Finite Group Databasebeta

← C32×#2678 #11769727

Subgroups — C32×#2678 #11769727

Order 1152.

2406 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#123C211yesmaximal, characteristic, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C2×C32×#120C211yesmaximal, characteristic, complemented
4C2×C32×#120C211yesmaximal, characteristic, complemented
5C32×#397C211yesmaximal, characteristic, complemented
6C32×#396C211yesmaximal, characteristic, complemented
7C32×#394C211yesmaximal, characteristic, complemented
8C32×#394C211yesmaximal, characteristic, complemented
9C32×#392C211yesmaximal, characteristic, complemented
10C32×#392C211yesmaximal, characteristic, complemented
11C32×#390C211yesmaximal, characteristic, complemented
12C32×#390C211yesmaximal, characteristic, complemented
13C32×#388C211yesmaximal, characteristic, complemented
14C32×#386C211yesmaximal, characteristic, complemented
15C32×#379C211yesmaximal, characteristic, complemented
16C3×#2678C314yesmaximal, 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, complemented
26C32×#123—24no—
27C32×#121—24no—
28C32×#120—24no—
29C32×#120—24no—
30C2×C32×C4⋊C4C2211yescharacteristic, complemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×C32×C4⋊C4C2211yescharacteristic, complemented
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×C22⋊C4C2211yescharacteristic, complemented
47C2×C32×C22⋊C4C2211yescharacteristic, complemented
48C2×C32×C22⋊C4C2211yescharacteristic, complemented
49C2×C32×C22⋊C4C2211yescharacteristic, complemented
50C2×C32×C22⋊C4C2211yescharacteristic, complemented
51C2×C32×C42C2211yescharacteristic, complemented
52C32×#95C2211yescharacteristic, complemented
53C32×#95C2211yescharacteristic, complemented
54C32×#95C2211yescharacteristic, complemented
55C32×#95C2211yescharacteristic, complemented
56C2×C3×#123C2×C314yescomplemented
57C2×C3×#121C2×C314yescomplemented
58C2×C3×#120C2×C314yescomplemented
59C2×C3×#120C2×C314yescomplemented
60C3×#397C2×C314yescomplemented
61C3×#396C2×C314yescomplemented
62C3×#394C2×C314yescomplemented
63C3×#394C2×C314yescomplemented
64C3×#392C2×C314yescomplemented
65C3×#392C2×C314yescomplemented
66C3×#390C2×C314yescomplemented
67C3×#390C2×C314yescomplemented
68C3×#388C2×C314yescomplemented
69C3×#386C2×C314yescomplemented
70C3×#379C2×C314yescomplemented
71C24×C32—22no—
72C24×C32—22no—
73C24×C32—22no—
74C24×C32—41no—
75C24×C32—41no—
76C24×C32—41no—
77C24×C32—41no—
78C24×C32C2311yescharacteristic
79C24×C32C2311yescharacteristic
80C24×C32C2311yescharacteristic
81C24×C32C2311yescharacteristic
82C24×C32C2311yescharacteristic
83C2×C32×D4—22no—
84C2×C32×D4—22no—
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—41no—
94C2×C32×D4—41no—
95C2×C32×D4—41no—
96C2×C32×D4—41no—
97C2×C32×D4—41no—
98C2×C32×D4—41no—
99C2×C32×D4—41no—
100C2×C32×D4—41no—
101C2×C32×D4—41no—
102C2×C32×D4—41no—
103C2×C32×D4D414yescomplemented
104C22×C32×C4—22no—
105C22×C32×C4—22no—
106C22×C32×C4—41no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2311yescharacteristic
117C32×C4⋊C4—22no—
118C32×C4⋊C4—22no—
119C32×C4⋊C4—22no—
120C32×C4⋊C4—41no—
121C32×C22⋊C4—22no—
122C32×C22⋊C4—22no—
123C32×C22⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—22no—
127C32×C22⋊C4—22no—
128C32×C22⋊C4—22no—
129C32×C22⋊C4—22no—
130C32×C22⋊C4—41no—
131C32×C22⋊C4—41no—
132C32×C22⋊C4—41no—
133C32×C22⋊C4—41no—
134C32×C22⋊C4—41no—
135C32×C22⋊C4—41no—
136C32×C22⋊C4—41no—
