Finite Group Databasebeta

← C32×#2424 #11769473

Subgroups — C32×#2424 #11769473

Order 1152.

2766 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C2×C32×#120C211yesmaximal, characteristic, complemented
4C2×C32×#120C211yesmaximal, characteristic, complemented
5C2×C32×C4×D4C211yesmaximal, characteristic, complemented
6C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
7C32×#396C211yesmaximal, characteristic, complemented
8C32×#394C211yesmaximal, characteristic, complemented
9C32×#394C211yesmaximal, characteristic, complemented
10C32×#392C211yesmaximal, characteristic, complemented
11C32×#390C211yesmaximal, characteristic, complemented
12C32×#388C211yesmaximal, characteristic, complemented
13C32×#386C211yesmaximal, characteristic, complemented
14C32×#386C211yesmaximal, characteristic, complemented
15C32×#385C211yesmaximal, characteristic, complemented
16C3×#2424C314yesmaximal, direct product factor
17C25×C32C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic
22C22×C32×D4C2211yescharacteristic
23C22×C32×D4C2211yescharacteristic
24C22×C32×D4C2211yescharacteristic, complemented
25C23×C32×C4C2211yescharacteristic
26C23×C32×C4C2211yescharacteristic
27C23×C32×C4C2211yescharacteristic, complemented
28C32×#121—24no—
29C32×#121—24no—
30C32×#120—24no—
31C32×#120—24no—
32C32×C4×D4—24no—
33C2×C32×C4⋊C4C2211yescharacteristic, complemented
34C2×C32×C4⋊C4C2211yescharacteristic, complemented
35C2×C32×C4⋊C4C2211yescharacteristic, complemented
36C2×C32×C4⋊C4C2211yescharacteristic, complemented
37C2×C32×C22⋊C4—24no—
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, complemented
49C2×C32×C22⋊C4C2211yescharacteristic, complemented
50C2×C32×C22⋊C4C2211yescharacteristic, complemented
51C2×C32×C22⋊C4C2211yescharacteristic, complemented
52C2×C32×C22⋊C4C2211yescharacteristic, complemented
53C2×C32×C42C2211yescharacteristic, complemented
54C32×#95C2211yescharacteristic, complemented
55C32×#95C2211yescharacteristic, complemented
56C32×#95C2211yescharacteristic, complemented
57C32×#95C2211yescharacteristic, complemented
58C2×C3×#121C2×C314yescomplemented
59C2×C3×#121C2×C314yescomplemented
60C2×C3×#120C2×C314yescomplemented
61C2×C3×#120C2×C314yescomplemented
62C2×C3×C4×D4C2×C314yescomplemented
63C22×C3×C22⋊C4C2×C314yescomplemented
64C3×#396C2×C314yescomplemented
65C3×#394C2×C314yescomplemented
66C3×#394C2×C314yescomplemented
67C3×#392C2×C314yescomplemented
68C3×#390C2×C314yescomplemented
69C3×#388C2×C314yescomplemented
70C3×#386C2×C314yescomplemented
71C3×#386C2×C314yescomplemented
72C3×#385C2×C314yescomplemented
73C24×C32—22no—
74C24×C32—22no—
75C24×C32—22no—
76C24×C32—22no—
77C24×C32—22no—
78C24×C32—41no—
79C24×C32—41no—
80C24×C32C2311yescharacteristic
81C24×C32C2311yescharacteristic
82C24×C32C2311yescharacteristic
83C24×C32C2311yescharacteristic
84C24×C32C2311yescharacteristic
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—22no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—22no—
97C2×C32×D4—22no—
98C2×C32×D4—22no—
99C2×C32×D4—22no—
100C2×C32×D4—41no—
101C2×C32×D4—41no—
102C2×C32×D4—41no—
103C2×C32×D4—41no—
