Finite Group Databasebeta

← #10800526

Subgroups — #10800526

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic
2#73561C211yesmaximal, characteristic, complemented
3C4×D3×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×C4×#99C211yesmaximal, characteristic, complemented
5C4×#834C211yesmaximal, characteristic, complemented
6#70036C212yesmaximal, complemented
7#70030C212yesmaximal, complemented
8C4×#806C211yesmaximal, characteristic, complemented
9C4×#806C211yesmaximal, characteristic, complemented
10#68970C212yesmaximal, complemented
11#68955C212yesmaximal, complemented
12#21420—31nomaximal, Sylow
13C22×#235C411yescharacteristic, complemented
14C23×C4×D3C2211yescharacteristic
15C2×C3×C4×D4C2211yescharacteristic
16C2×#939C2211yescharacteristic
17C2×#937C2211yescharacteristic
18C2×C4×#67C411yescharacteristic, complemented
19C2×C4×#67C2211yescharacteristic
20#5547—21no—
21#5547—21no—
22#5547—21no—
23#5547—21no—
24#5547—21no—
25#5547—21no—
26#5547—21no—
27#5547—21no—
28C2×#896C411yescharacteristic, complemented
29C2×#894C411yescharacteristic, complemented
30C2×#884C411yescharacteristic, complemented
31C2×#883C411yescharacteristic, complemented
32C2×#882C2211yescharacteristic
33C2×D3×C22⋊C4C2212yes—
34C2×#878C2211yescharacteristic
35C2×C4×D12C411yescharacteristic, complemented
36C2×#872—21no—
37C2×#872C411yescharacteristic, complemented
38C2×C42×D3—21no—
39C2×C3×#99C2212yes—
40C3×C4×C22⋊C4C2211yescharacteristic
41C3×C4×C22⋊C4C2211yescharacteristic
42C2×#834C2212yes—
43C4×#217C2211yescharacteristic
44C4×#217C2211yescharacteristic
45#4955C2212yes—
46C2×#806C2212yes—
47C2×#806C2212yes—
48#4942C2212yes—
49Dic3×C22⋊C4C2212yes—
50C4×(C2×D3)⋊C4—21no—
51C4×(C2×D3)⋊C4—21no—
52#4667—21no—
53#4666—21no—
54#4664—21no—
55D3×#95—21no—
56C3×#342C2212yes—
57#4527C2212yes—
58#4527C2212yes—
59#4526C2212yes—
60C2×#525—31no—
61#2280—31no—
62C2×C4×C22⋊C4—31no—
63#1996—32no—
64#1964—32no—
65#1898—32no—
66#1898—32no—
67C4×#99—31no—
68C4×#99—31no—
69C4×#99—31no—
70C4×#99D311yescharacteristic, complemented
71C24×D3C2311yescharacteristic
72C22×C3×D4C2311yescharacteristic
73C23×C3×C4C2×C411yescharacteristic, complemented
74C23×C3×C4C2311yescharacteristic
75C22×#67C2×C411yescharacteristic
76C22×#67C2×C411yescharacteristic
77C22×#67C2×C411yescharacteristic, complemented
78C22×#67C2311yescharacteristic
79C23×Dic3C2311yescharacteristic
80C2×#235—21no—
81C2×#235—21no—
82C2×#235—21no—
83C2×#235—21no—
84C2×#235—44no—
85C22×D12C2×C411yescharacteristic
86C22×D12C2×C411yescharacteristic
87C22×C4×D3—22no—
88C22×C4×D3—44no—
89C22×C4×D3C2×C411yescharacteristic
90C22×C4×D3C2×C411yescharacteristic
91C22×C4×D3C2×C411yescharacteristic
92C22×C4×D3C2×C411yescharacteristic
93C22×C4×D3C2×C411yescharacteristic, complemented
94C22×C4×D3D411yescharacteristic
95C22×C4×D3D411yescharacteristic
96C22×C4×D3D411yescharacteristic
97C22×C4×D3D411yescharacteristic
98C22×C4×D3D411yescharacteristic
99C22×C4×D3D411yescharacteristic
100C22×C4×D3D411yescharacteristic
101C22×C4×D3D411yescharacteristic
102C22×Dic6C2×C411yescharacteristic, complemented
103C3×C4×D4—21no—
104C3×C4×D4—21no—
105C3×C4×D4—21no—
106C3×C4×D4—21no—
107C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
108C2×C3×C22⋊C4C2×C411yescharacteristic, complemented
109C2×C3×C22⋊C4C2312yes—
110C2×C3×C22⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4C2312yes—