137C32×C22⋊C4D414yescomplemented
138C32×C42—41no—
139#2678C3211yescharacteristic, direct product factor, Sylow
140C25×C3C22×C314yes—
141C22×C3×D4C22×C314yes—
142C22×C3×D4C22×C314yes—
143C22×C3×D4C22×C314yes—
144C22×C3×D4C22×C314yes—
145C22×C3×D4C22×C314yes—
146C22×C3×D4C22×C314yes—
147C22×C3×D4C22×C314yescomplemented
148C23×C3×C4C22×C314yescomplemented
149C3×#123—216no—
150C3×#121—216no—
151C3×#120—216no—
152C3×#120—216no—
153C2×C3×C4⋊C4C22×C314yescomplemented
154C2×C3×C4⋊C4C22×C314yescomplemented
155C2×C3×C4⋊C4C22×C314yescomplemented
156C2×C3×C4⋊C4C22×C314yescomplemented
157C2×C3×C22⋊C4C22×C314yes—
158C2×C3×C22⋊C4C22×C314yes—
159C2×C3×C22⋊C4C22×C314yes—
160C2×C3×C22⋊C4C22×C314yes—
161C2×C3×C22⋊C4C22×C314yes—
162C2×C3×C22⋊C4C22×C314yes—
163C2×C3×C22⋊C4C22×C314yes—
164C2×C3×C22⋊C4C22×C314yes—
165C2×C3×C22⋊C4C22×C314yes—
166C2×C3×C22⋊C4C22×C314yes—
167C2×C3×C22⋊C4C22×C314yes—
168C2×C3×C22⋊C4C22×C314yes—
169C2×C3×C22⋊C4C22×C314yescomplemented
170C2×C3×C22⋊C4C22×C314yescomplemented
171C2×C3×C22⋊C4C22×C314yescomplemented
172C2×C3×C22⋊C4C22×C314yescomplemented
173C2×C3×C22⋊C4C22×C314yescomplemented
174C2×C3×C42C22×C314yescomplemented
175C3×#95C22×C314yescomplemented
176C3×#95C22×C314yescomplemented
177C3×#95C22×C314yescomplemented
178C3×#95C22×C314yescomplemented
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—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—44no—
211C23×C32—44no—
212C23×C32—44no—
213C23×C32—44no—
214C23×C32—44no—
215C23×C32—44no—
216C23×C32—44no—
217C23×C32C2×D412yes—
218C23×C32C2×D412yes—
219C23×C32C2×D412yes—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
222C32×D4—44no—
223C32×D4—44no—
224C32×D4—44no—
225C32×D4—44no—
226C32×D4—44no—
227C32×D4—44no—
228C32×D4—44no—
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—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—44no—
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2×D412yes—
260C2×#123C2×C3211yescharacteristic, complemented
261C2×#121C2×C3211yescharacteristic, complemented
262C2×#120C2×C3211yescharacteristic, complemented
263C2×#120C2×C3211yescharacteristic, complemented
264#397C2×C3211yescharacteristic, complemented
265#396C2×C3211yescharacteristic, complemented
266#394C2×C3211yescharacteristic, complemented
267#394C2×C3211yescharacteristic, complemented
268#392C2×C3211yescharacteristic, complemented
269#392C2×C3211yescharacteristic, complemented
270#390C2×C3211yescharacteristic, complemented
271#390C2×C3211yescharacteristic, complemented
272#388C2×C3211yescharacteristic, complemented
273#386C2×C3211yescharacteristic, complemented
274#379C2×C3211yescharacteristic, complemented
275C24×C3—28no—
276C24×C3—28no—
277C24×C3—28no—
278C24×C3—44no—
279C24×C3—44no—
280C24×C3—44no—
281C24×C3—44no—
282C24×C3C23×C314yes—
283C24×C3C23×C314yes—
284C24×C3C23×C314yes—
285C24×C3C23×C314yes—
286C24×C3C23×C314yes—
287C2×C3×D4—28no—
288C2×C3×D4—28no—
289C2×C3×D4—28no—
290C2×C3×D4—28no—
291C2×C3×D4—28no—
292C2×C3×D4—28no—
293C2×C3×D4—28no—
294C2×C3×D4—28no—
295C2×C3×D4—28no—
296C2×C3×D4—28no—
297C2×C3×D4—44no—
298C2×C3×D4—44no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—44no—
303C2×C3×D4—44no—
304C2×C3×D4—44no—
305C2×C3×D4—44no—
306C2×C3×D4—44no—
307C2×C3×D4C3×D4116yescomplemented
308C22×C3×C4—28no—
309C22×C3×C4—28no—
310C22×C3×C4—44no—
311C22×C3×C4C23×C314yes—
312C22×C3×C4C23×C314yes—
313C22×C3×C4C23×C314yes—
