Finite Group Databasebeta

← C32×#2685 #11769734

Subgroups — C32×#2685 #11769734

Order 1152.

1998 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#126C211yesmaximal, characteristic, complemented
2C2×C32×#120C211yesmaximal, characteristic
3C32×#399C211yesmaximal, characteristic, complemented
4C32×#396C211yesmaximal, characteristic, complemented
5C32×#394C211yesmaximal, characteristic, complemented
6C32×#394C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8C32×#394C211yesmaximal, characteristic, complemented
9C32×#390C211yesmaximal, characteristic, complemented
10C32×#390C211yesmaximal, characteristic, complemented
11C32×#388C211yesmaximal, characteristic, complemented
12C32×#388C211yesmaximal, characteristic, complemented
13C32×#388C211yesmaximal, characteristic, complemented
14C32×#379C211yesmaximal, characteristic, complemented
15C32×#379C211yesmaximal, characteristic, complemented
16C3×#2685C314yesmaximal, direct product factor
17C25×C32C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C32×#126—24no—
22C32×#120—24no—
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C4⋊C4C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C32×C22⋊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, 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
54C2×C3×#126C2×C314yescomplemented
55C2×C3×#120C2×C314yes—
56C3×#399C2×C314yescomplemented
57C3×#396C2×C314yescomplemented
58C3×#394C2×C314yescomplemented
59C3×#394C2×C314yescomplemented
60C3×#394C2×C314yescomplemented
61C3×#394C2×C314yescomplemented
62C3×#390C2×C314yescomplemented
63C3×#390C2×C314yescomplemented
64C3×#388C2×C314yescomplemented
65C3×#388C2×C314yescomplemented
66C3×#388C2×C314yescomplemented
67C3×#379C2×C314yescomplemented
68C3×#379C2×C314yescomplemented
69C24×C32—22no—
70C24×C32—22no—
71C24×C32—22no—
72C24×C32—41no—
73C24×C32—41no—
74C24×C32—41no—
75C24×C32—41no—
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C24×C32C2311yescharacteristic
79C24×C32C2311yescharacteristic
80C2×C32×D4—22no—
81C2×C32×D4—22no—
82C2×C32×D4—22no—
83C2×C32×D4—22no—
84C2×C32×D4—22no—
85C2×C32×D4—41no—
86C2×C32×D4—41no—
87C2×C32×D4—41no—
88C2×C32×D4—41no—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C32×C4⋊C4—22no—
101C32×C4⋊C4—22no—
102C32×C4⋊C4—22no—
103C32×C4⋊C4—41no—
104C32×C4⋊C4—41no—
105C32×C4⋊C4—41no—
106C32×C22⋊C4—22no—
107C32×C22⋊C4—22no—
108C32×C22⋊C4—22no—
109C32×C22⋊C4—22no—
110C32×C22⋊C4—22no—
111C32×C22⋊C4—22no—
112C32×C22⋊C4—41no—
113C32×C22⋊C4—41no—
114C32×C22⋊C4—41no—
115C32×C22⋊C4—41no—
116C32×C22⋊C4—41no—
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⋊C4D414yes—
125C32×C42—22no—
126C32×C42—41no—
127#2685C3211yescharacteristic, direct product factor, Sylow
128C25×C3C22×C314yes—
129C22×C3×D4C22×C314yes—
130C22×C3×D4C22×C314yes—
131C22×C3×D4C22×C314yes—
132C3×#126—216no—
133C3×#120—216no—
134C2×C3×C4⋊C4C22×C314yescomplemented
135C2×C3×C4⋊C4C22×C314yescomplemented
136C2×C3×C4⋊C4C22×C314yescomplemented
137C2×C3×C4⋊C4C22×C314yescomplemented
138C2×C3×C4⋊C4C22×C314yescomplemented
139C2×C3×C4⋊C4C22×C314yescomplemented
140C2×C3×C22⋊C4C22×C314yes—
141C2×C3×C22⋊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×C314yescomplemented
156C2×C3×C22⋊C4C22×C314yescomplemented
157C2×C3×C22⋊C4C22×C314yescomplemented
158C2×C3×C22⋊C4C22×C314yescomplemented