104C2×C32×D4—41no—
105C2×C32×D4D414yescomplemented
106C22×C32×C4—22no—
107C22×C32×C4—22no—
108C22×C32×C4—22no—
109C22×C32×C4—22no—
110C22×C32×C4—22no—
111C22×C32×C4—22no—
112C22×C32×C4—41no—
113C22×C32×C4—41no—
114C22×C32×C4—41no—
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C22×C32×C4C2311yescharacteristic
124C22×C32×C4C2311yescharacteristic
125C32×C4⋊C4—22no—
126C32×C4⋊C4—22no—
127C32×C4⋊C4—22no—
128C32×C4⋊C4—41no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—22no—
131C32×C22⋊C4—22no—
132C32×C22⋊C4—22no—
133C32×C22⋊C4—22no—
134C32×C22⋊C4—22no—
135C32×C22⋊C4—22no—
136C32×C22⋊C4—22no—
137C32×C22⋊C4—22no—
138C32×C22⋊C4—22no—
139C32×C22⋊C4—22no—
140C32×C22⋊C4—22no—
141C32×C22⋊C4—41no—
142C32×C22⋊C4D414yescomplemented
143C32×C22⋊C4D414yescomplemented
144C32×C42—22no—
145#2424C3211yescharacteristic, direct product factor, Sylow
146C25×C3C22×C314yes—
147C22×C3×D4C22×C314yes—
148C22×C3×D4C22×C314yes—
149C22×C3×D4C22×C314yes—
150C22×C3×D4C22×C314yes—
151C22×C3×D4C22×C314yes—
152C22×C3×D4C22×C314yes—
153C22×C3×D4C22×C314yescomplemented
154C23×C3×C4C22×C314yes—
155C23×C3×C4C22×C314yes—
156C23×C3×C4C22×C314yescomplemented
157C3×#121—216no—
158C3×#121—216no—
159C3×#120—216no—
160C3×#120—216no—
161C3×C4×D4—216no—
162C2×C3×C4⋊C4C22×C314yescomplemented
163C2×C3×C4⋊C4C22×C314yescomplemented
164C2×C3×C4⋊C4C22×C314yescomplemented
165C2×C3×C4⋊C4C22×C314yescomplemented
166C2×C3×C22⋊C4—216no—
167C2×C3×C22⋊C4C22×C314yes—
168C2×C3×C22⋊C4C22×C314yes—
169C2×C3×C22⋊C4C22×C314yes—
170C2×C3×C22⋊C4C22×C314yes—
171C2×C3×C22⋊C4C22×C314yes—
172C2×C3×C22⋊C4C22×C314yes—
173C2×C3×C22⋊C4C22×C314yes—
174C2×C3×C22⋊C4C22×C314yes—
175C2×C3×C22⋊C4C22×C314yes—
176C2×C3×C22⋊C4C22×C314yes—
177C2×C3×C22⋊C4C22×C314yescomplemented
178C2×C3×C22⋊C4C22×C314yescomplemented
179C2×C3×C22⋊C4C22×C314yescomplemented
180C2×C3×C22⋊C4C22×C314yescomplemented
181C2×C3×C22⋊C4C22×C314yescomplemented
182C2×C3×C42C22×C314yescomplemented
183C3×#95C22×C314yescomplemented
184C3×#95C22×C314yescomplemented
185C3×#95C22×C314yescomplemented
186C3×#95C22×C314yescomplemented
187C23×C32—21no—
188C23×C32—21no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—28no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—21no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—44no—
218C23×C32—44no—
219C23×C32—44no—
220C23×C32—44no—
221C23×C32—44no—
222C23×C32—44no—
223C23×C32C2×D412yes—
224C23×C32C2×D412yes—
225C23×C32C2×D412yes—
226C23×C32C2×D412yes—
227C23×C32#4112yes—
228C23×C32#4112yes—
229C23×C32C2411yescharacteristic
230C32×D4—28no—
231C32×D4—44no—
232C32×D4—44no—
233C32×D4—44no—
234C32×D4—44no—
235C32×D4—44no—
236C32×D4—44no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—44no—
263C2×C32×C4—44no—
264C2×C32×C4—44no—
265C2×C32×C4C2×D412yes—
266C2×C32×C4C2×D412yes—
267C2×C32×C4C2×D412yes—
268C2×C32×C4C2×D412yes—
269C2×C32×C4C2×D412yes—
270C2×#121C2×C3211yescharacteristic, complemented
271C2×#121C2×C3211yescharacteristic, complemented
272C2×#120C2×C3211yescharacteristic, complemented
273C2×#120C2×C3211yescharacteristic, complemented
274C2×C4×D4C2×C3211yescharacteristic, complemented
