Finite Group Databasebeta

← #11635857

Subgroups — #11635857

Order 768.

3082 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5817C212yesmaximal, complemented
3C2×#5726C211yesmaximal, characteristic, complemented
4#84068C212yesmaximal, complemented
5#83265C214yesmaximal, complemented
6#83259C211yesmaximal, characteristic, complemented
7#83257C212yesmaximal, complemented
8#83255C212yesmaximal, complemented
9#83254C212yesmaximal, complemented
10#83240C211yesmaximal, characteristic, complemented
11#83233C212yesmaximal, complemented
12#83229C211yesmaximal, characteristic, complemented
13#82195C214yesmaximal, complemented
14#82193C212yesmaximal, complemented
15C4⋊C4×#67C212yesmaximal, complemented
16C4×#930C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic, complemented
18#59125—31nomaximal, Sylow
19C23×C3×Q8C2212yes—
20C22×#239C2212yes—
21C2×C3×C4⋊Q8—28no—
22C2×C3×C4⋊Q8C2212yes—
23C2×C3×C4⋊Q8C2211yescharacteristic
24C2×C3×C4⋊Q8C2212yes—
25C2×C3×C4⋊Q8C2212yes—
26C2×C3×C4⋊Q8C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28C22×C3×C4⋊C4C2212yes—
29C22×C3×C42C2211yescharacteristic
30#5817—216no—
31C2×#947C2212yes—
32C2×#947C2214yes—
33C2×#946C2214yes—
34C2×#946C2212yes—
35C2×#946C2212yes—
36C2×#946C2212yes—
37C2×Q8×Dic3C2212yes—
38C2×#930C2211yescharacteristic
39C2×#930C2214yes—
40C2×#930C2211yescharacteristic
41C2×C4×#67C2212yes—
42C2×C4×#67C2214yes—
43C2×C4×#67C2212yes—
44#5726—28no—
45C2×#895C2212yes—
46C2×#894C2214yes—
47C2×D3×C4⋊C4C2212yes—
48C2×C4×D12C2211yescharacteristic
49C2×C4×D12C2211yescharacteristic
50#5231C2214yes—
51#5230C2214yes—
52#5229C2212yes—
53#5229C2212yes—
54#5213C2214yes—
55#5213C2212yes—
56#5213C2212yes—
57#5212C2211yescharacteristic
58#5212C2211yescharacteristic
59#5210C2214yes—
60#4994C2214yes—
61#4993C2214yes—
62#4992C2214yes—
63#4991C2214yes—
64#4991C2214yes—
65#4990C2214yes—
66#4989C2214yes—
67#4989C2214yes—
68#4988C2212yes—
69#4987C2212yes—
70#4987C2212yes—
71#4984C2212yes—
72#4982C2214yes—
73#4980C2214yes—
74#4976C2214yes—
75#4975C2212yes—
76Dic3×C4⋊C4C2212yes—
77#4940C2212yes—
78#4940C2212yes—
79#4939C2211yescharacteristic
80#4939C2211yescharacteristic
81C4×(C2×D3)⋊C4C2212yes—
82C4×(C2×D3)⋊C4C2212yes—
83C4×C4⋊Dic3C2211yescharacteristic
84C4×C4⋊Dic3C2211yescharacteristic
85#4928C2211yescharacteristic
86#4928C2211yescharacteristic
87C2×#548—32no—
88C2×#547—31no—
89C22×C4⋊Q8D311yescharacteristic, complemented
90#2674—34no—
91#2547—31no—
92#2542—31no—
93#2491—32no—
94#2443—34no—
95#2440—32no—
96#2432—32no—
97#2429—32no—
98#2416—32no—
99#2409—32no—
100#2365—31no—
101D4×C4⋊C4—32no—
102C4×#121—31no—
103C4×#121—31no—
104C22×C3×Q8—28no—
105C22×C3×Q8—28no—
106C22×C3×Q8—44no—
107C22×C3×Q8C2312yes—
108C22×C3×Q8C2314yes—
109C22×C3×Q8C2312yes—
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2314yes—
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2311yescharacteristic
114C22×#67C2312yes—
115C22×#67C2312yes—
116C2×#239—28no—
117C2×#239—28no—
118C2×#239—44no—
119C22×D12C2311yescharacteristic
120C22×D12C2314yes—
121C22×D12C2311yescharacteristic
122C22×C4×D3C2312yes—
123C22×C4×D3C2312yes—
124C22×C4×D3C2314yes—
125C3×C4⋊Q8—28no—
126C3×C4⋊Q8—28no—
127C3×C4⋊Q8—28no—
128C3×C4⋊Q8—24no—