159C2×C3×C42C22×C314yescomplemented
160C2×C3×C42C22×C314yescomplemented
161C3×#95C22×C314yescomplemented
162C3×#95C22×C314yescomplemented
163C3×#95C22×C314yescomplemented
164C3×#95C22×C314yescomplemented
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—44no—
191C23×C32—44no—
192C23×C32—44no—
193C23×C32—44no—
194C23×C32—44no—
195C23×C32—44no—
196C23×C32—44no—
197C23×C32C2×D412yes—
198C23×C32#4112yes—
199C23×C32#4112yes—
200C23×C32C2411yescharacteristic
201C32×D4—44no—
202C32×D4—44no—
203C32×D4—44no—
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—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2×D412yes—
236C2×C32×C4C2×D412yes—
237C2×#126C2×C3211yescharacteristic, complemented
238C2×#120C2×C3211yescharacteristic
239#399C2×C3211yescharacteristic, complemented
240#396C2×C3211yescharacteristic, complemented
241#394C2×C3211yescharacteristic, complemented
242#394C2×C3211yescharacteristic, complemented
243#394C2×C3211yescharacteristic, complemented
244#394C2×C3211yescharacteristic, complemented
245#390C2×C3211yescharacteristic, complemented
246#390C2×C3211yescharacteristic, complemented
247#388C2×C3211yescharacteristic, complemented
248#388C2×C3211yescharacteristic, complemented
249#388C2×C3211yescharacteristic, complemented
250#379C2×C3211yescharacteristic, complemented
251#379C2×C3211yescharacteristic, complemented
252C24×C3—28no—
253C24×C3—28no—
254C24×C3—28no—
255C24×C3—44no—
256C24×C3—44no—
257C24×C3—44no—
258C24×C3—44no—
259C24×C3C23×C314yes—
260C24×C3C23×C314yes—
261C24×C3C23×C314yes—
262C24×C3C23×C314yes—
263C2×C3×D4—28no—
264C2×C3×D4—28no—
265C2×C3×D4—28no—
266C2×C3×D4—28no—
267C2×C3×D4—28no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
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—
279C22×C3×C4C23×C314yes—
280C22×C3×C4C23×C314yes—
281C22×C3×C4C23×C314yes—
282C22×C3×C4C23×C314yes—
283C3×C4⋊C4—28no—
284C3×C4⋊C4—28no—
285C3×C4⋊C4—28no—
286C3×C4⋊C4—44no—
287C3×C4⋊C4—44no—
288C3×C4⋊C4—44no—
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⋊C4—44no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—44no—
302C3×C22⋊C4—44no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—44no—
305C3×C22⋊C4—44no—
306C3×C22⋊C4—44no—
307C3×C22⋊C4C3×D4116yes—
308C3×C42—28no—
309C3×C42—44no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—416no—
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×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—41no—
339C22×C32C22×D411yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32H(5,𝔽2)11yescharacteristic
343C22×C32H(5,𝔽2)11yescharacteristic
344C22×C32H(5,𝔽2)11yescharacteristic
345C22×C32H(5,𝔽2)11yescharacteristic
346C32×C4—22no—
347C32×C4—22no—
348C32×C4—41no—
349C32×C4—41no—
350C32×C4—41no—
351C32×C4—41no—
352C32×C4—41no—
353C32×C4—41no—
354C32×C4—41no—
355C32×C4—41no—
356C32×C4—41no—
357C25C22×C3211yescharacteristic
358C22×D4C22×C3211yescharacteristic
359C22×D4C22×C3211yescharacteristic
360C22×D4C22×C3211yescharacteristic
361#126—24no—
362#120—24no—
363C2×C4⋊C4C22×C3211yescharacteristic, complemented
364C2×C4⋊C4C22×C3211yescharacteristic, complemented
365C2×C4⋊C4C22×C3211yescharacteristic, complemented
366C2×C4⋊C4C22×C3211yescharacteristic, complemented
367C2×C4⋊C4C22×C3211yescharacteristic, complemented
368C2×C4⋊C4C22×C3211yescharacteristic, complemented
