Finite Group Databasebeta

← #528352

Subgroups — #528352

Order 512.

2526 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2734C211yesmaximal, characteristic
2C2×#2331C211yesmaximal, characteristic
3C2×C4×C4⋊Q8C211yesmaximal, characteristic
4#14704C211yesmaximal, characteristic
5#14548C211yesmaximal, characteristic
6#14524C211yesmaximal, characteristic
7#14450C211yesmaximal, characteristic
8#14439C211yesmaximal, characteristic
9#14414C211yesmaximal, characteristic
10#14406C211yesmaximal, characteristic
11#14404C211yesmaximal, characteristic
12#14327C211yesmaximal, characteristic
13#14320C211yesmaximal, characteristic
14#14236C211yesmaximal, characteristic
15#14219C211yesmaximal, characteristic
16#14217C211yesmaximal, characteristic
17#14214C211yesmaximal, characteristic
18#14212C211yesmaximal, characteristic
19#14211C211yesmaximal, characteristic
20#14186C211yesmaximal, characteristic
21#14174C211yesmaximal, characteristic
22#14092C211yesmaximal, characteristic
23#14087C211yesmaximal, characteristic
24#14035C211yesmaximal, characteristic
25#14024C211yesmaximal, characteristic
26#14017C211yesmaximal, characteristic
27#13985C211yesmaximal, characteristic
28#13821C211yesmaximal, characteristic
29#13815C211yesmaximal, characteristic
30#13793C211yesmaximal, characteristic
31C4×#387C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36#2734C4116yescomplemented
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#395C2211yescharacteristic
40C2×#395C2211yescharacteristic
41C2×#395C2211yescharacteristic
42C2×#395C2211yescharacteristic
43#2331—28no—
44C4×C4⋊Q8—28no—
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#389C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#389C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#387C2211yescharacteristic
66C2×#387C2211yescharacteristic
67C2×#387C2211yescharacteristic
68C2×#387C2211yescharacteristic
69C2×#387C2211yescharacteristic
70C2×#387C2211yescharacteristic
71C2×#387C2211yescharacteristic
72C2×#387C2211yescharacteristic
73C2×#387C2211yescharacteristic
74C2×#387C2211yescharacteristic
75C2×#387C2211yescharacteristic
76C2×#387C2211yescharacteristic
77C2×#384C2211yescharacteristic
78C2×#382C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C4⋊C4C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic
87C2×C4×C4⋊C4C2211yescharacteristic
88C2×#376C2211yescharacteristic
89C2×C43C2211yescharacteristic
90#1446C2211yescharacteristic
91#1446C2211yescharacteristic
92#1445C2211yescharacteristic
93#1445C2211yescharacteristic
94#1444C2211yescharacteristic
95#1444C2211yescharacteristic
96#1444C2211yescharacteristic
97#1444C2211yescharacteristic
98#1444C2211yescharacteristic
99#1444C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1442C2211yescharacteristic
106#1442C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1442C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1441C2211yescharacteristic
121#1441C2211yescharacteristic
122#1441C2211yescharacteristic
123#1441C2211yescharacteristic
124#1436C2211yescharacteristic
125#1436C2211yescharacteristic
126#1436C2211yescharacteristic
127#1436C2211yescharacteristic
128#1436C2211yescharacteristic
129#1436C2211yescharacteristic
130#1436C2211yescharacteristic
131#1436C2211yescharacteristic