275C22×C22⋊C4C2×C3211yescharacteristic, complemented
276#396C2×C3211yescharacteristic, complemented
277#394C2×C3211yescharacteristic, complemented
278#394C2×C3211yescharacteristic, complemented
279#392C2×C3211yescharacteristic, complemented
280#390C2×C3211yescharacteristic, complemented
281#388C2×C3211yescharacteristic, complemented
282#386C2×C3211yescharacteristic, complemented
283#386C2×C3211yescharacteristic, complemented
284#385C2×C3211yescharacteristic, complemented
285C24×C3—28no—
286C24×C3—28no—
287C24×C3—28no—
288C24×C3—28no—
289C24×C3—28no—
290C24×C3—44no—
291C24×C3—44no—
292C24×C3C23×C314yes—
293C24×C3C23×C314yes—
294C24×C3C23×C314yes—
295C24×C3C23×C314yes—
296C24×C3C23×C314yes—
297C2×C3×D4—28no—
298C2×C3×D4—28no—
299C2×C3×D4—28no—
300C2×C3×D4—28no—
301C2×C3×D4—28no—
302C2×C3×D4—28no—
303C2×C3×D4—28no—
304C2×C3×D4—28no—
305C2×C3×D4—28no—
306C2×C3×D4—28no—
307C2×C3×D4—28no—
308C2×C3×D4—28no—
309C2×C3×D4—28no—
310C2×C3×D4—28no—
311C2×C3×D4—28no—
312C2×C3×D4—44no—
313C2×C3×D4—44no—
314C2×C3×D4—44no—
315C2×C3×D4—44no—
316C2×C3×D4—44no—
317C2×C3×D4C3×D4116yescomplemented
318C22×C3×C4—28no—
319C22×C3×C4—28no—
320C22×C3×C4—28no—
321C22×C3×C4—28no—
322C22×C3×C4—28no—
323C22×C3×C4—28no—
324C22×C3×C4—44no—
325C22×C3×C4—44no—
326C22×C3×C4—44no—
327C22×C3×C4C23×C314yes—
328C22×C3×C4C23×C314yes—
329C22×C3×C4C23×C314yes—
330C22×C3×C4C23×C314yes—
331C22×C3×C4C23×C314yes—
332C22×C3×C4C23×C314yes—
333C22×C3×C4C23×C314yes—
334C22×C3×C4C23×C314yes—
335C22×C3×C4C23×C314yes—
336C22×C3×C4C23×C314yes—
337C3×C4⋊C4—28no—
338C3×C4⋊C4—28no—
339C3×C4⋊C4—28no—
340C3×C4⋊C4—44no—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—28no—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—28no—
345C3×C22⋊C4—28no—
346C3×C22⋊C4—28no—
347C3×C22⋊C4—28no—
348C3×C22⋊C4—28no—
349C3×C22⋊C4—28no—
350C3×C22⋊C4—28no—
351C3×C22⋊C4—28no—
352C3×C22⋊C4—28no—
353C3×C22⋊C4—44no—
354C3×C22⋊C4C3×D4116yescomplemented
355C3×C22⋊C4C3×D4116yescomplemented
356C3×C42—28no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—22no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—416no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32—41no—
380C22×C32—41no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32#12114yescomplemented
393C22×C32C22×D411yescharacteristic
394C22×C32C22×D411yescharacteristic
395C22×C32C22×D411yescharacteristic
396C22×C32C2×#4111yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32H(5,𝔽2)11yescharacteristic
399C22×C32H(5,𝔽2)11yescharacteristic
400C32×C4—22no—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—22no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4—41no—
410C25C22×C3211yescharacteristic
411C22×D4C22×C3211yescharacteristic
412C22×D4C22×C3211yescharacteristic
413C22×D4C22×C3211yescharacteristic
414C22×D4C22×C3211yescharacteristic
415C22×D4C22×C3211yescharacteristic
416C22×D4C22×C3211yescharacteristic
417C22×D4C22×C3211yescharacteristic, complemented
418C23×C4C22×C3211yescharacteristic
419C23×C4C22×C3211yescharacteristic
420C23×C4C22×C3211yescharacteristic, complemented
421#121—24no—
422#121—24no—
423#120—24no—