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×C22⋊C4C22×C3211yescharacteristic
383C2×C22⋊C4C22×C3211yescharacteristic
384C2×C22⋊C4C22×C3211yescharacteristic, complemented
385C2×C22⋊C4C22×C3211yescharacteristic, complemented
386C2×C22⋊C4C22×C3211yescharacteristic, complemented
387C2×C22⋊C4C22×C3211yescharacteristic, complemented
388C2×C42C22×C3211yescharacteristic, complemented
389C2×C42C22×C3211yescharacteristic, complemented
390#95C22×C3211yescharacteristic, complemented
391#95C22×C3211yescharacteristic, complemented
392#95C22×C3211yescharacteristic, complemented
393#95C22×C3211yescharacteristic, complemented
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×C3—24no—
418C23×C3—24no—
419C23×C3—416no—
420C23×C3—416no—
421C23×C3—416no—
422C23×C3—416no—
423C23×C3—416no—
424C23×C3—416no—
425C23×C3—416no—
426C23×C3C2×C3×D418yes—
427C23×C3C3×#4118yes—
428C23×C3C3×#4118yes—
429C23×C3C24×C314yes—
430C3×D4—416no—
431C3×D4—416no—
432C3×D4—416no—
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—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×C4C2×C3×D418yes—
465C2×C3×C4C2×C3×D418yes—
466C2×C32—42no—
467C2×C32—42no—
468C2×C32—42no—
469C2×C32—81no—
470C2×C32#53511yescharacteristic
471C2×C32#53811yescharacteristic
472C2×C32#53811yescharacteristic
473C2×C32#54611yescharacteristic
474C2×C32#54611yescharacteristic
475C2×C32#55111yescharacteristic
476C2×C32#56011yescharacteristic
477C24—22no—
478C24—22no—
479C24—22no—
480C24—41no—
481C24—41no—
482C24—41no—
483C24—41no—
484C24C23×C3211yescharacteristic
485C24C23×C3211yescharacteristic
486C24C23×C3211yescharacteristic
487C24C23×C3211yescharacteristic
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—41no—
496C2×D4—41no—
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
506C22×C4C23×C3211yescharacteristic
507C22×C4C23×C3211yescharacteristic
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4C32×D414yes—
533C42—22no—
534C42—41no—
535C22×C3—28no—
536C22×C3—28no—
537C22×C3—28no—
538C22×C3—28no—
539C22×C3—28no—
540C22×C3—28no—
541C22×C3—28no—
542C22×C3—28no—
543C22×C3—28no—
544C22×C3—464no—
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×C3—44no—
557C22×C3—44no—
558C22×C3—44no—
559C22×C3—44no—
560C22×C3—44no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3C22×C3×D414yes—
565C22×C3C2×C3×#4114yes—
566C22×C3C2×C3×#4114yes—
567C22×C3C3×H(5,𝔽2)14yes—
568C22×C3C3×H(5,𝔽2)14yes—
569C22×C3C3×H(5,𝔽2)14yes—
570C22×C3C3×H(5,𝔽2)14yes—
571C3×C4—28no—
572C3×C4—28no—
573C3×C4—44no—
574C3×C4—44no—
575C3×C4—44no—
576C3×C4—44no—
577C3×C4—44no—
578C3×C4—44no—
579C3×C4—44no—
580C3×C4—44no—
581C3×C4—44no—
582C32#268511yescharacteristic, direct product factor, Sylow
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—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×C32×D412yes—
616C23C32×#4112yes—
617C23C32×#4112yes—
618C23C24×C3211yescharacteristic
619D4—44no—
620D4—44no—
621D4—44no—
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—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×C4C2×C32×D412yes—
654C2×C4C2×C32×D412yes—
655C2×C3—48no—
656C2×C3—48no—
657C2×C3—48no—
658C2×C3—84no—
659C2×C3C3×#53514yes—
660C2×C3C3×#53814yes—
661C2×C3C3×#53814yes—
662C2×C3C3×#54614yes—
663C2×C3C3×#54614yes—
664C2×C3C3×#55114yes—
