Finite Group Databasebeta

← #10798798

Subgroups — #10798798

Order 768.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic
2C2×#4839C211yesmaximal, characteristic, complemented
3C2×#4727C211yesmaximal, characteristic, complemented
4C2×#4727C211yesmaximal, characteristic, complemented
5C2×#4726C211yesmaximal, characteristic, complemented
6C2×D3×C22⋊C8C211yesmaximal, characteristic, complemented
7C2×#4708C211yesmaximal, characteristic, complemented
8C3×#1955C211yesmaximal, characteristic, complemented
9#71614C211yesmaximal, characteristic, complemented
10#70470C211yesmaximal, characteristic, complemented
11#69917C211yesmaximal, characteristic, complemented
12#69917C211yesmaximal, characteristic, complemented
13#69916C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69837C211yesmaximal, characteristic, complemented
16#21191—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#939C411yescharacteristic
21C2×#937C411yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C22×ΓL(1,𝔽25)C2211yescharacteristic
25C22×ΓL(1,𝔽25)C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5547—24no—
29#5547—24no—
30C2×#896C411yescharacteristic
31C2×#894C411yescharacteristic
32C2×#884C411yescharacteristic
33C2×#883C411yescharacteristic
34C2×#882C411yescharacteristic
35C2×#878C411yescharacteristic
36C2×C4×D12C2211yescharacteristic
37C2×#872C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic, complemented
42C2×C3×C22⋊C8C2211yescharacteristic, complemented
43C2×C3×#97C2211yescharacteristic, complemented
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C2×#830C2211yescharacteristic, complemented
47C2×#830C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C2×#815C2211yescharacteristic, complemented
57C2×Dic3⋊C8C2211yescharacteristic, complemented
58C2×Dic3⋊C8C2211yescharacteristic, complemented
59C2×C8×Dic3C2211yescharacteristic, complemented
60C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C2×C4×C3⋊C8C2211yescharacteristic, complemented
62#4839—24no—
63#4727—24no—
64#4727—24no—
65#4726—24no—
66D3×C22⋊C8—24no—
67#4708—24no—
68C2×#525—31no—
69C2×#424—31no—
70C2×#408—31no—
71C2×#408—31no—
72C2×#407—31no—
73C22×C22⋊C8—31no—
74C2×#405—31no—
75#1955—31no—
76#1955—31no—
77#1955—31no—
78#1955D311yescharacteristic, complemented
79#1954—31no—
80#1954—31no—
81#1954—31no—
82#1954—31no—
83C24×D3C2×C411yescharacteristic
84C22×C3×D4C2×C411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67C2×C411yescharacteristic
88C22×#67C2×C411yescharacteristic
89C22×#67C2×C411yescharacteristic
90C22×#67C2×C411yescharacteristic
91C23×Dic3C2×C411yescharacteristic
92C2×#235—22no—
93C2×#235—22no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C22×D12C2×C411yescharacteristic
99C22×D12C2×C411yescharacteristic
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3C2×C411yescharacteristic
107C22×C4×D3C2×C411yescharacteristic
108C22×C4×D3C2311yescharacteristic
109C22×C4×D3C2311yescharacteristic
110C22×C4×D3C2311yescharacteristic
111C22×Dic6C2×C411yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C3×C4×D4—22no—
117C3×C4×D4—22no—
118C2×C3×C4⋊C4C2×C411yescharacteristic
119C2×C3×C22⋊C4C2×C411yescharacteristic
120C2×C3×C22⋊C4C2×C411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×#217C2×C411yescharacteristic
123C2×#217C2×C411yescharacteristic
124#939—24no—
125#937—24no—
126C4×#67—22no—
127C4×#67—22no—
128C4×#67—22no—
129C4×#67—22no—
130C2×(C2×D3)⋊C4C2×C411yescharacteristic
131C2×(C2×D3)⋊C4C2×C411yescharacteristic
