristic
379#124—24no—
380C22⋊Q8—24no—
381#120—24no—
382C2×C4⋊C4C22×C3211yescharacteristic, complemented
383C2×C4⋊C4C22×C3211yescharacteristic, complemented
384C2×C4⋊C4C22×C3211yescharacteristic, complemented
385C2×C22⋊C4—24no—
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×C22⋊C4C22×C3211yescharacteristic, complemented
400C2×C22⋊C4C22×C3211yescharacteristic, complemented
401C2×C22⋊C4C22×C3211yescharacteristic, complemented
402C2×C22⋊C4C22×C3211yescharacteristic, complemented
403C2×C42C22×C3211yescharacteristic, complemented
404C2×C42C22×C3211yescharacteristic, complemented
405#95C22×C3211yescharacteristic, complemented
406#95C22×C3211yescharacteristic, complemented
407#95C22×C3211yescharacteristic, complemented
408#95C22×C3211yescharacteristic, complemented
409#95C22×C3211yescharacteristic, complemented
410#95C22×C3211yescharacteristic, complemented
411C23×C3—24no—
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—232no—
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×C3—24no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—416no—
436C23×C3—416no—
437C23×C3—416no—
438C23×C3—416no—
439C23×C3—416no—
440C23×C3—416no—
441C23×C3C2×C3×D418yes—
442C23×C3C2×C3×D418yes—
443C23×C3C3×#4118yes—
444C23×C3C3×#4118yes—
445C23×C3C3×#4118yes—
446C23×C3C24×C314yes—
447C3×Q8—416no—
448C3×D4—416no—
449C3×D4—416no—
450C3×D4—416no—
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—24no—
471C2×C3×C4—24no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—24no—
480C2×C3×C4—416no—
481C2×C3×C4—416no—
482C2×C3×C4C2×C3×D418yes—
483C2×C3×C4C2×C3×D418yes—
484C2×C3×C4C2×C3×D418yes—
485C2×C3×C4C2×C3×D418yes—
486C2×C32—24no—
487C2×C32—42no—
488C2×C32—42no—
489C2×C32—81no—
490C2×C32#52511yescharacteristic
491C2×C32C2×#12411yescharacteristic
492C2×C32#53811yescharacteristic
493C2×C32D4211yescharacteristic
494C2×C32#54611yescharacteristic
495C2×C32#54611yescharacteristic
496C2×C32#55111yescharacteristic
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—41no—
503C24—41no—
504C24C23×C3211yescharacteristic
505C24C23×C3211yescharacteristic
506C24C23×C3211yescharacteristic
507C24C23×C3211yescharacteristic
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—41no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4C23×C3211yescharacteristic
527C22×C4C23×C3211yescharacteristic
528C22×C4C23×C3211yescharacteristic
529C22×C4C23×C3211yescharacteristic
530C22×C4C23×C3211yescharacteristic
531C22×C4C23×C3211yescharacteristic
532C22×C4C23×C3211yescharacteristic
533C22×C4C23×C3211yescharacteristic
534C22×C4C23×C3211yescharacteristic
535C22×C4C23×C3211yescharacteristic
536C22×C4C23×C3211yescharacteristic
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
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—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4C32×D414yes—
556C22⋊C4C32×D414yescomplemented
557C42—22no—
558C42—41no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—28no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—464no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3C3×#124116yescomplemented
588C22×C3C22×C3×D414yes—
589C22×C3C22×C3×D414yes—
590C22×C3C2×C3×#4114yes—
591C22×C3C2×C3×#4114yes—
592C22×C3C2×C3×#4114yes—
593C22×C3C3×H(5,𝔽2)14yes—
594C22×C3C3×H(5,𝔽2)14yes—
595C3×C4—28no—
596C3×C4—28no—
597C3×C4—28no—
598C3×C4—28no—
599C3×C4—44no—
600C3×C4—44no—
601C3×C4—44no—
602C3×C4—44no—
603C3×C4—44no—
604C3×C4—44no—
605C3×C4—44no—
606C32#247211yescharacteristic, direct product factor, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—28no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23C2×C32×D412yes—
638C23C2×C32×D412yes—
639C23C32×#4112yes—
640C23C32×#4112yes—
641C23C32×#4112yes—
642C23C24×C3211yescharacteristic
643Q8—44no—
644D4—44no—
645D4—44no—
646D4—44no—
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—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4C2×C32×D412yes—
679C2×C4C2×C32×D412yes—
680C2×C4C2×C32×D412yes—
681C2×C4C2×C32×D412yes—
682C2×C3—216no—
683C2×C3—48no—
684C2×C3—48no—
685C2×C3—84no—