112C2×C3×C42—21no—
113C2×C3×C42—21no—
114C2×C3×C42C2×C411yescharacteristic, complemented
115C2×#217C2×C411yescharacteristic, complemented
116C2×#217C2312yes—
117C2×#217C2311yescharacteristic
118C2×#217C2312yes—
119#939—21no—
120#939—21no—
121#939—21no—
122#939—21no—
123#937—21no—
124#937—21no—
125#937—21no—
126#937—21no—
127C4×#67—21no—
128C4×#67—21no—
129C4×#67—21no—
130C4×#67—21no—
131C4×#67—21no—
132C4×#67—21no—
133C4×#67—21no—
134C4×#67—21no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4C2×C411yescharacteristic
139C2×(C2×D3)⋊C4C2×C411yescharacteristic
140C2×(C2×D3)⋊C4C2×C411yescharacteristic
141C2×(C2×D3)⋊C4C2×C411yescharacteristic
142C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
143C2×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
144C2×C4⋊Dic3C2×C411yescharacteristic, complemented
145C2×Dic3⋊C4—22no—
146C2×Dic3⋊C4C2×C411yescharacteristic, complemented
147C2×Dic3⋊C4C2×C411yescharacteristic, complemented
148C2×Dic3⋊C4C2×C411yescharacteristic, complemented
149C2×Dic3⋊C4C2×C411yescharacteristic, complemented
150C2×C4×Dic3—21no—
151C2×C4×Dic3—21no—
152C2×C4×Dic3—22no—
153C2×C4×Dic3C2×C411yescharacteristic, complemented
154#896—21no—
155#896—21no—
156#896—21no—
157#896—21no—
158#894—21no—
159#894—21no—
160#894—21no—
161#894—21no—
162#884—21no—
163#884—21no—
164#884—21no—
165#884—21no—
166#883—21no—
167#883—21no—
168#883—21no—
169#883—21no—
170#882—21no—
171#882—21no—
172#882—21no—
173#882—21no—
174D3×C22⋊C4—24no—
175D3×C22⋊C4—24no—
176#878—21no—
177#878—21no—
178#878—21no—
179#878—21no—
180C4×D12—21no—
181C4×D12—21no—
182C4×D12—21no—
183C4×D12—21no—
184#872—21no—
185#872—21no—
186#872—21no—
187#872—21no—
188#872—44no—
189C42×D3—44no—
190C3×#99—24no—
191C3×#95—21no—
192C3×#95—21no—
193#834—24no—
194C3⋊#95—21no—
195C3⋊#95—21no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198#806—24no—
199#806—24no—
200C22×#41—31no—
201C24×C4—31no—
202#525—61no—
203#525—61no—
204#525—61no—
205#525—61no—
206#525—61no—
207#525—61no—
208#525—61no—
209#525—61no—
210C2×#123—31no—
211C2×#123—31no—
212C2×C22⋊Q8—31no—
213C2×C22⋊Q8—31no—
214C2×#121—31no—
215C2×#121—31no—
216C2×#120—31no—
217C2×#120—31no—
218C2×C4×D4—31no—
219C2×C4×D4—31no—
220C2×C4×D4—31no—
221C2×C4×D4C2×D311yescharacteristic
222C2×#117—31no—
223C2×#117—61no—
224C22×C22⋊C4—32no—
225C22×C42—61no—
226C2×#99—32no—
227C2×#99—32no—
228C2×#99—32no—
229C2×#99C2×D312yes—
230#381—61no—
231#380—32no—
232#380—61no—
233#379—32no—
234C4×C22⋊C4—31no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—32no—
237C4×C22⋊C4—61no—
238C4×C22⋊C4—61no—
239C4×C22⋊C4—61no—
240C4×C22⋊C4C2×D311yescharacteristic
241C4×C22⋊C4C2×D311yescharacteristic
242C2×#95—61no—
243#342—32no—
244#342—32no—
245#342—32no—
246#342C2×D312yes—
247C24×C3C22×C411yescharacteristic
248C24×C3C2411yescharacteristic
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—42no—
252C23×D3—42no—
253C23×D3C22×C411yescharacteristic
254C23×D3C22×C411yescharacteristic
255C23×D3C22×C411yescharacteristic
256C23×D3C2×D411yescharacteristic
257C23×D3C2×D411yescharacteristic
258C23×D3C2×D411yescharacteristic
259C23×D3C2×D411yescharacteristic
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—22no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4C22×C411yescharacteristic
271C22×C3×C4C22×C411yescharacteristic
272C22×C3×C4C22×C411yescharacteristic