132C2×(C2×D3)⋊C4C2×C411yescharacteristic
133C2×(C2×D3)⋊C4C2×C411yescharacteristic
134C2×(C2×D3)⋊C4C2×C411yescharacteristic
135C2×(C2×D3)⋊C4C2×C411yescharacteristic
136C2×C4⋊Dic3C2×C411yescharacteristic
137C2×Dic3⋊C4C2×C411yescharacteristic
138C2×Dic3⋊C4C2×C411yescharacteristic
139C2×Dic3⋊C4C2×C411yescharacteristic
140C2×Dic3⋊C4C2×C411yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C2×ΓL(1,𝔽25)—22no—
147C2×ΓL(1,𝔽25)—22no—
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—22no—
150C2×ΓL(1,𝔽25)—22no—
151C2×ΓL(1,𝔽25)D414yescomplemented
152C2×D3×C8—22no—
153C2×D3×C8—22no—
154C2×D3×C8—22no—
155C2×D3×C8—22no—
156C2×D3×C8—22no—
157C2×D3×C8D414yescomplemented
158#896—24no—
159#894—24no—
160#884—24no—
161#883—24no—
162#882—24no—
163#878—24no—
164C4×D12—22no—
165C4×D12—22no—
166#872D414yes—
167#872D414yes—
168C3×C4⋊C8—22no—
169C3×C22⋊C8—22no—
170C3×C22⋊C8—22no—
171C3×C22⋊C8—22no—
172C3×C22⋊C8—22no—
173C3×#97—22no—
174#830—22no—
175#830—22no—
176#830—22no—
177#830—22no—
178(C2×D3)⋊C8—22no—
179(C2×D3)⋊C8—22no—
180(C2×D3)⋊C8—22no—
181(C2×D3)⋊C8—22no—
182(C2×D3)⋊C8—22no—
183(C2×D3)⋊C8—22no—
184(C2×D3)⋊C8—22no—
185(C2×D3)⋊C8—22no—
186#815—22no—
187Dic3⋊C8—22no—
188Dic3⋊C8—22no—
189C8×Dic3—22no—
190C4⋊(C3⋊C8)—22no—
191C4×C3⋊C8—22no—
192C22×#41—31no—
193C24×C4—31no—
194C22×M16—31no—
195C22×M16—31no—
196C23×C8—31no—
197C23×C8—31no—
198#525—64no—
199#525—64no—
200C2×#123—31no—
201C2×#123—31no—
202C2×C22⋊Q8—31no—
203C2×C22⋊Q8—31no—
204C2×#121—31no—
205C2×#121—31no—
206C2×#120—31no—
207C2×#120—31no—
208C2×C4×D4—31no—
209C2×C4×D4—31no—
210C2×C4×D4—31no—
211C2×C4×D4C2×D311yescharacteristic
212C2×#117—31no—
213#424—64no—
214C2×C4⋊C8—31no—
215C2×C4⋊C8—31no—
216C2×C4⋊C8—31no—
217C2×C4⋊C8C2×D311yescharacteristic, complemented
218#408—64no—
219#408—64no—
220#407—64no—
221C2×C22⋊C8—31no—
222C2×C22⋊C8—31no—
223C2×C22⋊C8—31no—
224C2×C22⋊C8—31no—
225C2×C22⋊C8—31no—
226C2×C22⋊C8—31no—
227C2×C22⋊C8—31no—
228C2×C22⋊C8—31no—
229C2×C22⋊C8—31no—
230C2×C22⋊C8—31no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—64no—
234C2×C22⋊C8C2×D311yescharacteristic
235C2×C22⋊C8C2×D311yescharacteristic
236C2×C22⋊C8C2×D311yescharacteristic, complemented
237C2×C22⋊C8C2×D311yescharacteristic, complemented
238#405—64no—
239C2×#97—31no—
240C2×#97C2×D311yescharacteristic, complemented
241C2×C4×C8—31no—
242C2×C4×C8—31no—
243C24×C3C22×C411yescharacteristic
244C24×C3C22×C411yescharacteristic
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—41no—
251C23×D3—41no—
252C23×D3C22×C411yescharacteristic
253C23×D3C22×C411yescharacteristic
254C23×D3C22×C411yescharacteristic
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—41no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4C22×C411yescharacteristic
271C22×C3×C4C22×C411yescharacteristic
272C22×C3×C4C22×C411yescharacteristic
273C22×C3×C4C22×C411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C2×#67—22no—
276C2×#67—22no—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—22no—
281C2×#67—22no—
282C2×#67—22no—
283C2×#67—22no—
284C2×#67—22no—
285C2×#67—41no—
286C2×#67—41no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3C22×C411yescharacteristic
291C22×Dic3C22×C411yescharacteristic
292C22×Dic3C22×C411yescharacteristic
293C22×Dic3C22×C411yescharacteristic
294C22×Dic3C22×C411yescharacteristic
295#235—44no—
296#235—44no—
297#235—44no—
298#235—44no—
299C2×D12—22no—
300C2×D12—22no—
301C2×D12—22no—
302C2×D12—22no—
303C2×D12—22no—
