Finite Group Databasebeta

← #10804990

Subgroups — #10804990

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic
2D3×#380C211yesmaximal, characteristic, complemented
3#73862C211yesmaximal, characteristic, complemented
4C3×#1799C211yesmaximal, characteristic, complemented
5#71619C211yesmaximal, characteristic, complemented
6#70036C212yesmaximal, complemented
7#70030C212yesmaximal, complemented
8#69530C211yesmaximal, characteristic, complemented
9#69530C211yesmaximal, characteristic, complemented
10#68970C212yesmaximal, complemented
11#68955C212yesmaximal, complemented
12#21874—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×#892—21no—
31C2×D3×C4⋊C4—21no—
32C2×#884C411yescharacteristic, complemented
33C2×#883C411yescharacteristic, complemented
34C2×#882C2211yescharacteristic
35C2×D3×C22⋊C4C2212yes—
36C2×#878C2211yescharacteristic
37C2×C4×D12C411yescharacteristic, complemented
38C2×#872C411yescharacteristic, complemented
39C2×C3×#99C2212yes—
40C3×#380C2211yescharacteristic
41C3×#380C2211yescharacteristic
42C2×#834C2212yes—
43#5212C2211yescharacteristic
44#5212C2211yescharacteristic
45#4987—21no—
46#4987—21no—
47#4955C2212yes—
48C2×#806C2212yes—
49C2×#806C2212yes—
50#4942C2212yes—
51Dic3×C22⋊C4C2212yes—
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×#380—31no—
63#1996—32no—
64#1964—32no—
65#1898—32no—
66#1898—32no—
67#1799—31no—
68#1799—31no—
69#1799—31no—
70#1799D311yescharacteristic, 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⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
110C2×C3×C22⋊C4C2×C411yescharacteristic, complemented
111C2×C3×C22⋊C4C2312yes—
112C2×C3×C22⋊C4C2312yes—
113C2×C3×C22⋊C4C2311yescharacteristic
114C2×C3×C42C2×C411yescharacteristic, complemented
115C2×#217C2×C411yescharacteristic, complemented
116C2×#217C2312yes—
117C2×#217C2312yes—
118C2×#217C2311yescharacteristic
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⋊Dic3—21no—
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3C2×C411yescharacteristic, complemented
147C2×Dic3⋊C4—22no—
148C2×Dic3⋊C4C2×C411yescharacteristic, complemented
149C2×Dic3⋊C4C2×C411yescharacteristic, complemented
150C2×Dic3⋊C4C2×C411yescharacteristic, complemented
151C2×Dic3⋊C4C2×C411yescharacteristic, complemented
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#892—44no—
163D3×C4⋊C4—44no—
164#884—21no—
165#884—21no—
166#884—21no—
167#884—21no—
168#883—21no—
169#883—21no—
170#883—21no—
171#883—21no—
172#882—21no—
173#882—21no—
174#882—21no—
175#882—21no—
176D3×C22⋊C4—42no—
177D3×C22⋊C4—42no—
178#878—21no—
179#878—21no—
180#878—21no—
181#878—21no—
182C4×D12—21no—
183C4×D12—21no—
184C4×D12—21no—
185C4×D12—21no—
186#872—21no—
187#872—21no—
188#872—21no—
189#872—21no—
190C3×#99—42no—
191C3×#95—21no—
192C3×#95—21no—
193#834—42no—
194C3⋊#95—21no—
195C3⋊#95—21no—
196C3⋊#95—22no—
197C3⋊#95—22no—
198#806—42no—
199#806—42no—
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×C4⋊C4—61no—
225C22×C22⋊C4—32no—
226C2×#99—32no—
227C2×#99—32no—
228C2×#99—32no—
229C2×#99C2×D312yes—
230#381—61no—
231#380—31no—
232#380—31no—
233#380—32no—
234#380—61no—
235#380—61no—
236#380—61no—
237#380C2×D311yescharacteristic
238#380C2×D311yescharacteristic
239#379—32no—
240C4×C22⋊C4—32no—
241C4×C22⋊C4—61no—
242C2×#95—61no—
243#342—32no—
244#342—32no—
245#342—32no—
246#342C2×D312yes—
247C24×C3C22×C411yescharacteristic
248C24×C3C2411yescharacteristic
249C23×D3—21no—
250C23×D3—21no—
251C23×D3—21no—
252C23×D3—21no—
253C23×D3—42no—
254C23×D3—42no—