314C22×C3×C4C23×C314yes—
315C22×C3×C4C23×C314yes—
316C22×C3×C4C23×C314yes—
317C22×C3×C4C23×C314yes—
318C22×C3×C4C23×C314yes—
319C22×C3×C4C23×C314yes—
320C22×C3×C4C23×C314yes—
321C3×C4⋊C4—28no—
322C3×C4⋊C4—28no—
323C3×C4⋊C4—28no—
324C3×C4⋊C4—44no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—28no—
328C3×C22⋊C4—28no—
329C3×C22⋊C4—28no—
330C3×C22⋊C4—28no—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—28no—
333C3×C22⋊C4—28no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4C3×D4116yescomplemented
342C3×C42—44no—
343C22×C32—22no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—416no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—41no—
359C22×C32—41no—
360C22×C32—41no—
361C22×C32—41no—
362C22×C32—41no—
363C22×C32—41no—
364C22×C32—41no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32C22×D411yescharacteristic
380C22×C32C22×D411yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32H(5,𝔽2)11yescharacteristic
383C22×C32H(5,𝔽2)11yescharacteristic
384C22×C32H(5,𝔽2)11yescharacteristic
385C22×C32H(5,𝔽2)11yescharacteristic
386C32×C4—22no—
387C32×C4—22no—
388C32×C4—22no—
389C32×C4—41no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4—41no—
395C32×C4—41no—
396C25C22×C3211yescharacteristic
397C22×D4C22×C3211yescharacteristic
398C22×D4C22×C3211yescharacteristic
399C22×D4C22×C3211yescharacteristic
400C22×D4C22×C3211yescharacteristic
401C22×D4C22×C3211yescharacteristic
402C22×D4C22×C3211yescharacteristic
403C22×D4C22×C3211yescharacteristic, complemented
404C23×C4C22×C3211yescharacteristic, complemented
405#123—24no—
406#121—24no—
407#120—24no—
408#120—24no—
409C2×C4⋊C4C22×C3211yescharacteristic, complemented
410C2×C4⋊C4C22×C3211yescharacteristic, complemented
411C2×C4⋊C4C22×C3211yescharacteristic, complemented
412C2×C4⋊C4C22×C3211yescharacteristic, complemented
413C2×C22⋊C4C22×C3211yescharacteristic
414C2×C22⋊C4C22×C3211yescharacteristic
415C2×C22⋊C4C22×C3211yescharacteristic
416C2×C22⋊C4C22×C3211yescharacteristic
417C2×C22⋊C4C22×C3211yescharacteristic
418C2×C22⋊C4C22×C3211yescharacteristic
419C2×C22⋊C4C22×C3211yescharacteristic
420C2×C22⋊C4C22×C3211yescharacteristic
421C2×C22⋊C4C22×C3211yescharacteristic
422C2×C22⋊C4C22×C3211yescharacteristic
423C2×C22⋊C4C22×C3211yescharacteristic
424C2×C22⋊C4C22×C3211yescharacteristic
425C2×C22⋊C4C22×C3211yescharacteristic, complemented
426C2×C22⋊C4C22×C3211yescharacteristic, complemented
427C2×C22⋊C4C22×C3211yescharacteristic, complemented
428C2×C22⋊C4C22×C3211yescharacteristic, complemented
429C2×C22⋊C4C22×C3211yescharacteristic, complemented
430C2×C42C22×C3211yescharacteristic, complemented
431#95C22×C3211yescharacteristic, complemented
432#95C22×C3211yescharacteristic, complemented
433#95C22×C3211yescharacteristic, complemented
434#95C22×C3211yescharacteristic, complemented
435C23×C3—24no—
436C23×C3—24no—
437C23×C3—24no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—24no—
442C23×C3—24no—
443C23×C3—24no—
444C23×C3—24no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3—24no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
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—416no—
467C23×C3—416no—
468C23×C3—416no—
469C23×C3—416no—
470C23×C3—416no—
471C23×C3—416no—
472C23×C3—416no—
473C23×C3C2×C3×D418yes—
474C23×C3C2×C3×D418yes—
475C23×C3C2×C3×D418yes—
476C23×C3C3×#4118yes—
477C23×C3C24×C314yes—
478C3×D4—416no—
479C3×D4—416no—
480C3×D4—416no—
481C3×D4—416no—