304C2×D12—41no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—22no—
323C2×C4×D3—44no—
324C2×C4×D3—44no—
325C2×C4×D3—44no—
326C2×C4×D3—44no—
327C2×C4×D3C2×D412yes—
328C2×C4×D3C2×D412yes—
329C2×C4×D3C2×D412yes—
330C2×C4×D3C2×D412yes—
331C2×C4×D3#4112yes—
332C2×C4×D3#4112yes—
333C2×Dic6—22no—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8C2×D412yes—
347C2×C3×C8C2×D412yes—
348C3×C4⋊C4—22no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C42C2×D412yes—
352C3×C42C2×D412yes—
353#217—22no—
354#217—22no—
355(C2×D3)⋊C4—22no—
356(C2×D3)⋊C4—22no—
357(C2×D3)⋊C4—22no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4C22⋊C414yes—
360(C2×D3)⋊C4C22⋊C414yes—
361C4⋊Dic3—22no—
362Dic3⋊C4—22no—
363Dic3⋊C4—22no—
364Dic3⋊C4C22⋊C414yes—
365Dic3⋊C4C22⋊C414yes—
366C4×Dic3C2×D412yes—
367C4×Dic3C2×D412yes—
368C2×C3⋊C8—21no—
369C2×C3⋊C8—21no—
370C2×C3⋊C8—21no—
371C2×C3⋊C8—21no—
372C2×C3⋊C8—21no—
373C2×C3⋊C8—21no—
374C2×C3⋊C8—21no—
375C2×C3⋊C8—21no—
376C2×C3⋊C8—21no—
377C2×C3⋊C8—21no—
378C2×C3⋊C8C2×D412yes—
379C2×C3⋊C8C2×D412yes—
380ΓL(1,𝔽25)—28no—
381ΓL(1,𝔽25)—44no—
382D3×C8—28no—
383D3×C8—44no—
384C25—31no—
385C2×#41—62no—
386C2×#41—62no—
387C2×#41—62no—
388C2×#41—62no—
389C2×#41—62no—
390C2×#41—62no—
391C22×Q8—31no—
392C22×D4—31no—
393C22×D4—31no—
394C22×D4—31no—
395C22×D4—31no—
396C22×D4—31no—
397C22×D4—31no—
398C22×D4C4×D311yescharacteristic
399C23×C4—31no—
400C23×C4—31no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—62no—
410C23×C4—62no—
411C23×C4C22×D311yescharacteristic
412C23×C4C22×D311yescharacteristic
413C2×M16—34no—
414C2×M16—62no—
415C2×M16—62no—
416C2×M16—62no—
417C2×M16—62no—
418C2×M16—62no—
419C22×C8—31no—
420C22×C8—31no—
421C22×C8—34no—
422C22×C8—31no—
423C22×C8—31no—
424C22×C8—62no—
425C22×C8—62no—
426C22×C8—62no—
427C22×C8—62no—
428C22×C8—62no—
429C22×C8C22×D311yescharacteristic
430C22×C8C22×D311yescharacteristic
431C22×C8C22×D311yescharacteristic
432C22×C8C22×D311yescharacteristic
433#123—64no—
434#123—64no—
435C22⋊Q8—64no—
436C22⋊Q8—64no—
437#121—64no—
438#121—64no—
439#120—64no—
440#120—64no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—62no—
444C4×D4—62no—
445C4×D4—62no—
446C4×D4—62no—
447C4×D4—62no—
448C4×D4—62no—
449#117—34no—
450#117—34no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4C4×D311yescharacteristic
457C2×C22⋊C4—31no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—31no—
462C2×C22⋊C4—31no—
463C2×C22⋊C4—31no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4C4×D311yescharacteristic
466C2×C22⋊C4C4×D311yescharacteristic
467C2×C42—31no—
468C2×C42C22×D311yescharacteristic
469C4⋊C8—22no—
470C4⋊C8—62no—
471C4⋊C8—62no—
472C4⋊C8—62no—
473C22⋊C8—22no—
474C22⋊C8—22no—
475C22⋊C8—22no—
476C22⋊C8—22no—
477C22⋊C8—62no—
478C22⋊C8—62no—
479C22⋊C8—62no—
480C22⋊C8—62no—
481C22⋊C8—62no—
482C22⋊C8—62no—
483C22⋊C8—62no—
484C22⋊C8—62no—
485C22⋊C8—62no—
486C22⋊C8—62no—
487C22⋊C8—62no—
488C22⋊C8—62no—
489#97—22no—
490#97—62no—
491C4×C8—62no—
492C4×C8—62no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3#13112yes—
507C23×C3C23×C411yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—28no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—21no—
522C22×D3—21no—
523C22×D3—21no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3C2×C22⋊C412yes—
533C22×D3C4×D412yes—
534C22×D3C4×D412yes—
535C22×D3#13112yes—
536C3×D4—44no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4C2×C22⋊C412yes—
556C2×C3×C4C2×C22⋊C412yes—
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C2×#4111yescharacteristic