255C23×D3C22×C411yescharacteristic
256C23×D3C22×C411yescharacteristic
257C23×D3C22×C411yescharacteristic
258C23×D3C2×D411yescharacteristic
259C23×D3C2×D411yescharacteristic
260C23×D3C2×D411yescharacteristic
261C23×D3C2×D411yescharacteristic
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4C22×C411yescharacteristic
275C22×C3×C4C22×C411yescharacteristic
276C22×C3×C4C22×C411yescharacteristic
277C22×C3×C4C22×C411yescharacteristic
278C22×C3×C4C22×C411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C2×#67—21no—
284C2×#67—21no—
285C2×#67—21no—
286C2×#67—21no—
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—21no—
290C2×#67—21no—
291C2×#67—21no—
292C2×#67—21no—
293C2×#67—21no—
294C2×#67—21no—
295C2×#67—42no—
296C2×#67—42no—
297C2×#67—42no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—42no—
301C22×Dic3C22×C411yescharacteristic
302C22×Dic3C22×C411yescharacteristic
303C22×Dic3C22×C411yescharacteristic
304C22×Dic3C22×C411yescharacteristic
305C22×Dic3C22×C411yescharacteristic
306C22×Dic3C2×D411yescharacteristic
307C22×Dic3C2×D411yescharacteristic
308C22×Dic3C2×D411yescharacteristic
309C22×Dic3C2×D411yescharacteristic
310#235—44no—
311#235—44no—
312#235—44no—
313#235—44no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12—42no—
319C2×D12—42no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—24no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—42no—
326C2×C4×D3—42no—
327C2×C4×D3—42no—
328C2×C4×D3—42no—
329C2×C4×D3—42no—
330C2×C4×D3—42no—
331C2×C4×D3—42no—
332C2×C4×D3—42no—
333C2×C4×D3—42no—
334C2×C4×D3—42no—
335C2×C4×D3—44no—
336C2×C4×D3—44no—
337C2×C4×D3—44no—
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×C4×D3C22⋊C411yescharacteristic
349C2×C4×D3C22⋊C411yescharacteristic
350C2×C4×D3C22⋊C411yescharacteristic
351C2×C4×D3C22⋊C411yescharacteristic
352C2×C4×D3C22⋊C411yescharacteristic
353C2×C4×D3C22⋊C411yescharacteristic
354C2×Dic6—21no—
355C2×Dic6—21no—
356C2×Dic6—42no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—42no—
360C3×C4⋊C4—42no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—22no—
366C3×C22⋊C4—22no—
367C3×C22⋊C4—22no—
368C3×C22⋊C4—22no—
369C3×C42—21no—
370C3×C42—21no—
371#217—21no—
372#217—21no—
373#217—21no—
374#217—21no—
375#217—22no—
376#217—22no—
377#217—22no—
378#217—22no—
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—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—44no—
392(C2×D3)⋊C4—44no—
393(C2×D3)⋊C4—44no—
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3—42no—
397C4⋊Dic3—42no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4—21no—
406Dic3⋊C4—44no—
407C4×Dic3—21no—
408C4×Dic3—21no—
409C4×Dic3—44no—
410C25—31no—
411C2×#41—61no—
412C2×#41—61no—
413C2×#41—61no—
414C2×#41—61no—
415C2×#41—124no—
416C22×Q8—31no—
417C22×D4—31no—
418C22×D4—31no—
419C22×D4—31no—
420C22×D4—31no—
421C22×D4—31no—
422C22×D4—31no—
423C22×D4C22×D311yescharacteristic
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—31no—
433C23×C4—31no—
434C23×C4—31no—
435C23×C4—31no—
436C23×C4—31no—
437C23×C4—31no—
438C23×C4—62no—
439C23×C4—124no—
440C23×C4C4×D311yescharacteristic, complemented
441C23×C4C22×D311yescharacteristic
442#123—61no—
443#123—61no—
444#123—61no—
445#123—61no—
446#123—61no—
447#123—61no—
448#123—61no—
449#123—61no—
450C22⋊Q8—61no—
451C22⋊Q8—61no—
452C22⋊Q8—61no—
453C22⋊Q8—61no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8—61no—
457C22⋊Q8—61no—
458#121—61no—
459#121—61no—
460#121—61no—
461#121—61no—
462#121—61no—
463#121—61no—
464#121—61no—
465#121—61no—