129C3×C4⋊Q8D418yescomplemented
130C2×C3×C4⋊C4—28no—
131C2×C3×C4⋊C4—28no—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C4⋊C4C2314yes—
135C2×C3×C4⋊C4C2312yes—
136C2×C3×C4⋊C4C2312yes—
137C2×C3×C4⋊C4C2312yes—
138C2×C3×C42—24no—
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×#217C2312yes—
144C2×#217C2312yes—
145#947—28no—
146#947—216no—
147#946—28no—
148#946—216no—
149#946—28no—
150#946—44no—
151Q8×Dic3—28no—
152#930—24no—
153#930—216no—
154#930D418yescomplemented
155C4×#67—28no—
156C4×#67—28no—
157C4×#67—216no—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2312yes—
162C2×(C2×D3)⋊C4C2312yes—
163C2×(C2×D3)⋊C4C2312yes—
164C2×(C2×D3)⋊C4C2312yes—
165C2×(C2×D3)⋊C4C2314yes—
166C2×(C2×D3)⋊C4C2314yes—
167C2×(C2×D3)⋊C4C2314yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2312yes—
171C2×C4⋊Dic3C2311yescharacteristic
172C2×C4⋊Dic3C2311yescharacteristic
173C2×C4⋊Dic3C2311yescharacteristic
174C2×C4⋊Dic3C2311yescharacteristic
175C2×C4⋊Dic3C2311yescharacteristic
176C2×C4⋊Dic3C2314yes—
177C2×C4⋊Dic3C2311yescharacteristic
178C2×Dic3⋊C4C2312yes—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2314yes—
181C2×Dic3⋊C4C2314yes—
182C2×Dic3⋊C4C2314yes—
183C2×C4×Dic3C2312yes—
184C2×C4×Dic3C2312yes—
185C2×C4×Dic3C2314yes—
186#895—28no—
187#894—216no—
188D3×C4⋊C4—28no—
189C4×D12—24no—
190C4×D12—24no—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2312yes—
195C3⋊#95C2312yes—
196C3⋊#95C2312yes—
197C3⋊#95C2314yes—
198C3⋊#95C2314yes—
199C3⋊#95C2314yes—
200C3⋊#95C2314yes—
201C22×#41—32no—
202C23×Q8C2×D312yes—
203#548—616no—
204#547—68no—
205C2×C4⋊Q8—28no—
206C2×C4⋊Q8C2×D312yes—
207C2×C4⋊Q8C2×D312yes—
208C2×C4⋊Q8C2×D312yes—
209C2×C4⋊Q8C2×D311yescharacteristic
210C2×C4⋊Q8C2×D311yescharacteristic
211C2×#124—34no—
212C2×#124—32no—
213C2×#123—34no—
214C2×C22⋊Q8—32no—
215C2×C22⋊Q8—34no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8—32no—
218C2×#121—31no—
219C2×#121—31no—
220C2×#121—34no—
221C2×#121—32no—
222C2×C4×Q8—32no—
223C2×C4×D4—32no—
224C2×C4×D4—34no—
225C2×C4×D4—32no—
226C2×C4×D4—31no—
227C2×C4×D4—31no—
228C22×C4⋊C4—32no—
229C22×C4⋊C4C2×D312yes—
230C22×C4⋊C4C2×D312yes—
231C22×C42C2×D311yescharacteristic
232#399—34no—
233#398—34no—
234#397—34no—
235#396—34no—
236#395—34no—
237#394—34no—
238#394—34no—
239#393—34no—
240#391—32no—
241#391—32no—
242#390—32no—
243#390—31no—
244#390—31no—
245#389—34no—
246#389—32no—
247#389—31no—
248#389—31no—
249#388—34no—
250#388—32no—
251#388—32no—
252#387—34no—
253#386—34no—
254#386—32no—
255#386—32no—
256#385—34no—
257#385—34no—
258#385—34no—
259#384—32no—
260#380—31no—
261#380—31no—
262#380—32no—
263#380—32no—
264C4×C4⋊C4—32no—
265C4×C4⋊C4—31no—
266C4×C4⋊C4—31no—
267C4×C22⋊C4—32no—
268C4×C22⋊C4—32no—
269C24×C3C2411yescharacteristic
270C23×D3C2412yes—
271C23×D3C2412yes—
272C2×C3×Q8—24no—
273C2×C3×Q8—28no—
274C2×C3×Q8—24no—
275C2×C3×Q8—28no—
276C2×C3×Q8—24no—
277C2×C3×Q8—24no—
278C2×C3×Q8—24no—
279C2×C3×Q8—44no—
280C2×C3×Q8—432no—
281C2×C3×Q8C2×D418yes—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—28no—
290C22×C3×C4—28no—
291C22×C3×C4—44no—
292C22×C3×C4C2×D414yes—
293C22×C3×C4#4114yescomplemented
294C22×C3×C4C2414yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2414yes—