562C2×C3×C4C2×#4111yescharacteristic
563#67—44no—
564#67—44no—
565#67—44no—
566#67—44no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—44no—
578C2×Dic3C2×C22⋊C412yes—
579C2×Dic3C2×C22⋊C412yes—
580C2×Dic3C2×C22⋊C412yes—
581C2×Dic3C4×D412yes—
582C2×Dic3C4×D412yes—
583D12—44no—
584D12—44no—
585C4×D3—44no—
586C4×D3—41no—
587C4×D3—41no—
588C4×D3—41no—
589C4×D3—41no—
590C4×D3—41no—
591C4×D3—41no—
592C4×D3—41no—
593C4×D3—41no—
594C4×D3—44no—
595C4×D3#12114yes—
596C4×D3#12114yes—
597C4×D3#12414yes—
598C4×D3#12714yes—
599Dic6—44no—
600C3×C8—22no—
601C3×C8—22no—
602C3×C8—41no—
603C3×C8—41no—
604C3⋊C8—22no—
605C3⋊C8—22no—
606C3⋊C8—41no—
607C3⋊C8—41no—
608C24—31no—
609C24—31no—
610C24—31no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—121no—
617C24—121no—
618C24C2×C4×D311yescharacteristic
619C24C2×C4×D311yescharacteristic
620#41—124no—
621#41—124no—
622#41—124no—
623#41—124no—
624C2×Q8—62no—
625C2×Q8—62no—
626C2×Q8—62no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—41no—
630C2×D4—62no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—62no—
634C2×D4—62no—
635C2×D4—62no—
636C2×D4—62no—
637C2×D4—62no—
638C2×D4—62no—
639C2×D4—62no—
640C2×D4—62no—
641C2×D4—62no—
642C2×D4—62no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—121no—
646C2×D4—121no—
647C2×D4—121no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—31no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—32no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—62no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—62no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—62no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—61no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—124no—
693C22×C4—124no—
694C22×C4—124no—
695C22×C4—124no—
696C22×C4C2×C4×D311yescharacteristic
697C22×C4C2×C4×D311yescharacteristic
698C22×C4C2×C4×D311yescharacteristic
699C22×C4C2×C4×D311yescharacteristic
700C22×C4C23×D311yescharacteristic
701M16—68no—
702M16—124no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—32no—
714C2×C8—32no—
715C2×C8—68no—
716C2×C8—61no—
717C2×C8—61no—
718C2×C8—61no—
719C2×C8—61no—
720C2×C8—61no—
721C2×C8—61no—
722C2×C8—61no—
723C2×C8—61no—
724C2×C8—61no—
725C2×C8—61no—
726C2×C8—124no—
727C2×C8D3×D412yes—
728C2×C8D3×D412yes—
729C4⋊C4—22no—
730C4⋊C4—34no—
731C4⋊C4—34no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4—62no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C42—32no—
746C42—32no—
747C42D3×D412yes—
748C42D3×D412yes—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3C22×C22⋊C411yescharacteristic
764C22×C3C2×C4×D411yescharacteristic
765C22×C3C2×C4×D411yescharacteristic
766C22×C3C2×#13111yescharacteristic
767C22×C3C2×#13111yescharacteristic
768C22×C3#56811yescharacteristic
769C22×C3#56811yescharacteristic
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—416no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3#39014yes—
792C3×C4—22no—
793C3×C4—22no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4C2×#12111yescharacteristic
797C3×C4C2×#12111yescharacteristic
798C3×C4C2×#12411yescharacteristic
799C3×C4C2×#12711yescharacteristic
800Dic3—22no—
801Dic3—22no—
802Dic3—41no—
803Dic3—41no—
804Dic3#39014yes—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—32no—
819C23—32no—
820C23—32no—
821C23—32no—
822C23—68no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—124no—
841C23—124no—
842C23—124no—
843C23—124no—
844C23—124no—
845C23—124no—