466#120—61no—
467#120—61no—
468#120—61no—
469#120—61no—
470#120—61no—
471#120—61no—
472#120—61no—
473#120—61no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4—61no—
485C4×D4—61no—
486C4×D4—61no—
487C4×D4—61no—
488C4×D4—61no—
489C4×D4—61no—
490#117—61no—
491#117—61no—
492#117—61no—
493#117—61no—
494#117—124no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—62no—
503C2×C4⋊C4—61no—
504C2×C4⋊C4—61no—
505C2×C4⋊C4—124no—
506C2×C4⋊C4C4×D311yescharacteristic, complemented
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—32no—
516C2×C22⋊C4—32no—
517C2×C22⋊C4—62no—
518C2×C22⋊C4—62no—
519C2×C22⋊C4—62no—
520C2×C22⋊C4—122no—
521C2×C22⋊C4—122no—
522C2×C22⋊C4C4×D311yescharacteristic, complemented
523C2×C22⋊C4C22×D312yes—
524C2×C22⋊C4C22×D312yes—
525C2×C22⋊C4C22×D311yescharacteristic
526C2×C42—31no—
527C2×C42—62no—
528C2×C42C4×D311yescharacteristic, complemented
529#99—42no—
530#99—122no—
531#99—122no—
532#99—122no—
533#95—21no—
534#95—21no—
535#95—62no—
536#95—62no—
537#95—61no—
538#95—61no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3C23×C411yescharacteristic
547C23×C3C22×D411yescharacteristic
548C23×C3C22×D411yescharacteristic
549C23×C3H(5,𝔽2)11yescharacteristic
550C23×C3H(5,𝔽2)11yescharacteristic
551C23×C32−1+411yescharacteristic
552C23×C32−1+411yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3—41no—
578C22×D3—41no—
579C22×D3—41no—
580C22×D3—44no—
581C22×D3—44no—
582C22×D3—44no—
583C22×D3—44no—
584C22×D3—41no—
585C22×D3—41no—
586C22×D3C2×C22⋊C411yescharacteristic
587C22×D3C2×C22⋊C411yescharacteristic
588C22×D3C2×C22⋊C411yescharacteristic
589C22×D3C2×C22⋊C411yescharacteristic
590C3×D4—41no—
591C3×D4—41no—
592C3×D4—41no—
593C3×D4—41no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—42no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4C2×C22⋊C411yescharacteristic
616C2×C3×C4C2×C22⋊C411yescharacteristic
617C2×C3×C4C2×C22⋊C411yescharacteristic
618C2×C3×C4C2×C22⋊C411yescharacteristic
619#67—42no—
620#67—42no—
621#67—42no—
622#67—41no—
623#67—41no—
624#67—41no—
625#67—41no—
626#67—42no—
627#67—42no—
628#67—42no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—42no—
643C2×Dic3—42no—
644C2×Dic3—42no—
645C2×Dic3—42no—
646C2×Dic3—42no—
647C2×Dic3—42no—
648C2×Dic3C2×C22⋊C411yescharacteristic
649C2×Dic3C2×C22⋊C411yescharacteristic
650C2×Dic3C2×C22⋊C411yescharacteristic
651C2×Dic3C2×C22⋊C411yescharacteristic
652D12—42no—
653D12—42no—
654D12—42no—
655D12—42no—
656C4×D3—22no—
657C4×D3—22no—
658C4×D3—22no—
659C4×D3—22no—
660C4×D3—22no—
661C4×D3—22no—
662C4×D3—22no—
663C4×D3—22no—
664C4×D3—22no—
665C4×D3—41no—
666C4×D3—41no—
667C4×D3—41no—
668C4×D3—41no—
669C4×D3—41no—
670C4×D3—41no—
671C4×D3—42no—
672C4×D3—42no—
673C4×D3—88no—
674C4×D3#9914yescomplemented
675Dic6—42no—
676Dic6—42no—
677C24—31no—
678C24—31no—
679C24—31no—
680C24—31no—
681C24—31no—
682C24—31no—
683C24—31no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—122no—
689C24—122no—
690C24C2×C4×D311yescharacteristic
691C24C23×D311yescharacteristic
692#41—124no—
693#41—124no—
694#41—124no—
695#41—124no—
696C2×Q8—61no—
697C2×Q8—61no—
698C2×Q8—122no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—61no—
706C2×D4—61no—
707C2×D4—61no—
708C2×D4—61no—
709C2×D4—61no—
710C2×D4—61no—
711C2×D4—61no—
712C2×D4—61no—
713C2×D4—61no—
714C2×D4—61no—
715C2×D4—61no—
716C2×D4—61no—
717C2×D4—61no—
718C2×D4—61no—
719C2×D4—61no—
720C2×D4—61no—
721C2×D4—122no—
722C2×D4—122no—
723C2×D4—122no—
724C2×D4—122no—