297C22×C3×C4C2411yescharacteristic
298C22×C3×C4C2411yescharacteristic
299C22×C3×C4C2411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C22×C3×C4C2411yescharacteristic
302C2×#67—24no—
303C2×#67—24no—
304C2×#67—24no—
305C2×#67—24no—
306C2×#67—24no—
307C2×#67C2×D418yes—
308C22×Dic3C2412yes—
309C22×Dic3C2412yes—
310C22×Dic3C2412yes—
311C22×Dic3C2412yes—
312C22×Dic3C2412yes—
313C22×Dic3C2412yes—
314#239—432no—
315C2×D12—22no—
316C2×D12—22no—
317C2×D12—28no—
318C2×D12—22no—
319C2×D12—28no—
320C2×D12—22no—
321C2×D12—22no—
322C2×D12—44no—
323C2×D12C2×D414yes—
324C2×C4×D3—28no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—28no—
328C2×C4×D3—24no—
329C2×C4×D3—24no—
330C2×C4×D3—24no—
331C2×C4×D3—24no—
332C2×C4×D3—44no—
333C3×C4⋊C4—28no—
334C3×C4⋊C4—28no—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—24no—
337C3×C4⋊C4C2×D418yes—
338C3×C4⋊C4C2×D418yes—
339C3×C42—22no—
340C3×C42—22no—
341C3×C42—22no—
342C3×C42C2×D414yes—
343#217—24no—
344#217—24no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—28no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—24no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4—28no—
356(C2×D3)⋊C4—44no—
357(C2×D3)⋊C4C2×D418yes—
358C4⋊Dic3—22no—
359C4⋊Dic3—22no—
360C4⋊Dic3—22no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—28no—
364C4⋊Dic3C2×D414yes—
365Dic3⋊C4—28no—
366Dic3⋊C4—24no—
367Dic3⋊C4—24no—
368Dic3⋊C4—28no—
369Dic3⋊C4—44no—
370C4×Dic3—24no—
371C4×Dic3—24no—
372C4×Dic3—28no—
373C2×#41—68no—
374C2×#41—68no—
375C2×#41—124no—
376C22×Q8—28no—
377C22×Q8—28no—
378C22×Q8—44no—
379C22×Q8C22×D312yes—
380C22×Q8C22×D314yes—
381C22×Q8C22×D312yes—
382C22×D4—32no—
383C22×D4—32no—
384C22×D4—31no—
385C22×D4—31no—
386C22×D4—34no—
387C23×C4—32no—
388C23×C4—32no—
389C23×C4—34no—
390C23×C4C22×D311yescharacteristic
391C23×C4C22×D314yes—
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C4⋊Q8—28no—
395C4⋊Q8—28no—
396C4⋊Q8—28no—
397C4⋊Q8—24no—
398C4⋊Q8#6718yescomplemented
399#124—616no—
400#124—68no—
401#123—616no—
402C22⋊Q8—616no—
403C22⋊Q8—68no—
404C22⋊Q8—68no—
405C22⋊Q8—124no—
406#121—38no—
407#121—616no—
408#121—64no—
409#121—68no—
410C4×Q8—68no—
411C4×D4—616no—
412C4×D4—68no—
413C4×D4—68no—
414C4×D4—64no—
415C4×D4—64no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—34no—
430C2×C4⋊C4—68no—
431C2×C4⋊C4C22×D312yes—
432C2×C4⋊C4C22×D314yes—
433C2×C4⋊C4C22×D314yes—
434C2×C4⋊C4C22×D312yes—
435C2×C4⋊C4C22×D312yes—
436C2×C4⋊C4C22×D312yes—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—32no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—32no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—34no—
448C2×C22⋊C4—32no—
449C2×C22⋊C4—32no—
450C2×C22⋊C4—32no—
451C2×C22⋊C4—34no—
452C2×C42—24no—
453C2×C42—32no—
454C2×C42—34no—
455C2×C42—32no—
456C2×C42C22×D311yescharacteristic
457C2×C42C22×D311yescharacteristic
458C2×C42C22×D311yescharacteristic
459C2×C42C22×D311yescharacteristic
460#95—32no—
461#95—32no—
462#95—32no—
463#95—32no—
464#95—34no—
465#95—32no—
466#95—32no—
467#95—34no—
468#95—34no—
469#95—34no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3C22×D412yes—
475C23×C3C2×#4112yes—
476C23×C32−1+412yes—
477C23×C3C2511yescharacteristic
478C22×D3—22no—
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3C22×D414yes—