686C2×C3C3×#52514yes—
687C2×C3C2×C3×#12414yes—
688C2×C3C3×#53814yes—
689C2×C3C3×D4214yes—
690C2×C3C3×#54614yes—
691C2×C3C3×#54614yes—
692C2×C3C3×#55114yes—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—416no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C32×#12414yescomplemented
722C22C22×C32×D411yescharacteristic
723C22C22×C32×D411yescharacteristic
724C22C2×C32×#4111yescharacteristic
725C22C2×C32×#4111yescharacteristic
726C22C2×C32×#4111yescharacteristic
727C22C32×H(5,𝔽2)11yescharacteristic
728C22C32×H(5,𝔽2)11yescharacteristic
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C3C3×#247214yesdirect product factor
741C2—24no—
742C2—42no—
743C2—42no—
744C2—81no—
745C2C32×#52511yescharacteristic
746C2C2×C32×#12411yescharacteristic
747C2C32×#53811yescharacteristic
748C2C32×D4211yescharacteristic
749C2C32×#54611yescharacteristic
750C2C32×#54611yescharacteristic
751C2C32×#55111yescharacteristic
subgroupG/H
center, socleC23×C32C24
commutator, Frattini, cosocleC23C24×C32
prime radicalC2×C32×#120C2
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
4. C22×C32×C22⋊C4C2semidirect
5. C32×#397C2semidirect
6. C32×#394C2semidirect
7. C32×#394C2semidirect
8. C32×#393C2semidirect
9. C32×#390C2semidirect
10. C32×#388C2semidirect
11. C32×#388C2semidirect
12. C32×#386C2semidirect
13. C32×#386C2semidirect
14. C32×#379C2semidirect
15. C32×C4×C22⋊C4C2semidirect
16. C3×#2472C3direct (N × H)
18. C22×C32×Q8C22semidirect
27. C2×C32×C4⋊C4C22semidirect
28. C2×C32×C4⋊C4C22semidirect
29. C2×C32×C4⋊C4C22semidirect
44. C2×C32×C22⋊C4C22semidirect
45. C2×C32×C22⋊C4C22semidirect
46. C2×C32×C22⋊C4C22semidirect
47. C2×C32×C22⋊C4C22semidirect
48. C2×C32×C42C22semidirect
49. C2×C32×C42C22semidirect
50. C32×#95C22semidirect
51. C32×#95C22semidirect
52. C32×#95C22semidirect
53. C32×#95C22semidirect
54. C32×#95C22semidirect
55. C32×#95C22semidirect
56. C2×C3×#124C2×C3semidirect
57. C2×C3×C22⋊Q8C2×C3semidirect
59. C22×C3×C22⋊C4C2×C3semidirect
60. C3×#397C2×C3semidirect
61. C3×#394C2×C3semidirect
62. C3×#394C2×C3semidirect
63. C3×#393C2×C3semidirect
64. C3×#390C2×C3semidirect
65. C3×#388C2×C3semidirect
66. C3×#388C2×C3semidirect
67. C3×#386C2×C3semidirect
68. C3×#386C2×C3semidirect
69. C3×#379C2×C3semidirect
70. C3×C4×C22⋊C4C2×C3semidirect
130. C32×C22⋊C4D4semidirect
133. #2472C32direct (N × H)
135. C22×C3×Q8C22×C3semidirect
144. C2×C3×C4⋊C4C22×C3semidirect
145. C2×C3×C4⋊C4C22×C3semidirect
146. C2×C3×C4⋊C4C22×C3semidirect
161. C2×C3×C22⋊C4C22×C3semidirect
162. C2×C3×C22⋊C4C22×C3semidirect
163. C2×C3×C22⋊C4C22×C3semidirect
164. C2×C3×C22⋊C4C22×C3semidirect
165. C2×C3×C42C22×C3semidirect
166. C2×C3×C42C22×C3semidirect
167. C3×#95C22×C3semidirect
168. C3×#95C22×C3semidirect
169. C3×#95C22×C3semidirect
170. C3×#95C22×C3semidirect
171. C3×#95C22×C3semidirect
172. C3×#95C22×C3semidirect
248. C2×#124C2×C32semidirect
249. C2×C22⋊Q8C2×C32semidirect
251. C22×C22⋊C4C2×C32semidirect
252. #397C2×C32semidirect
253. #394C2×C32semidirect
254. #394C2×C32semidirect
255. #393C2×C32semidirect
256. #390C2×C32semidirect
257. #388C2×C32semidirect
258. #388C2×C32semidirect
259. #386C2×C32semidirect
260. #386C2×C32semidirect
261. #379C2×C32semidirect
262. C4×C22⋊C4C2×C32semidirect
322. C3×C22⋊C4C3×D4semidirect
353. C22×C32#124semidirect
373. C22×Q8C22×C32semidirect
382. C2×C4⋊C4C22×C32semidirect
383. C2×C4⋊C4C22×C32semidirect
384. C2×C4⋊C4C22×C32semidirect
399. C2×C22⋊C4C22×C32semidirect
400. C2×C22⋊C4C22×C32semidirect
401. C2×C22⋊C4C22×C32semidirect
402. C2×C22⋊C4C22×C32semidirect
403. C2×C42C22×C32semidirect
404. C2×C42C22×C32semidirect
405. #95C22×C32semidirect
406. #95C22×C32semidirect
407. #95C22×C32semidirect
408. #95C22×C32semidirect
409. #95C22×C32semidirect
410. #95C22×C32semidirect
556. C22⋊C4C32×D4semidirect
587. C22×C3C3×#124semidirect
606. C32#2472direct (N × H)
721. C22C32×#124semidirect
740. C3C3×#2472direct (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×#1202
C22×C32×C22⋊C42
C32×#3972
C32×#3942
C32×#3932
C32×#3902
C32×#3882
C32×#3862
C32×#3792
C32×C4×C22⋊C42
C3×#24723