132#1436C2211yescharacteristic
133#1436C2211yescharacteristic
134#1436C2211yescharacteristic
135#1436C2211yescharacteristic
136#1436C2211yescharacteristic
137#1436C2211yescharacteristic
138#1436C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
145#1436C2211yescharacteristic
146#1436C2211yescharacteristic
147#1436C2211yescharacteristic
148#1436C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164C4⋊#95C2211yescharacteristic
165C4⋊#95C2211yescharacteristic
166C4⋊#95C2211yescharacteristic
167C4⋊#95C2211yescharacteristic
168C4⋊#95C2211yescharacteristic
169#1434C2211yescharacteristic
170#1434C2211yescharacteristic
171#1434C2211yescharacteristic
172#1434C2211yescharacteristic
173#1434C2211yescharacteristic
174#1434C2211yescharacteristic
175#1434C2211yescharacteristic
176#1434C2211yescharacteristic
177#1434C2211yescharacteristic
178#1434C2211yescharacteristic
179#1434C2211yescharacteristic
180#1434C2211yescharacteristic
181#1434C2211yescharacteristic
182C4×#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C4×#95C2211yescharacteristic
189C4×#95C2211yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192C23×Q8C2311yescharacteristic
193C2×C4⋊Q8—24no—
194C2×C4⋊Q8—24no—
195C2×C4⋊Q8—24no—
196C2×C4⋊Q8—24no—
197C2×C4⋊Q8C2×C418yes—
198C2×C4⋊Q8C2×C418yes—
199C2×C4×Q8—24no—
200C2×C4×Q8—24no—
201C2×C4×Q8—42no—
202C2×C4×Q8—42no—
203C2×C4×Q8—42no—
204C2×C4×Q8—42no—
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263#398C2×C418yes—
264#398C2×C418yes—
265#395C2×C418yes—
266#395C2×C418yes—
267#395C2×C418yes—
268#395C2×C418yes—
269#391—24no—
270#391—24no—
271#391—24no—
272#391—24no—
273#391—24no—
274#391—42no—
275#391—42no—
276#391C2×C418yes—
277#391D418yes—
278#389—24no—
279#389—24no—
280#389—24no—
281#389—24no—
282#389—24no—
283#389—24no—
284#389—24no—
285#389—42no—
286#389—42no—
287#389C2×C418yes—
288#389C2×C418yes—
289#387—24no—
290#387—24no—
291#387—24no—
292#387—24no—
293#387—24no—
294#387—24no—
295#387—42no—
296#387—42no—
297#387C2×C418yes—
298#387C2×C418yes—
299#387C2×C418yes—
300#387C2×C418yes—
301#384—24no—
302#382—24no—
303C4×C4⋊C4—24no—
304C4×C4⋊C4—24no—
305C4×C4⋊C4—24no—
306C4×C4⋊C4—24no—
307C4×C4⋊C4—24no—
308C4×C4⋊C4—24no—
309C4×C4⋊C4—42no—
310C4×C4⋊C4—42no—
311C4×C4⋊C4Q818yescomplemented
312#376—24no—
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2311yescharacteristic
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2311yescharacteristic
384C2×#95C2311yescharacteristic
385C2×#95C2311yescharacteristic
386C2×#95C2311yescharacteristic
387C2×#95C2311yescharacteristic
388C2×#95C2311yescharacteristic
389C2×#95C2311yescharacteristic
390C2×#95C2311yescharacteristic
391C2×#95C2311yescharacteristic
392C2×#95C2311yescharacteristic
393C2×#95C2311yescharacteristic
394C2×#95C2311yescharacteristic
395C2×#95C2311yescharacteristic
396C2×#95C2311yescharacteristic
397C2×#95C2311yescharacteristic
398C2×#95C2311yescharacteristic
399C2×#95C2311yescharacteristic
400C2×#95C2311yescharacteristic
401C2×#95C2311yescharacteristic
402C2×#95C2311yescharacteristic
403C2×#95C2311yescharacteristic
404C2×#95C2311yescharacteristic
405C2×#95C2311yescharacteristic
406C2×#95C2311yescharacteristic
407C43—24no—
408C22×Q8—22no—
409C22×Q8—22no—
410C22×Q8—22no—
411C22×Q8—22no—
412C22×Q8—41no—