492C3×Q8—216no—
493C3×Q8—416no—
494C3×Q8—48no—
495C2×C3×C4—28no—
496C2×C3×C4—24no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—24no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—28no—
507C2×C3×C4—28no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—416no—
512C2×C3×C4C22×D412yes—
513C2×C3×C4C22×D412yes—
514C2×C3×C4C22×D418yes—
515C2×C3×C4C22×D412yes—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C2×#4112yes—
519C2×C3×C4C2×#4112yes—
520C2×C3×C4H(5,𝔽2)12yes—
521C2×C3×C42−1+412yes—
522C2×C3×C42−1+412yes—
523#67—216no—
524#67—48no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3C22×D414yes—
543D12—28no—
544D12—416no—
545D12—44no—
546C4×D3—416no—
547C4×D3—48no—
548C4×D3—48no—
549C24—32no—
550C24—32no—
551C24C23×D311yescharacteristic
552#41—1232no—
553C2×Q8—24no—
554C2×Q8—28no—
555C2×Q8—24no—
556C2×Q8—24no—
557C2×Q8—24no—
558C2×Q8—28no—
559C2×Q8—24no—
560C2×Q8—44no—
561C2×Q8—432no—
562C2×Q8C2×#6718yes—
563C2×D4—38no—
564C2×D4—34no—
565C2×D4—68no—
566C2×D4—64no—
567C2×D4—64no—
568C2×D4—64no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—62no—
572C2×D4—62no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4—62no—
576C2×D4—68no—
577C2×D4—124no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—32no—
588C22×C4—32no—
589C22×C4—32no—
590C22×C4—32no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—44no—
594C22×C4—68no—
595C22×C4—64no—
596C22×C4—64no—
597C22×C4—64no—
598C22×C4—64no—
599C22×C4—64no—
600C22×C4—68no—
601C22×C4—64no—
602C22×C4—124no—
603C22×C4D3×D414yes—
604C22×C4#23914yescomplemented
605C22×C4C23×D314yes—
606C22×C4C23×D311yescharacteristic
607C22×C4C23×D311yescharacteristic
608C22×C4C23×D311yescharacteristic
609C22×C4C23×D311yescharacteristic
610C22×C4C23×D314yes—
611C22×C4C23×D311yescharacteristic
612C22×C4C23×D311yescharacteristic
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—34no—
618C4⋊C4—68no—
619C4⋊C4—68no—
620C4⋊C4—64no—
621C4⋊C4—62no—
622C4⋊C4—64no—
623C4⋊C4—62no—
624C4⋊C4—62no—
625C4⋊C4—62no—
626C4⋊C4—68no—
627C4⋊C4—62no—
628C4⋊C4—124no—
629C4⋊C4C2×#6718yes—
630C4⋊C4C2×#6718yes—
631C22⋊C4—38no—
632C22⋊C4—68no—
633C22⋊C4—68no—
634C22⋊C4—68no—
635C22⋊C4—64no—
636C22⋊C4—64no—
637C22⋊C4—64no—
638C22⋊C4—64no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—64no—
644C22⋊C4—68no—
645C22⋊C4—124no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—68no—
650C42—64no—
651C42—64no—
652C42C2×#6714yes—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3#54714yescomplemented
660C22×C3C23×D411yescharacteristic
661C22×C3C23×D411yescharacteristic
662C22×C3C22×#4111yescharacteristic
663C22×C3C2×H(5,𝔽2)11yescharacteristic
664C22×C3C2×2−1+411yescharacteristic
665C22×C3C2×2−1+411yescharacteristic
666C22×C3C2×2−1+411yescharacteristic
667C2×D3—24no—
668C2×D3—24no—
669C2×D3—24no—
670C2×D3—42no—
671C2×D3—42no—
672C2×D3—42no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—42no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C2×D3—42no—
680C2×D3—42no—
681C3×C4—28no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—44no—
687C3×C4D4214yes—
688C3×C4#54814yescomplemented
689Dic3—24no—
690Dic3—42no—
691Dic3—42no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—34no—