273C22×C3×C4C22×C411yescharacteristic
274C22×C3×C4C22×C411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C2×#67—21no—
280C2×#67—21no—
281C2×#67—22no—
282C2×#67—22no—
283C2×#67—21no—
284C2×#67—21no—
285C2×#67—21no—
286C2×#67—21no—
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—42no—
290C2×#67—42no—
291C2×#67—42no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—42no—
295C22×Dic3C22×C411yescharacteristic
296C22×Dic3C22×C411yescharacteristic
297C22×Dic3C22×C411yescharacteristic
298C22×Dic3C22×C411yescharacteristic
299C22×Dic3C22×C411yescharacteristic
300C22×Dic3C2×D411yescharacteristic
301C22×Dic3C2×D411yescharacteristic
302C22×Dic3C2×D411yescharacteristic
303C22×Dic3C2×D411yescharacteristic
304#235—44no—
305#235—44no—
306#235—44no—
307#235—44no—
308C2×D12—21no—
309C2×D12—21no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—42no—
313C2×D12—42no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—28no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—42no—
321C2×C4×D3—42no—
322C2×C4×D3—42no—
323C2×C4×D3—42no—
324C2×C4×D3—42no—
325C2×C4×D3—42no—
326C2×C4×D3—42no—
327C2×C4×D3—42no—
328C2×C4×D3—42no—
329C2×C4×D3—44no—
330C2×C4×D3—44no—
331C2×C4×D3—42no—
332C2×C4×D3C22⋊C411yescharacteristic
333C2×C4×D3C22⋊C411yescharacteristic
334C2×C4×D3C22⋊C411yescharacteristic
335C2×C4×D3C22⋊C411yescharacteristic
336C2×C4×D3C22⋊C411yescharacteristic
337C2×C4×D3C22⋊C411yescharacteristic
338C2×C4×D3C22⋊C411yescharacteristic
339C2×C4×D3C22⋊C411yescharacteristic
340C2×C4×D3C22⋊C411yescharacteristic
341C2×C4×D3C22⋊C411yescharacteristic
342C2×C4×D3C22⋊C411yescharacteristic
343C2×C4×D3C22⋊C411yescharacteristic
344C2×C4×D3C22⋊C411yescharacteristic
345C2×C4×D3C22⋊C411yescharacteristic
346C2×C4×D3C22⋊C411yescharacteristic
347C2×C4×D3C22⋊C411yescharacteristic
348C2×Dic6—21no—
349C2×Dic6—21no—
350C2×Dic6—42no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—22no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4#4114yescomplemented
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—42no—
364C3×C42—42no—
365#217—21no—
366#217—21no—
367#217—22no—
368#217—21no—
369#217—21no—
370#217—22no—
371#217—22no—
372#217#4114yescomplemented
373(C2×D3)⋊C4—28no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—44no—
387(C2×D3)⋊C4—44no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—44no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3—44no—
402C4×Dic3—42no—
403C4×Dic3—42no—
404C25—31no—
405C2×#41—61no—
406C2×#41—61no—
407C2×#41—61no—
408C2×#41—61no—
409C2×#41—124no—
410C22×Q8—31no—
411C22×D4—31no—
412C22×D4—31no—
413C22×D4—31no—
414C22×D4—31no—
415C22×D4—31no—
416C22×D4—31no—
417C22×D4C22×D311yescharacteristic
418C23×C4—31no—
419C23×C4—31no—
420C23×C4—31no—
421C23×C4—31no—
422C23×C4—31no—
423C23×C4—31no—
424C23×C4—31no—
425C23×C4—31no—
426C23×C4—31no—
427C23×C4—31no—
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4—31no—
432C23×C4—62no—
433C23×C4—124no—
434C23×C4C4×D311yescharacteristic, complemented
435C23×C4C22×D311yescharacteristic
436#123—61no—
437#123—61no—
438#123—61no—
439#123—61no—
440#123—61no—
441#123—61no—
442#123—61no—
443#123—61no—
444C22⋊Q8—61no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448C22⋊Q8—61no—
449C22⋊Q8—61no—
450C22⋊Q8—61no—
451C22⋊Q8—61no—
452#121—61no—
453#121—61no—
454#121—61no—
455#121—61no—
456#121—61no—