482C3×D4—416no—
483C3×D4—416no—
484C3×D4—416no—
485C2×C3×C4—24no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—24no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
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—416no—
513C2×C3×C4C2×C3×D418yes—
514C2×C3×C4C2×C3×D418yes—
515C2×C3×C4C2×C3×D418yes—
516C2×C32—42no—
517C2×C32—42no—
518C2×C32—42no—
519C2×C32—42no—
520C2×C32—81no—
521C2×C32#53411yescharacteristic
522C2×C32#53511yescharacteristic
523C2×C32#53811yescharacteristic
524C2×C32D4211yescharacteristic
525C2×C32#54611yescharacteristic
526C2×C32#54611yescharacteristic
527C2×C32#56011yescharacteristic
528C24—22no—
529C24—22no—
530C24—22no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—41no—
535C24C23×C3211yescharacteristic
536C24C23×C3211yescharacteristic
537C24C23×C3211yescharacteristic
538C24C23×C3211yescharacteristic
539C24C23×C3211yescharacteristic
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4C32×D414yescomplemented
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4C23×C3211yescharacteristic
565C22×C4C23×C3211yescharacteristic
566C22×C4C23×C3211yescharacteristic
567C22×C4C23×C3211yescharacteristic
568C22×C4C23×C3211yescharacteristic
569C22×C4C23×C3211yescharacteristic
570C22×C4C23×C3211yescharacteristic
571C22×C4C23×C3211yescharacteristic
572C22×C4C23×C3211yescharacteristic
573C22×C4C23×C3211yescharacteristic
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—41no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4C32×D414yescomplemented
595C42—41no—
596C22×C3—28no—
597C22×C3—28no—
598C22×C3—28no—
599C22×C3—28no—
600C22×C3—28no—
601C22×C3—28no—
602C22×C3—28no—
603C22×C3—28no—
604C22×C3—28no—
605C22×C3—28no—
606C22×C3—28no—
607C22×C3—28no—
608C22×C3—464no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—44no—
612C22×C3—44no—
613C22×C3—44no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3C22×C3×D414yes—
633C22×C3C22×C3×D414yes—
634C22×C3C2×C3×#4114yes—
635C22×C3C3×H(5,𝔽2)14yes—
636C22×C3C3×H(5,𝔽2)14yes—
637C22×C3C3×H(5,𝔽2)14yes—
638C22×C3C3×H(5,𝔽2)14yes—
639C3×C4—28no—
640C3×C4—28no—
641C3×C4—28no—
642C3×C4—44no—
643C3×C4—44no—
644C3×C4—44no—
645C3×C4—44no—
646C3×C4—44no—
647C3×C4—44no—
648C3×C4—44no—
649C32#267811yescharacteristic, direct product factor, Sylow
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23C2×C32×D412yes—
689C23C2×C32×D412yes—
690C23C2×C32×D412yes—
691C23C32×#4112yes—
692C23C24×C3211yescharacteristic
693D4—44no—
694D4—44no—
695D4—44no—
696D4—44no—
697D4—44no—
698D4—44no—
699D4—44no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4C2×C32×D412yes—
729C2×C4C2×C32×D412yes—
730C2×C4C2×C32×D412yes—
731C2×C3—48no—
732C2×C3—48no—
733C2×C3—48no—
734C2×C3—48no—
735C2×C3—84no—
736C2×C3C3×#53414yes—
737C2×C3C3×#53514yes—
738C2×C3C3×#53814yes—
739C2×C3C3×D4214yes—
740C2×C3C3×#54614yes—
741C2×C3C3×#54614yes—
742C2×C3C3×#56014yes—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—416no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22C22×C32×D411yescharacteristic
780C22C22×C32×D411yescharacteristic
781C22C2×C32×#4111yescharacteristic
782C22C32×H(5,𝔽2)11yescharacteristic
783C22C32×H(5,𝔽2)11yescharacteristic
784C22C32×H(5,𝔽2)11yescharacteristic
785C22C32×H(5,𝔽2)11yescharacteristic
786C4—22no—
787C4—22no—
788C4—22no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C3C3×#267814yesdirect product factor
797C2—42no—
798C2—42no—