700C23—62no—
701C23—62no—
702C23—62no—
703C23—62no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23C2×D3×D412yes—
714C23C2×#23912yes—
715C23#100712yes—
716C23C24×D311yescharacteristic
717Q8—216no—
718Q8—416no—
719Q8—48no—
720D4—616no—
721D4—68no—
722D4—1216no—
723D4—128no—
724D4—124no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—21no—
728C2×C4—24no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—28no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—34no—
742C2×C4—416no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—62no—
758C2×C4—62no—
759C2×C4—62no—
760C2×C4—1216no—
761C2×C4—128no—
762C2×C4—128no—
763C2×C4C2×D3×D412yes—
764C2×C4C2×D3×D412yes—
765C2×C4#100412yes—
766C2×C4C2×#23912yes—
767C2×C4C2×#23912yes—
768C2×C4#100712yes—
769C2×C4#100712yes—
770C2×C4C22×#6712yes—
771C2×C4C22×#6718yes—
772C2×C4C22×#6712yes—
773C2×C4C22×#6712yes—
774C2×C3—24no—
775C2×C3C2×D4211yescharacteristic
776C2×C3C2×#54711yescharacteristic
777C2×C3C2×#54811yescharacteristic
778C2×C3#348611yescharacteristic
779C2×C3#349911yescharacteristic
780C2×C3#351111yescharacteristic
781C2×C3#355211yescharacteristic
782D3—44no—
783D3—82no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—64no—
791C22—64no—
792C22—64no—
793C22—122no—
794C22—122no—
795C22—122no—
796C22—122no—
797C22—122no—
798C22—122no—
799C22—122no—
800C22—122no—
801C22—122no—
802C22—122no—
803C22—122no—
804C22#572614yescomplemented
805C22C22×D3×D411yescharacteristic
806C22C2×#100411yescharacteristic
807C22C22×#23911yescharacteristic
808C22C2×#100711yescharacteristic
809C22C2×#100711yescharacteristic
810C22C2×#100711yescharacteristic
811C22C23×#6711yescharacteristic
812C4—22no—
813C4—28no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—44no—
818C4—64no—
819C4—122no—
820C4—122no—
821C4—122no—
822C4—122no—
823C4—122no—
824C4D4×#6714yes—
825C4#581714yescomplemented
826C3#5912511yescharacteristic, complemented, Sylow
827C2—24no—
828C2—124no—
829C2—242no—
830C2#8620511yescharacteristic
831C2C2×#572611yescharacteristic
832C2#8621411yescharacteristic
833C2#8621811yescharacteristic
834C2C2×D4×#6711yescharacteristic
835C2C2×#581711yescharacteristic
836C2#8725111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC22×C3×C4⋊Q8C2
hypercenterC22×C4⋊Q8D3
hypocenterC3#59125
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊Q8C2semidirect
2. C2×#5817C2semidirect
3. C2×#5726C2semidirect
4. #84068C2semidirect
5. #83265C2semidirect
6. #83259C2semidirect
7. #83257C2semidirect
8. #83255C2semidirect
9. #83254C2semidirect
10. #83240C2semidirect
11. #83233C2semidirect
12. #83229C2semidirect
13. #82195C2semidirect
14. #82193C2semidirect
15. C4⋊C4×#67C2semidirect
16. C4×#930C2semidirect
17. C4×#930C2semidirect
89. C22×C4⋊Q8D3semidirect
129. C3×C4⋊Q8D4semidirect
154. #930D4semidirect
293. C22×C3×C4#41semidirect
398. C4⋊Q8#67semidirect
604. C22×C4#239semidirect
659. C22×C3#547semidirect
688. C3×C4#548semidirect
804. C22#5726semidirect
825. C4#5817semidirect
826. C3#59125semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Q82
C2×#58172
C2×#57262
#840682
#832652
#832592
#832572
#832552
#832542
#832402
#832332
#832292
#821952
#821932
C4⋊C4×#672
C4×#9302
#591253