457#121—61no—
458#121—61no—
459#121—61no—
460#120—61no—
461#120—61no—
462#120—61no—
463#120—61no—
464#120—61no—
465#120—61no—
466#120—61no—
467#120—61no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4—61no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484#117—61no—
485#117—61no—
486#117—61no—
487#117—61no—
488#117—124no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4C4×D311yescharacteristic, complemented
496C2×C22⋊C4—32no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—32no—
506C2×C22⋊C4—64no—
507C2×C22⋊C4—62no—
508C2×C22⋊C4—64no—
509C2×C22⋊C4—62no—
510C2×C22⋊C4—62no—
511C2×C22⋊C4C4×D311yescharacteristic, complemented
512C2×C22⋊C4C22×D312yes—
513C2×C22⋊C4C22×D311yescharacteristic
514C2×C22⋊C4C22×D312yes—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—31no—
518C2×C42—62no—
519C2×C42—61no—
520C2×C42—61no—
521C2×C42—124no—
522C2×C42C4×D311yescharacteristic, complemented
523#99—24no—
524#99—64no—
525#99—64no—
526#99—64no—
527#95—21no—
528#95—21no—
529#95—62no—
530#95—62no—
531#95—61no—
532#95—61no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—41no—
540C23×C3C23×C411yescharacteristic
541C23×C3C22×D411yescharacteristic
542C23×C3C22×D411yescharacteristic
543C23×C3C2×#4112yes—
544C23×C3C2×#4112yes—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—48no—
569C22×D3—48no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3C2×C22⋊C411yescharacteristic
573C22×D3C2×C22⋊C411yescharacteristic
574C22×D3C2×C22⋊C411yescharacteristic
575C22×D3C2×C22⋊C411yescharacteristic
576C3×D4—42no—
577C3×D4—42no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—24no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598C2×C3×C4—42no—
599C2×C3×C4C2×C22⋊C411yescharacteristic
600C2×C3×C4C2×C22⋊C411yescharacteristic
601C2×C3×C4C2×C22⋊C411yescharacteristic
602C2×C3×C4C2×C22⋊C411yescharacteristic
603#67—42no—
604#67—42no—
605#67—42no—
606#67—42no—
607#67—42no—
608#67—42no—
609#67—42no—
610#67—42no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—24no—
620C2×Dic3—41no—
621C2×Dic3—41no—
622C2×Dic3—41no—
623C2×Dic3—42no—
624C2×Dic3—42no—
625C2×Dic3—41no—
626C2×Dic3—41no—
627C2×Dic3—42no—
628C2×Dic3—42no—
629C2×Dic3—42no—
630C2×Dic3C2×C22⋊C411yescharacteristic
631C2×Dic3C2×C22⋊C411yescharacteristic
632C2×Dic3C2×C22⋊C411yescharacteristic
633C2×Dic3C2×C22⋊C411yescharacteristic
634D12—42no—
635D12—42no—
636D12—42no—
637D12—42no—
638C4×D3—22no—
639C4×D3—22no—
640C4×D3—22no—
641C4×D3—22no—
642C4×D3—22no—
643C4×D3—22no—
644C4×D3—22no—
645C4×D3—22no—
646C4×D3—22no—
647C4×D3—41no—
648C4×D3—41no—
649C4×D3—41no—
650C4×D3—41no—
651C4×D3—41no—
652C4×D3—41no—
653C4×D3—42no—
654C4×D3—416no—
655C4×D3—42no—
656C4×D3#9914yescomplemented
657Dic6—42no—
658Dic6—42no—
659C24—31no—
660C24—31no—
661C24—31no—
662C24—31no—
663C24—31no—
664C24—31no—
665C24—31no—
666C24—62no—
667C24—62no—
668C24—122no—
669C24—122no—
670C24C2×C4×D311yescharacteristic
671C24C23×D311yescharacteristic
672#41—124no—
673#41—124no—
674#41—124no—
675#41—124no—
676C2×Q8—61no—
677C2×Q8—61no—
678C2×Q8—122no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—62no—
697C2×D4—122no—
698C2×D4—122no—
699C2×D4—122no—
700C2×D4—122no—
701C2×D4—122no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—22no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—31no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—64no—