424#120—24no—
425C4×D4—24no—
426C2×C4⋊C4C22×C3211yescharacteristic, complemented
427C2×C4⋊C4C22×C3211yescharacteristic, complemented
428C2×C4⋊C4C22×C3211yescharacteristic, complemented
429C2×C4⋊C4C22×C3211yescharacteristic, complemented
430C2×C22⋊C4—24no—
431C2×C22⋊C4C22×C3211yescharacteristic
432C2×C22⋊C4C22×C3211yescharacteristic
433C2×C22⋊C4C22×C3211yescharacteristic
434C2×C22⋊C4C22×C3211yescharacteristic
435C2×C22⋊C4C22×C3211yescharacteristic
436C2×C22⋊C4C22×C3211yescharacteristic
437C2×C22⋊C4C22×C3211yescharacteristic
438C2×C22⋊C4C22×C3211yescharacteristic
439C2×C22⋊C4C22×C3211yescharacteristic
440C2×C22⋊C4C22×C3211yescharacteristic
441C2×C22⋊C4C22×C3211yescharacteristic, complemented
442C2×C22⋊C4C22×C3211yescharacteristic, complemented
443C2×C22⋊C4C22×C3211yescharacteristic, complemented
444C2×C22⋊C4C22×C3211yescharacteristic, complemented
445C2×C22⋊C4C22×C3211yescharacteristic, complemented
446C2×C42C22×C3211yescharacteristic, complemented
447#95C22×C3211yescharacteristic, complemented
448#95C22×C3211yescharacteristic, complemented
449#95C22×C3211yescharacteristic, complemented
450#95C22×C3211yescharacteristic, complemented
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—232no—
456C23×C3—24no—
457C23×C3—24no—
458C23×C3—24no—
459C23×C3—24no—
460C23×C3—24no—
461C23×C3—24no—
462C23×C3—24no—
463C23×C3—24no—
464C23×C3—24no—
465C23×C3—24no—
466C23×C3—24no—
467C23×C3—24no—
468C23×C3—24no—
469C23×C3—24no—
470C23×C3—24no—
471C23×C3—24no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—24no—
477C23×C3—24no—
478C23×C3—24no—
479C23×C3—24no—
480C23×C3—24no—
481C23×C3—416no—
482C23×C3—416no—
483C23×C3—416no—
484C23×C3—416no—
485C23×C3—416no—
486C23×C3—416no—
487C23×C3C2×C3×D418yes—
488C23×C3C2×C3×D418yes—
489C23×C3C2×C3×D418yes—
490C23×C3C2×C3×D418yes—
491C23×C3C3×#4118yes—
492C23×C3C3×#4118yes—
493C23×C3C24×C314yes—
494C3×D4—232no—
495C3×D4—416no—
496C3×D4—416no—
497C3×D4—416no—
498C3×D4—416no—
499C3×D4—416no—
500C3×D4—416no—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—24no—
504C2×C3×C4—24no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—24no—
516C2×C3×C4—24no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—24no—
526C2×C3×C4—416no—
527C2×C3×C4—416no—
528C2×C3×C4—416no—
529C2×C3×C4C2×C3×D418yes—
530C2×C3×C4C2×C3×D418yes—
531C2×C3×C4C2×C3×D418yes—
532C2×C3×C4C2×C3×D418yes—
533C2×C3×C4C2×C3×D418yes—
534C2×C32—24no—
535C2×C32—42no—
536C2×C32—42no—
537C2×C32—42no—
538C2×C32—81no—
539C2×C32C2×#12111yescharacteristic
540C2×C32#52511yescharacteristic
541C2×C32#53811yescharacteristic
542C2×C32D4211yescharacteristic
543C2×C32D4211yescharacteristic
544C2×C32#54611yescharacteristic
545C2×C32#54611yescharacteristic
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—41no—
552C24—41no—
553C24C23×C3211yescharacteristic
554C24C23×C3211yescharacteristic
555C24C23×C3211yescharacteristic
556C24C23×C3211yescharacteristic
557C24C23×C3211yescharacteristic
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4C32×D414yescomplemented
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4C23×C3211yescharacteristic