725C2×D4—122no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—31no—
731C22×C4—31no—
732C22×C4—31no—
733C22×C4—31no—
734C22×C4—31no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—64no—
758C22×C4—64no—
759C22×C4—64no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—62no—
763C22×C4—62no—
764C22×C4—122no—
765C22×C4—122no—
766C22×C4—122no—
767C22×C4—122no—
768C22×C4—122no—
769C22×C4—122no—
770C22×C4—122no—
771C22×C4—122no—
772C22×C4—122no—
773C22×C4—122no—
774C22×C4—124no—
775C22×C4—124no—
776C22×C4—124no—
777C22×C4—122no—
778C22×C4C2×C4×D311yescharacteristic
779C22×C4C2×C4×D311yescharacteristic
780C22×C4C2×C4×D311yescharacteristic
781C22×C4C2×C4×D311yescharacteristic
782C22×C4C2×C4×D311yescharacteristic
783C22×C4D3×D411yescharacteristic
784C22×C4D3×D411yescharacteristic
785C22×C4D3×D411yescharacteristic
786C22×C4D3×D411yescharacteristic
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—42no—
790C4⋊C4—42no—
791C4⋊C4—61no—
792C4⋊C4—61no—
793C4⋊C4—61no—
794C4⋊C4—61no—
795C4⋊C4—61no—
796C4⋊C4—61no—
797C4⋊C4—61no—
798C4⋊C4—61no—
799C4⋊C4—61no—
800C4⋊C4—61no—
801C4⋊C4—122no—
802C4⋊C4—122no—
803C4⋊C4—124no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—61no—
813C22⋊C4—61no—
814C22⋊C4—61no—
815C22⋊C4—61no—
816C22⋊C4—61no—
817C22⋊C4—61no—
818C22⋊C4—61no—
819C22⋊C4—61no—
820C22⋊C4—61no—
821C22⋊C4—61no—
822C22⋊C4—61no—
823C22⋊C4—61no—
824C22⋊C4—61no—
825C22⋊C4—61no—
826C22⋊C4—61no—
827C22⋊C4—61no—
828C22⋊C4—62no—
829C22⋊C4—62no—
830C22⋊C4—62no—
831C22⋊C4—62no—
832C22⋊C4—124no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C42—21no—
836C42—21no—
837C42—61no—
838C42—61no—
839C42—124no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—81no—
854C22×C3—81no—
855C22×C3C22×C22⋊C411yescharacteristic
856C22×C3#52011yescharacteristic
857C22×C3#52011yescharacteristic
858C22×C3#53511yescharacteristic
859C22×C3#53611yescharacteristic
860C22×C3#53711yescharacteristic
861C22×C3#53711yescharacteristic
862C2×D3—24no—
863C2×D3—24no—
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—42no—
879C2×D3—42no—
880C2×D3—42no—
881C2×D3—42no—
882C2×D3—42no—
883C2×D3—42no—
884C2×D3—41no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—81no—
888C2×D3—81no—
889C2×D3C2×#9912yes—
890C2×D3#41012yes—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—82no—
898C3×C4—82no—
899C3×C4C2×#9912yes—
900Dic3—21no—
901Dic3—21no—
902Dic3—21no—
903Dic3—41no—
904Dic3—41no—
905Dic3—41no—
906Dic3—82no—
907Dic3—82no—
908Dic3C2×#9912yes—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—31no—
913C23—31no—
914C23—31no—
915C23—31no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—121no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—124no—
950C23—124no—
951C23—124no—
952C23—124no—
953C23C22×C4×D311yescharacteristic
954C23C2×D3×D411yescharacteristic
955C23C2×D3×D411yescharacteristic
956C23#100411yescharacteristic
957C23#100711yescharacteristic
958C23#100911yescharacteristic
959C23#101011yescharacteristic
960Q8—122no—
961Q8—122no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—122no—
967D4—122no—
968D4—122no—
969D4—122no—
970D4—122no—
971D4—122no—
972D4—122no—
973D4—122no—
974D4—122no—
975D4—122no—
976D4—121no—
977D4—121no—
978D4—121no—
979D4—121no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—31no—
989C2×C4—34no—
990C2×C4—31no—
991C2×C4—31no—
992C2×C4—31no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—42no—
997C2×C4—42no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—62no—
1007C2×C4—62no—
1008C2×C4—62no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—121no—