413C22×Q8—41no—
414C22×Q8—41no—
415C22×Q8—41no—
416C22×Q8—41no—
417C22×Q8—41no—
418C22×Q8—41no—
419C22×Q8—41no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8—41no—
423C22×Q8—41no—
424C22×Q8C22×C414yes—
425C22×Q8C22×C414yes—
426C22×Q8C22×C414yes—
427C22×Q8C2×D414yes—
428C22×Q8#4114yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C4⋊Q8—232no—
461C4⋊Q8—232no—
462C4×Q8—416no—
463C4×Q8—416no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4C22×C414yes—
551C2×C4⋊C4C22×C414yes—
552C2×C4⋊C4C22×C414yes—
553C2×C4⋊C4C22×C414yes—
554C2×C4⋊C4C22×C414yes—
555C2×C4⋊C4C22×C414yes—
556C2×C4⋊C4C22×C414yes—
557C2×C4⋊C4C22×C414yes—
558C2×C4⋊C4C22×C414yes—
559C2×C4⋊C4C22×C414yes—
560C2×C4⋊C4C22×C414yes—
561C2×C4⋊C4C22×C414yes—
562C2×C4⋊C4C22×C414yes—
563C2×C4⋊C4C22×C414yes—
564C2×C4⋊C4C22×C414yes—
565C2×C4⋊C4C2×D414yes—
566C2×C4⋊C4C2×Q814yes—
567C2×C4⋊C4C2×Q814yes—
568C2×C4⋊C4#4114yes—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—41no—
622C2×C42—41no—
623C2×C42—41no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42C22×C414yes—
632C2×C42C22×C414yes—
633C2×C42C22×C414yes—
634C2×C42C2×D414yes—
635C2×C42C2×Q814yes—
636C2×C42C2×Q814yes—
637C2×C42C2×Q814yes—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95C22×C414yes—
713#95C22×C414yes—
714#95C22×C414yes—
715#95C22×C414yes—
716#95C22×C414yes—
717#95C22×C414yes—
718#95C22×C414yes—
719#95C22×C414yes—
720#95C22×C414yes—
721#95C22×C414yes—
722#95C22×C414yes—
723#95C22×C414yes—
724#95C22×C414yes—
725#95C22×C414yes—
726#95C2×D414yes—
727#95C2×D414yes—
728#95C2×D414yes—
729#95C2×D414yes—
730#95C2×Q814yes—
731#95C2×Q814yes—
732C24C2511yescharacteristic
733C2×Q8—28no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—44no—
741C2×Q8—44no—
742C2×Q8—44no—
743C2×Q8—44no—
744C2×Q8—44no—
745C2×Q8—44no—
746C2×Q8—44no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—82no—
750C2×Q8—82no—
751C2×Q8—82no—
752C2×Q8—82no—
753C2×Q8C4×D4116yes—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4C23×C412yes—
931C22×C4C23×C412yes—
932C22×C4C23×C412yes—
933C22×C4C23×C412yes—
934C22×C4C23×C412yes—
935C22×C4C23×C412yes—
936C22×C4C23×C412yes—
937C22×C4C23×C412yes—
938C22×C4C23×C412yes—
939C22×C4C23×C412yes—
940C22×C4C23×C412yes—
941C22×C4C23×C412yes—
942C22×C4C23×C412yes—
943C22×C4C23×C412yes—
944C22×C4C23×C412yes—
945C22×C4C22×D412yes—
946C22×C4C22×D412yes—
947C22×C4C22×D412yes—
948C22×C4C22×D412yes—
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C22×D412yes—
952C22×C4C22×Q812yes—
953C22×C4C22×Q812yes—
954C22×C4C22×Q812yes—
955C22×C4C22×Q812yes—
956C22×C4C22×Q812yes—
957C22×C4C22×Q812yes—
958C22×C4C22×Q812yes—
959C22×C4C2×#4112yes—
960C22×C4C2×#4112yes—
961C22×C4C2×#4112yes—
962C22×C4C2×#4112yes—
963C22×C4C2×#4112yes—
964C22×C4C2×#4112yes—
965C22×C4H(5,𝔽2)12yes—
966C22×C4H(5,𝔽2)12yes—
967C22×C42−1+412yes—
968C22×C42−1+412yes—
969C22×C42−1+412yes—
970C22×C42−1+412yes—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—44no—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—44no—
992C4⋊C4—44no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—82no—
1000C4⋊C4—82no—
1001C4⋊C4—82no—
1002C4⋊C4—82no—
1003C4⋊C4—82no—
1004C4⋊C4—82no—
1005C4⋊C4C4×Q8116yescomplemented
1006C42—28no—
1007C42—28no—
1008C42—28no—
1009C42—28no—
1010C42—28no—