589C22×C4C23×C3211yescharacteristic
590C22×C4C23×C3211yescharacteristic
591C22×C4C23×C3211yescharacteristic
592C22×C4C23×C3211yescharacteristic
593C22×C4C23×C3211yescharacteristic
594C22×C4C23×C3211yescharacteristic
595C22×C4C23×C3211yescharacteristic
596C22×C4C23×C3211yescharacteristic
597C22×C4C23×C3211yescharacteristic
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—41no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—41no—
615C22⋊C4C32×D414yescomplemented
616C22⋊C4C32×D414yescomplemented
617C42—22no—
618C22×C3—28no—
619C22×C3—28no—
620C22×C3—28no—
621C22×C3—28no—
622C22×C3—28no—
623C22×C3—28no—
624C22×C3—28no—
625C22×C3—28no—
626C22×C3—28no—
627C22×C3—28no—
628C22×C3—28no—
629C22×C3—28no—
630C22×C3—28no—
631C22×C3—28no—
632C22×C3—28no—
633C22×C3—464no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—44no—
652C22×C3—44no—
653C22×C3C3×#121116yescomplemented
654C22×C3C22×C3×D414yes—
655C22×C3C22×C3×D414yes—
656C22×C3C22×C3×D414yes—
657C22×C3C2×C3×#4114yes—
658C22×C3C2×C3×#4114yes—
659C22×C3C3×H(5,𝔽2)14yes—
660C22×C3C3×H(5,𝔽2)14yes—
661C3×C4—28no—
662C3×C4—28no—
663C3×C4—28no—
664C3×C4—28no—
665C3×C4—28no—
666C3×C4—44no—
667C3×C4—44no—
668C3×C4—44no—
669C3×C4—44no—
670C3×C4—44no—
671C32#242411yescharacteristic, direct product factor, Sylow
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—28no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23C2×C32×D412yes—
709C23C2×C32×D412yes—
710C23C2×C32×D412yes—
711C23C2×C32×D412yes—
712C23C32×#4112yes—
713C23C32×#4112yes—
714C23C24×C3211yescharacteristic
715D4—28no—
716D4—44no—
717D4—44no—
718D4—44no—
719D4—44no—
720D4—44no—
721D4—44no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4C2×C32×D412yes—
751C2×C4C2×C32×D412yes—
752C2×C4C2×C32×D412yes—
753C2×C4C2×C32×D412yes—
754C2×C4C2×C32×D412yes—
755C2×C3—216no—
756C2×C3—48no—
757C2×C3—48no—
758C2×C3—48no—
759C2×C3—84no—
760C2×C3C2×C3×#12114yes—
761C2×C3C3×#52514yes—
762C2×C3C3×#53814yes—
763C2×C3C3×D4214yes—
764C2×C3C3×D4214yes—
765C2×C3C3×#54614yes—
766C2×C3C3×#54614yes—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—416no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22C32×#12114yescomplemented
803C22C22×C32×D411yescharacteristic
804C22C22×C32×D411yescharacteristic
805C22C22×C32×D411yescharacteristic
806C22C2×C32×#4111yescharacteristic
807C22C2×C32×#4111yescharacteristic
808C22C32×H(5,𝔽2)11yescharacteristic
809C22C32×H(5,𝔽2)11yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—22no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C3C3×#242414yesdirect product factor
821C2—24no—
822C2—42no—
823C2—42no—
824C2—42no—
825C2—81no—
826C2C2×C32×#12111yescharacteristic
827C2C32×#52511yescharacteristic
828C2C32×#53811yescharacteristic
829C2C32×D4211yescharacteristic
830C2C32×D4211yescharacteristic
831C2C32×#54611yescharacteristic
832C2C32×#54611yescharacteristic
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×#121C2semidirect
2. C2×C32×#121C2semidirect
3. C2×C32×#120C2semidirect
4. C2×C32×#120C2semidirect
5. C2×C32×C4×D4C2semidirect
6. C22×C32×C22⋊C4C2semidirect
7. C32×#396C2semidirect