1024C2×C4—121no—
1025C2×C4—121no—
1026C2×C4—121no—
1027C2×C4—121no—
1028C2×C4—121no—
1029C2×C4—122no—
1030C2×C4—121no—
1031C2×C4—121no—
1032C2×C4—121no—
1033C2×C4—122no—
1034C2×C4—121no—
1035C2×C4—121no—
1036C2×C4—122no—
1037C2×C4—122no—
1038C2×C4—122no—
1039C2×C4—122no—
1040C2×C4—122no—
1041C2×C4—122no—
1042C2×C4—248no—
1043C2×C4D3×C22⋊C411yescharacteristic
1044C2×C4D3×C22⋊C411yescharacteristic
1045C2×C4D3×C22⋊C411yescharacteristic
1046C2×C4D3×C22⋊C411yescharacteristic
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—81no—
1054C2×C3#231111yescharacteristic
1055C2×C3C22×#9911yescharacteristic
1056C2×C3C2×#41011yescharacteristic
1057D3—22no—
1058D3—22no—
1059D3—41no—
1060D3—41no—
1061D3—81no—
1062C22—21no—
1063C22—21no—
1064C22—21no—
1065C22—21no—
1066C22—21no—
1067C22—21no—
1068C22—32no—
1069C22—32no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—41no—
1075C22—41no—
1076C22—41no—
1077C22—64no—
1078C22—64no—
1079C22—61no—
1080C22—61no—
1081C22—61no—
1082C22—61no—
1083C22—61no—
1084C22—61no—
1085C22—61no—
1086C22—61no—
1087C22—61no—
1088C22—61no—
1089C22—81no—
1090C22—81no—
1091C22—122no—
1092C22—122no—
1093C22—122no—
1094C22—122no—
1095C22—122no—
1096C22—122no—
1097C22—122no—
1098C22—122no—
1099C22—122no—
1100C22—122no—
1101C22—121no—
1102C22—121no—
1103C22—121no—
1104C22—241no—
1105C22—241no—
1106C22C2×D3×C22⋊C411yescharacteristic
1107C22#550411yescharacteristic
1108C22#552311yescharacteristic
1109C22#560711yescharacteristic
1110C22#560811yescharacteristic
1111C22#562811yescharacteristic
1112C22#562911yescharacteristic
1113C4—21no—
1114C4—21no—
1115C4—21no—
1116C4—32no—
1117C4—41no—
1118C4—41no—
1119C4—41no—
1120C4—61no—
1121C4—61no—
1122C4—61no—
1123C4—82no—
1124C4—82no—
1125C4—121no—
1126C4—121no—
1127C4—121no—
1128C4—242no—
1129C4—242no—
1130C4D3×#9912yes—
1131C3#2187411yescharacteristic, complemented, Sylow
1132C2—21no—
1133C2—21no—
1134C2—21no—
1135C2—21no—
1136C2—21no—
1137C2—21no—
1138C2—62no—
1139C2—62no—
1140C2—81no—
1141C2—121no—
1142C2—121no—
1143C2—241no—
1144C2#7400311yescharacteristic
1145C2C2×D3×#9911yescharacteristic
1146C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1799C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5547C2
cosocleC24×C3C24
hypercenter#1799D3
hypocenterC3#21874
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. D3×#380C2semidirect
3. #73862C2semidirect
4. C3×#1799C2semidirect
5. #71619C2semidirect
6. #70036C2semidirect
7. #70030C2semidirect
8. #69530C2semidirect
9. #69530C2semidirect
10. #68970C2semidirect
11. #68955C2semidirect
13. C22×#235C4semidirect
18. C2×C4×#67C4semidirect
28. C2×#896C4semidirect
29. C2×#894C4semidirect
32. C2×#884C4semidirect
33. C2×#883C4semidirect
37. C2×C4×D12C4semidirect
38. C2×#872C4semidirect
70. #1799D3semidirect
73. C23×C3×C4C2×C4semidirect
77. C22×#67C2×C4semidirect
93. C22×C4×D3C2×C4semidirect
102. C22×Dic6C2×C4semidirect
109. C2×C3×C4⋊C4C2×C4semidirect
110. 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
146. C2×C4⋊Dic3C2×C4semidirect
148. C2×Dic3⋊C4C2×C4semidirect
149. C2×Dic3⋊C4C2×C4semidirect
150. C2×Dic3⋊C4C2×C4semidirect
151. C2×Dic3⋊C4C2×C4semidirect
153. C2×C4×Dic3C2×C4semidirect
440. C23×C4C4×D3semidirect
506. C2×C4⋊C4C4×D3semidirect
522. C2×C22⋊C4C4×D3semidirect
528. C2×C42C4×D3semidirect
674. C4×D3#99semidirect
1131. C3#21874semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
D3×#3802
#738622
C3×#17992
#716192
#700362
#700302
#695302
#689702
#689552
#218743