846C23#90712yes—
847C23C22×C4×D311yescharacteristic
848Q8—124no—
849D4—44no—
850D4—124no—
851D4—124no—
852D4—124no—
853D4—124no—
854D4—124no—
855D4—124no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—34no—
870C2×C4—34no—
871C2×C4—34no—
872C2×C4—34no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4—124no—
896C2×C4—121no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—121no—
903C2×C4—121no—
904C2×C4D3×C22⋊C412yes—
905C2×C4D3×C22⋊C412yes—
906C2×C4C2×D3×D411yescharacteristic
907C2×C4C2×D3×D411yescharacteristic
908C2×C4C2×D3×D411yescharacteristic
909C2×C4C2×D3×D411yescharacteristic
910C2×C4D3×#4111yescharacteristic
911C2×C4D3×#4111yescharacteristic
912C8—22no—
913C8—22no—
914C8—41no—
915C8—41no—
916C8—62no—
917C8—62no—
918C8—121no—
919C8—121no—
920C2×C3—42no—
921C2×C3—81no—
922C2×C3C2×#39011yescharacteristic
923C2×C3#288011yescharacteristic
924C2×C3#288011yescharacteristic
925C2×C3#292911yescharacteristic
926C2×C3#293011yescharacteristic
927C2×C3#293311yescharacteristic
928C2×C3#293311yescharacteristic
929D3—24no—
930D3—42no—
931D3—81no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—34no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—1216no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—121no—
962C22—121no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22C2×D3×C22⋊C411yescharacteristic
969C22C4×D3×D411yescharacteristic
970C22C4×D3×D411yescharacteristic
971C22C2×#90711yescharacteristic
972C22#574511yescharacteristic
973C22D3×#13111yescharacteristic
974C22#575011yescharacteristic
975C4—22no—
976C4—22no—
977C4—34no—
978C4—41no—
979C4—41no—
980C4—62no—
981C4—62no—
982C4—121no—
983C4—121no—
984C4D3×#12111yescharacteristic
985C4D3×#12111yescharacteristic
986C4D3×#12411yescharacteristic
987C4D3×#12711yescharacteristic
988C3#2119111yescharacteristic, complemented, Sylow
989C2—42no—
990C2—64no—
991C2—81no—
992C2—122no—
993C2—241no—
994C2D3×#39011yescharacteristic
995C2#7863111yescharacteristic
996C2#7866311yescharacteristic
997C2#7947811yescharacteristic
998C2#7947911yescharacteristic
999C2#7948111yescharacteristic
1000C2#7948211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1955C2
prime radicalC2×#5547C2
cosocleC22×C3×C4C24
hypercenter#1955D3
hypocenterC3#21191
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#4839C2semidirect
3. C2×#4727C2semidirect
4. C2×#4727C2semidirect
5. C2×#4726C2semidirect
6. C2×D3×C22⋊C8C2semidirect
7. C2×#4708C2semidirect
8. C3×#1955C2semidirect
9. #71614C2semidirect
10. #70470C2semidirect
11. #69917C2semidirect
12. #69917C2semidirect
13. #69916C2semidirect
14. #69916C2semidirect
15. #69837C2semidirect
38. C2×C3×C4⋊C8C22semidirect
41. C2×C3×C22⋊C8C22semidirect
42. C2×C3×C22⋊C8C22semidirect
43. C2×C3×#97C22semidirect
46. C2×#830C22semidirect
47. C2×#830C22semidirect
52. C2×(C2×D3)⋊C8C22semidirect
53. C2×(C2×D3)⋊C8C22semidirect
54. C2×(C2×D3)⋊C8C22semidirect
55. C2×(C2×D3)⋊C8C22semidirect
56. C2×#815C22semidirect
57. C2×Dic3⋊C8C22semidirect
58. C2×Dic3⋊C8C22semidirect
59. C2×C8×Dic3C22semidirect
60. C2×C4⋊(C3⋊C8)C22semidirect
61. C2×C4×C3⋊C8C22semidirect
78. #1955D3semidirect
151. C2×ΓL(1,𝔽25)D4semidirect
157. C2×D3×C8D4semidirect
217. C2×C4⋊C8C2×D3semidirect
236. C2×C22⋊C8C2×D3semidirect
237. C2×C22⋊C8C2×D3semidirect
240. C2×#97C2×D3semidirect
988. C3#21191semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
C2×#48392
C2×#47272
C2×#47262
C2×D3×C22⋊C82
C2×#47082
C3×#19552
#716142
#704702
#699172
#699162
#698372
#211913