799C2—42no—
800C2—42no—
801C2—81no—
802C2C32×#53411yescharacteristic
803C2C32×#53511yescharacteristic
804C2C32×#53811yescharacteristic
805C2C32×D4211yescharacteristic
806C2C32×#54611yescharacteristic
807C2C32×#54611yescharacteristic
808C2C32×#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×#123C2semidirect
2. C2×C32×#121C2semidirect
3. C2×C32×#120C2semidirect
4. C2×C32×#120C2semidirect
5. C32×#397C2semidirect
6. C32×#396C2semidirect
7. C32×#394C2semidirect
8. C32×#394C2semidirect
9. C32×#392C2semidirect
10. C32×#392C2semidirect
11. C32×#390C2semidirect
12. C32×#390C2semidirect
13. C32×#388C2semidirect
14. C32×#386C2semidirect
15. C32×#379C2semidirect
16. C3×#2678C3direct (N × H)
24. C22×C32×D4C22semidirect
25. C23×C32×C4C22semidirect
30. C2×C32×C4⋊C4C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C2×C32×C4⋊C4C22semidirect
33. C2×C32×C4⋊C4C22semidirect
46. C2×C32×C22⋊C4C22semidirect
47. C2×C32×C22⋊C4C22semidirect
48. C2×C32×C22⋊C4C22semidirect
49. C2×C32×C22⋊C4C22semidirect
50. C2×C32×C22⋊C4C22semidirect
51. C2×C32×C42C22semidirect
52. C32×#95C22semidirect
53. C32×#95C22semidirect
54. C32×#95C22semidirect
55. C32×#95C22semidirect
56. C2×C3×#123C2×C3semidirect
57. C2×C3×#121C2×C3semidirect
58. C2×C3×#120C2×C3semidirect
59. C2×C3×#120C2×C3semidirect
60. C3×#397C2×C3semidirect
61. C3×#396C2×C3semidirect
62. C3×#394C2×C3semidirect
63. C3×#394C2×C3semidirect
64. C3×#392C2×C3semidirect
65. C3×#392C2×C3semidirect
66. C3×#390C2×C3semidirect
67. C3×#390C2×C3semidirect
68. C3×#388C2×C3semidirect
69. C3×#386C2×C3semidirect
70. C3×#379C2×C3semidirect
103. C2×C32×D4D4semidirect
137. C32×C22⋊C4D4semidirect
139. #2678C32direct (N × H)
147. C22×C3×D4C22×C3semidirect
148. C23×C3×C4C22×C3semidirect
153. C2×C3×C4⋊C4C22×C3semidirect
154. C2×C3×C4⋊C4C22×C3semidirect
155. C2×C3×C4⋊C4C22×C3semidirect
156. C2×C3×C4⋊C4C22×C3semidirect
169. C2×C3×C22⋊C4C22×C3semidirect
170. C2×C3×C22⋊C4C22×C3semidirect
171. C2×C3×C22⋊C4C22×C3semidirect
172. C2×C3×C22⋊C4C22×C3semidirect
173. C2×C3×C22⋊C4C22×C3semidirect
174. C2×C3×C42C22×C3semidirect
175. C3×#95C22×C3semidirect
176. C3×#95C22×C3semidirect
177. C3×#95C22×C3semidirect
178. C3×#95C22×C3semidirect
260. C2×#123C2×C32semidirect
261. C2×#121C2×C32semidirect
262. C2×#120C2×C32semidirect
263. C2×#120C2×C32semidirect
264. #397C2×C32semidirect
265. #396C2×C32semidirect
266. #394C2×C32semidirect
267. #394C2×C32semidirect
268. #392C2×C32semidirect
269. #392C2×C32semidirect
270. #390C2×C32semidirect
271. #390C2×C32semidirect
272. #388C2×C32semidirect
273. #386C2×C32semidirect
274. #379C2×C32semidirect
307. C2×C3×D4C3×D4semidirect
341. C3×C22⋊C4C3×D4semidirect
403. C22×D4C22×C32semidirect
404. C23×C4C22×C32semidirect
409. C2×C4⋊C4C22×C32semidirect
410. C2×C4⋊C4C22×C32semidirect
411. C2×C4⋊C4C22×C32semidirect
412. C2×C4⋊C4C22×C32semidirect
425. C2×C22⋊C4C22×C32semidirect
426. C2×C22⋊C4C22×C32semidirect
427. C2×C22⋊C4C22×C32semidirect
428. C2×C22⋊C4C22×C32semidirect
429. C2×C22⋊C4C22×C32semidirect
430. C2×C42C22×C32semidirect
431. #95C22×C32semidirect
432. #95C22×C32semidirect
433. #95C22×C32semidirect
434. #95C22×C32semidirect
560. C2×D4C32×D4semidirect
594. C22⋊C4C32×D4semidirect
649. C32#2678direct (N × H)
796. C3C3×#2678direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1232
C2×C32×#1212
C2×C32×#1202
C32×#3972
C32×#3962
C32×#3942
C32×#3922
C32×#3902
C32×#3882
C32×#3862
C32×#3792
C3×#26783