734C22×C4—64no—
735C22×C4—64no—
736C22×C4—68no—
737C22×C4—62no—
738C22×C4—61no—
739C22×C4—61no—
740C22×C4—62no—
741C22×C4—122no—
742C22×C4—122no—
743C22×C4—122no—
744C22×C4—122no—
745C22×C4—122no—
746C22×C4—122no—
747C22×C4—122no—
748C22×C4—122no—
749C22×C4—122no—
750C22×C4—122no—
751C22×C4—124no—
752C22×C4—124no—
753C22×C4—122no—
754C22×C4C2×C4×D311yescharacteristic
755C22×C4C2×C4×D311yescharacteristic
756C22×C4C2×C4×D311yescharacteristic
757C22×C4C2×C4×D311yescharacteristic
758C22×C4C2×C4×D311yescharacteristic
759C22×C4D3×D411yescharacteristic
760C22×C4D3×D411yescharacteristic
761C22×C4D3×D411yescharacteristic
762C22×C4D3×D411yescharacteristic
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—61no—
766C4⋊C4—61no—
767C4⋊C4—61no—
768C4⋊C4—61no—
769C4⋊C4—61no—
770C4⋊C4—61no—
771C4⋊C4—61no—
772C4⋊C4—61no—
773C4⋊C4—61no—
774C4⋊C4—61no—
775C4⋊C4—124no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—22no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—22no—
782C22⋊C4—22no—
783C22⋊C4—34no—
784C22⋊C4—61no—
785C22⋊C4—61no—
786C22⋊C4—61no—
787C22⋊C4—61no—
788C22⋊C4—61no—
789C22⋊C4—61no—
790C22⋊C4—61no—
791C22⋊C4—61no—
792C22⋊C4—61no—
793C22⋊C4—61no—
794C22⋊C4—68no—
795C22⋊C4—61no—
796C22⋊C4—61no—
797C22⋊C4—62no—
798C22⋊C4—61no—
799C22⋊C4—61no—
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—62no—
803C22⋊C4—62no—
804C22⋊C4—124no—
805C22⋊C4—124no—
806C22⋊C4#23514yescomplemented
807C42—21no—
808C42—21no—
809C42—42no—
810C42—42no—
811C42—61no—
812C42—61no—
813C42—122no—
814C42—122no—
815C42—124no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3C22×C22⋊C411yescharacteristic
830C22×C3C4×#4111yescharacteristic
831C22×C3C4×#4111yescharacteristic
832C22×C3#52512yes—
833C22×C3#53212yes—
834C2×D3—28no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—21no—
844C2×D3—21no—
845C2×D3—44no—
846C2×D3—42no—
847C2×D3—42no—
848C2×D3—44no—
849C2×D3—42no—
850C2×D3—42no—
851C2×D3—44no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—81no—
856C2×D3—81no—
857C2×D3C2×#9912yes—
858C2×D3#41012yes—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—44no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—82no—
867C3×C4C2×#9912yes—
868Dic3—21no—
869Dic3—21no—
870Dic3—21no—
871Dic3—44no—
872Dic3—41no—
873Dic3—41no—
874Dic3—41no—
875Dic3—82no—
876Dic3C2×#9912yes—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—31no—
881C23—31no—
882C23—31no—
883C23—31no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—62no—
889C23—62no—
890C23—62no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—61no—
903C23—61no—
904C23—61no—
905C23—121no—
906C23—121no—
907C23—121no—
908C23—121no—
909C23—121no—
910C23—121no—
911C23—121no—
912C23—121no—
913C23—128no—
914C23—128no—
915C23C22×C4×D311yescharacteristic
916C23C2×#23512yes—
917C23C2×D3×D411yescharacteristic
918C23C2×D3×D411yescharacteristic
919C23D3×#4112yes—
920Q8—122no—
921Q8—122no—
922D4—42no—
923D4—42no—
924D4—122no—
925D4—122no—
926D4—122no—
927D4—122no—
928D4—122no—
929D4—122no—
930D4—122no—
931D4—122no—
932D4—122no—
933D4—122no—
934D4—122no—
935D4—122no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—24no—
945C2×C4—31no—
946C2×C4—34no—
947C2×C4—31no—
948C2×C4—31no—
949C2×C4—31no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—64no—
980C2×C4—121no—
981C2×C4—121no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—121no—