665C2×C3C3×#56014yes—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—416no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22C22×C32×D411yescharacteristic
696C22C2×C32×#4111yescharacteristic
697C22C2×C32×#4111yescharacteristic
698C22C32×H(5,𝔽2)11yescharacteristic
699C22C32×H(5,𝔽2)11yescharacteristic
700C22C32×H(5,𝔽2)11yescharacteristic
701C22C32×H(5,𝔽2)11yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C3C3×#268514yesdirect product factor
714C2—42no—
715C2—42no—
716C2—42no—
717C2—81no—
718C2C32×#53511yescharacteristic
719C2C32×#53811yescharacteristic
720C2C32×#53811yescharacteristic
721C2C32×#54611yescharacteristic
722C2C32×#54611yescharacteristic
723C2C32×#55111yescharacteristic
724C2C32×#56011yescharacteristic
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×#126C2semidirect
3. C32×#399C2semidirect
4. C32×#396C2semidirect
5. C32×#394C2semidirect
6. C32×#394C2semidirect
7. C32×#394C2semidirect
8. C32×#394C2semidirect
9. C32×#390C2semidirect
10. C32×#390C2semidirect
11. C32×#388C2semidirect
12. C32×#388C2semidirect
13. C32×#388C2semidirect
14. C32×#379C2semidirect
15. C32×#379C2semidirect
16. C3×#2685C3direct (N × H)
23. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×C32×C4⋊C4C22semidirect
26. C2×C32×C4⋊C4C22semidirect
27. C2×C32×C4⋊C4C22semidirect
28. 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. C2×C3×#126C2×C3semidirect
56. C3×#399C2×C3semidirect
57. C3×#396C2×C3semidirect
58. C3×#394C2×C3semidirect
59. C3×#394C2×C3semidirect
60. C3×#394C2×C3semidirect
61. C3×#394C2×C3semidirect
62. C3×#390C2×C3semidirect
63. C3×#390C2×C3semidirect
64. C3×#388C2×C3semidirect
65. C3×#388C2×C3semidirect
66. C3×#388C2×C3semidirect
67. C3×#379C2×C3semidirect
68. C3×#379C2×C3semidirect
127. #2685C32direct (N × H)
134. C2×C3×C4⋊C4C22×C3semidirect
135. C2×C3×C4⋊C4C22×C3semidirect
136. C2×C3×C4⋊C4C22×C3semidirect
137. C2×C3×C4⋊C4C22×C3semidirect
138. C2×C3×C4⋊C4C22×C3semidirect
139. C2×C3×C4⋊C4C22×C3semidirect
155. C2×C3×C22⋊C4C22×C3semidirect
156. C2×C3×C22⋊C4C22×C3semidirect
157. C2×C3×C22⋊C4C22×C3semidirect
158. C2×C3×C22⋊C4C22×C3semidirect
159. C2×C3×C42C22×C3semidirect
160. C2×C3×C42C22×C3semidirect
161. C3×#95C22×C3semidirect
162. C3×#95C22×C3semidirect
163. C3×#95C22×C3semidirect
164. C3×#95C22×C3semidirect
237. C2×#126C2×C32semidirect
239. #399C2×C32semidirect
240. #396C2×C32semidirect
241. #394C2×C32semidirect
242. #394C2×C32semidirect
243. #394C2×C32semidirect
244. #394C2×C32semidirect
245. #390C2×C32semidirect
246. #390C2×C32semidirect
247. #388C2×C32semidirect
248. #388C2×C32semidirect
249. #388C2×C32semidirect
250. #379C2×C32semidirect
251. #379C2×C32semidirect
363. C2×C4⋊C4C22×C32semidirect
364. C2×C4⋊C4C22×C32semidirect
365. C2×C4⋊C4C22×C32semidirect
366. C2×C4⋊C4C22×C32semidirect
367. C2×C4⋊C4C22×C32semidirect
368. C2×C4⋊C4C22×C32semidirect
384. C2×C22⋊C4C22×C32semidirect
385. C2×C22⋊C4C22×C32semidirect
386. C2×C22⋊C4C22×C32semidirect
387. C2×C22⋊C4C22×C32semidirect
388. C2×C42C22×C32semidirect
389. C2×C42C22×C32semidirect
390. #95C22×C32semidirect
391. #95C22×C32semidirect
392. #95C22×C32semidirect
393. #95C22×C32semidirect
582. C32#2685direct (N × H)
713. C3C3×#2685direct (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×#1202
C32×#3992
C32×#3962
C32×#3942
C32×#3902
C32×#3882
C32×#3792
C3×#26853