8. C32×#394C2semidirect
9. C32×#394C2semidirect
10. C32×#392C2semidirect
11. C32×#390C2semidirect
12. C32×#388C2semidirect
13. C32×#386C2semidirect
14. C32×#386C2semidirect
15. C32×#385C2semidirect
16. C3×#2424C3direct (N × H)
24. C22×C32×D4C22semidirect
27. C23×C32×C4C22semidirect
33. C2×C32×C4⋊C4C22semidirect
34. C2×C32×C4⋊C4C22semidirect
35. C2×C32×C4⋊C4C22semidirect
36. C2×C32×C4⋊C4C22semidirect
48. C2×C32×C22⋊C4C22semidirect
49. C2×C32×C22⋊C4C22semidirect
50. C2×C32×C22⋊C4C22semidirect
51. C2×C32×C22⋊C4C22semidirect
52. C2×C32×C22⋊C4C22semidirect
53. C2×C32×C42C22semidirect
54. C32×#95C22semidirect
55. C32×#95C22semidirect
56. C32×#95C22semidirect
57. C32×#95C22semidirect
58. C2×C3×#121C2×C3semidirect
59. C2×C3×#121C2×C3semidirect
60. C2×C3×#120C2×C3semidirect
61. C2×C3×#120C2×C3semidirect
62. C2×C3×C4×D4C2×C3semidirect
63. C22×C3×C22⋊C4C2×C3semidirect
64. C3×#396C2×C3semidirect
65. C3×#394C2×C3semidirect
66. C3×#394C2×C3semidirect
67. C3×#392C2×C3semidirect
68. C3×#390C2×C3semidirect
69. C3×#388C2×C3semidirect
70. C3×#386C2×C3semidirect
71. C3×#386C2×C3semidirect
72. C3×#385C2×C3semidirect
105. C2×C32×D4D4semidirect
142. C32×C22⋊C4D4semidirect
143. C32×C22⋊C4D4semidirect
145. #2424C32direct (N × H)
153. C22×C3×D4C22×C3semidirect
156. C23×C3×C4C22×C3semidirect
162. C2×C3×C4⋊C4C22×C3semidirect
163. C2×C3×C4⋊C4C22×C3semidirect
164. C2×C3×C4⋊C4C22×C3semidirect
165. C2×C3×C4⋊C4C22×C3semidirect
177. C2×C3×C22⋊C4C22×C3semidirect
178. C2×C3×C22⋊C4C22×C3semidirect
179. C2×C3×C22⋊C4C22×C3semidirect
180. C2×C3×C22⋊C4C22×C3semidirect
181. C2×C3×C22⋊C4C22×C3semidirect
182. C2×C3×C42C22×C3semidirect
183. C3×#95C22×C3semidirect
184. C3×#95C22×C3semidirect
185. C3×#95C22×C3semidirect
186. C3×#95C22×C3semidirect
270. C2×#121C2×C32semidirect
271. C2×#121C2×C32semidirect
272. C2×#120C2×C32semidirect
273. C2×#120C2×C32semidirect
274. C2×C4×D4C2×C32semidirect
275. C22×C22⋊C4C2×C32semidirect
276. #396C2×C32semidirect
277. #394C2×C32semidirect
278. #394C2×C32semidirect
279. #392C2×C32semidirect
280. #390C2×C32semidirect
281. #388C2×C32semidirect
282. #386C2×C32semidirect
283. #386C2×C32semidirect
284. #385C2×C32semidirect
317. C2×C3×D4C3×D4semidirect
354. C3×C22⋊C4C3×D4semidirect
355. C3×C22⋊C4C3×D4semidirect
392. C22×C32#121semidirect
417. C22×D4C22×C32semidirect
420. C23×C4C22×C32semidirect
426. C2×C4⋊C4C22×C32semidirect
427. C2×C4⋊C4C22×C32semidirect
428. C2×C4⋊C4C22×C32semidirect
429. C2×C4⋊C4C22×C32semidirect
441. C2×C22⋊C4C22×C32semidirect
442. C2×C22⋊C4C22×C32semidirect
443. C2×C22⋊C4C22×C32semidirect
444. C2×C22⋊C4C22×C32semidirect
445. C2×C22⋊C4C22×C32semidirect
446. C2×C42C22×C32semidirect
447. #95C22×C32semidirect
448. #95C22×C32semidirect
449. #95C22×C32semidirect
450. #95C22×C32semidirect
578. C2×D4C32×D4semidirect
615. C22⋊C4C32×D4semidirect
616. C22⋊C4C32×D4semidirect
653. C22×C3C3×#121semidirect
671. C32#2424direct (N × H)
802. C22C32×#121semidirect
820. C3C3×#2424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C32×#1202
C2×C32×C4×D42
C22×C32×C22⋊C42
C32×#3962
C32×#3942
C32×#3922
C32×#3902
C32×#3882
C32×#3862
C32×#3852
C3×#24243