986C2×C4—122no—
987C2×C4—1216no—
988C2×C4—121no—
989C2×C4—121no—
990C2×C4—121no—
991C2×C4—122no—
992C2×C4—122no—
993C2×C4—122no—
994C2×C4—121no—
995C2×C4—121no—
996C2×C4—122no—
997C2×C4—122no—
998C2×C4—122no—
999C2×C4D3×C22⋊C411yescharacteristic
1000C2×C4D3×C22⋊C411yescharacteristic
1001C2×C4D3×C22⋊C411yescharacteristic
1002C2×C4D3×C22⋊C411yescharacteristic
1003C2×C3—22no—
1004C2×C3—22no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—81no—
1008C2×C3#229711yescharacteristic
1009C2×C3C22×#9911yescharacteristic
1010C2×C3C2×#41011yescharacteristic
1011D3—22no—
1012D3—22no—
1013D3—41no—
1014D3—41no—
1015D3—81no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—32no—
1023C22—32no—
1024C22—42no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—68no—
1030C22—61no—
1031C22—61no—
1032C22—61no—
1033C22—61no—
1034C22—61no—
1035C22—61no—
1036C22—61no—
1037C22—61no—
1038C22—61no—
1039C22—61no—
1040C22—81no—
1041C22—81no—
1042C22—124no—
1043C22—124no—
1044C22—122no—
1045C22—122no—
1046C22—122no—
1047C22—122no—
1048C22—124no—
1049C22—121no—
1050C22—121no—
1051C22—121no—
1052C22—241no—
1053C22—241no—
1054C22C4×#23511yescharacteristic
1055C22C2×D3×C22⋊C411yescharacteristic
1056C22#552211yescharacteristic
1057C22#554712yes—
1058C22#554812yes—
1059C4—21no—
1060C4—21no—
1061C4—21no—
1062C4—32no—
1063C4—44no—
1064C4—41no—
1065C4—41no—
1066C4—41no—
1067C4—61no—
1068C4—61no—
1069C4—61no—
1070C4—82no—
1071C4—124no—
1072C4—121no—
1073C4—121no—
1074C4—121no—
1075C4—242no—
1076C4D3×#9912yes—
1077C3#2142011yescharacteristic, complemented, Sylow
1078C2—22no—
1079C2—22no—
1080C2—21no—
1081C2—21no—
1082C2—62no—
1083C2—62no—
1084C2—81no—
1085C2—121no—
1086C2—121no—
1087C2—241no—
1088C2#7356311yescharacteristic
1089C2C2×D3×#9911yescharacteristic
1090C2D3×#41011yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×C4×#99C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5547C2
cosocleC24×C3C24
hypercenterC4×#99D3
hypocenterC3#21420
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #73561C2semidirect
3. C4×D3×C22⋊C4C2semidirect
4. C3×C4×#99C2semidirect
5. C4×#834C2semidirect
6. #70036C2semidirect
7. #70030C2semidirect
8. C4×#806C2semidirect
9. C4×#806C2semidirect
10. #68970C2semidirect
11. #68955C2semidirect
13. C22×#235C4semidirect
18. C2×C4×#67C4semidirect
28. C2×#896C4semidirect
29. C2×#894C4semidirect
30. C2×#884C4semidirect
31. C2×#883C4semidirect
35. C2×C4×D12C4semidirect
37. C2×#872C4semidirect
70. C4×#99D3semidirect
73. C23×C3×C4C2×C4semidirect
77. C22×#67C2×C4semidirect
93. C22×C4×D3C2×C4semidirect
102. C22×Dic6C2×C4semidirect
107. C2×C3×C4⋊C4C2×C4semidirect
108. C2×C3×C22⋊C4C2×C4semidirect
114. C2×C3×C42C2×C4semidirect
115. C2×#217C2×C4semidirect
142. C2×(C2×D3)⋊C4C2×C4semidirect
143. C2×(C2×D3)⋊C4C2×C4semidirect
144. C2×C4⋊Dic3C2×C4semidirect
146. C2×Dic3⋊C4C2×C4semidirect
147. C2×Dic3⋊C4C2×C4semidirect
148. C2×Dic3⋊C4C2×C4semidirect
149. C2×Dic3⋊C4C2×C4semidirect
153. C2×C4×Dic3C2×C4semidirect
360. C3×C22⋊C4#41semidirect
372. #217#41semidirect
434. C23×C4C4×D3semidirect
495. C2×C4⋊C4C4×D3semidirect
511. C2×C22⋊C4C4×D3semidirect
522. C2×C42C4×D3semidirect
656. C4×D3#99semidirect
806. C22⋊C4#235semidirect
1077. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
#735612
C4×D3×C22⋊C42
C3×C4×#992
C4×#8342
#700362
#700302
C4×#8062
#689702
#689552
#214203