1011C42—28no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—44no—
1016C42—44no—
1017C42—44no—
1018C42—44no—
1019C42—44no—
1020C42—44no—
1021C42—44no—
1022C42—44no—
1023C42—82no—
1024C42—82no—
1025C42—82no—
1026C42—82no—
1027C42—82no—
1028C42—82no—
1029C23C24×C411yescharacteristic
1030C23C23×D411yescharacteristic
1031C23C23×Q811yescharacteristic
1032C23C22×#4111yescharacteristic
1033C23C22×#4111yescharacteristic
1034C23C2×H(5,𝔽2)11yescharacteristic
1035C23C2×H(5,𝔽2)11yescharacteristic
1036C23C2×2−1+411yescharacteristic
1037C23C2×2−1+411yescharacteristic
1038C23C2×2−1+411yescharacteristic
1039C23C2×2−1+411yescharacteristic
1040C23#58511yescharacteristic
1041C23#58511yescharacteristic
1042C23#58511yescharacteristic
1043C23#58511yescharacteristic
1044Q8—416no—
1045Q8—416no—
1046Q8—88no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4C2×C4×D414yes—
1256C2×C4C2×C4×D414yes—
1257C2×C4C2×C4×D414yes—
1258C2×C4C2×C4×Q814yes—
1259C2×C4C2×C4×Q814yes—
1260C2×C4C2×C4×Q814yes—
1261C2×C4#51914yes—
1262C2×C4#54414yes—
1263C2×C4D4×Q814yes—
1264C22C22×C4×D411yescharacteristic
1265C22C22×C4×Q811yescharacteristic
1266C22C2×#51911yescharacteristic
1267C22C4×H(5,𝔽2)11yescharacteristic
1268C22C4×H(5,𝔽2)11yescharacteristic
1269C22C4×2−1+411yescharacteristic
1270C22C4×2−1+411yescharacteristic
1271C22C2×#54411yescharacteristic
1272C22#345811yescharacteristic
1273C22#346011yescharacteristic
1274C22#346111yescharacteristic
1275C22C2×D4×Q811yescharacteristic
1276C22D4×#4111yescharacteristic
1277C22Q8×#4111yescharacteristic
1278C22#348211yescharacteristic
1279C22#348411yescharacteristic
1280C22#348511yescharacteristic
1281C22#348611yescharacteristic
1282C22#348911yescharacteristic
1283C22#350211yescharacteristic
1284C22#350311yescharacteristic
1285C22#350511yescharacteristic
1286C22#350511yescharacteristic
1287C22#351611yescharacteristic
1288C22#351811yescharacteristic
1289C22#352211yescharacteristic
1290C22#352311yescharacteristic
1291C22#354411yescharacteristic
1292C22#354711yescharacteristic
1293C22#355211yescharacteristic
1294C22#355711yescharacteristic
1295C22#356011yescharacteristic
1296C22#356311yescharacteristic
1297C22#356411yescharacteristic
1298C22#356511yescharacteristic
1299C4—24no—
1300C4—24no—
1301C4—24no—
1302C4—24no—
1303C4—24no—
1304C4—24no—
1305C4—24no—
1306C4—24no—
1307C4—24no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C2C4×#54411yescharacteristic
1331C2C4×D4×Q811yescharacteristic
1332C2#3426411yescharacteristic
1333C2#3429111yescharacteristic
1334C2#3433511yescharacteristic
1335C2#3443511yescharacteristic
1336C2#3452511yescharacteristic
1337C2#3768611yescharacteristic
1338C2#3768911yescharacteristic
1339C2#3781011yescharacteristic
1340C2#3782311yescharacteristic
1341C2#3996911yescharacteristic
1342C2#3997511yescharacteristic
1343C2#4046311yescharacteristic
1344C2#4047111yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
36. #2734C4semidirect
311. C4×C4⋊C4Q8semidirect
1005. C4⋊C4C4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#27342
C2×#23312
C2×C4×C4⋊Q82
#147042
#145482
#145242
#144502
#144392
#144142
#144062
#144042
#143272
#143202
#142362
#142192
#142172
#142142
#142122
#142112
#141862
#141742
#140922
#140872
#140352
#140242
#140172
#139852
#138212
#138152
#137932
C4×#3872