Finite Group Databasebeta

← #11824506

Subgroups — #11824506

Order 1152.

1513 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4C2×C4×#626C211yesmaximal, characteristic
5C2×#63871C211yesmaximal, characteristic, complemented
6C2×#63856C211yesmaximal, characteristic, complemented
7#10591384C212yesmaximal
8#10591303C212yesmaximal, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591244C212yesmaximal, complemented
11#10591203C212yesmaximal, complemented
12#83259—31nomaximal
13#82780—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×Dic6C2211yescharacteristic
18C22×#626C2211yescharacteristic
19#64155—24no—
20C2×#3752C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2212yes—
23C3×#946—24no—
24C3×#944—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2212yes—
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2212yes—
34C2×#3722C2212yes—
35C2×#3722C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2212yes—
39C4×#626—24no—
40#63871—24no—
41#63856—24no—
42#63579C2212yes—
43C2×C3×C4⋊Q8—31no—
44C2×C3×C22⋊Q8—31no—
45C2×#946—31no—
46C2×#946—31no—
47C2×#946—31no—
48C2×#946—31no—
49C2×#946—61no—
50C2×#946D311yescharacteristic, complemented
51C2×#944D311yescharacteristic, complemented
52C2×C4×#67—31no—
53C2×#924—31no—
54C2×#897—31no—
55C2×C4×D12—31no—
56#4993—32no—
57#4993—32no—
58#4993—32no—
59#4988—32no—
60#4975—32no—
61#4975—32no—
62Dic3×C4⋊C4—31no—
63#4957—32no—
64#4949—32no—
65C4×C4⋊Dic3—31no—
66C23×C3⋊D3C2311yescharacteristic
67C23×C3×D3C2311yescharacteristic
68C2×C32×Q8—22no—
69C2×C32×Q8—22no—
70C2×C32×Q8—22no—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2312yes—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3—22no—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—22no—
89C2×#626—22no—
90C2×#626—22no—
91C2×#626Q814yescomplemented
92#3752—24no—
93C4⋊(C3⋊Dic3)D414yescomplemented
94#3750—24no—
95C3×(C2×D3)⋊C4—24no—
96C3×C4⋊Dic3D414yescomplemented
97C3×Dic3⋊C4—24no—
98C3×Dic3⋊C4—24no—
99C3×Dic3⋊C4—24no—
100C3×C4×Dic3D414yes—
101#3724—24no—
102Dic3⋊Dic3—24no—
103Dic3⋊Dic3—22no—
104#3722—24no—
105#3722—22no—
106(C2×D3)⋊Dic3—24no—
107(C2×D3)⋊Dic3—22no—
108Dic32—24no—
109#2542—91noSylow
110C22×C3×Q8—21no—
111C22×C3×Q8—31no—
112C22×C3×Q8C2×D311yescharacteristic
113C22×C3×Q8C2×D311yescharacteristic
114C23×C3×C4—31no—
115C22×#67—31no—
116C22×D12—31no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—61no—
120C22×C4×D3C2×D311yescharacteristic
121C22×Dic6C2×D311yescharacteristic
122C3×C4⋊Q8—64no—
123C3×C22⋊Q8—64no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—32no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C42—31no—
130C2×#217—31no—
131C2×#217—32no—
132#946—24no—
133#946—64no—
134#946—64no—
135#946—64no—
136#946—68no—
137#946—64no—
138#944—24no—
139C4×#67—64no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—62no—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—32no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—61no—
155C2×C4⋊Dic3C2×D311yescharacteristic
156#924—64no—
157C2×Dic3⋊C4—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—62no—
164C2×Dic3⋊C4C2×D312yes—
165C2×Dic3⋊C4C2×D312yes—
166C2×Dic3⋊C4C2×D312yes—
167C2×C4×Dic3—32no—
168C2×C4×Dic3—32no—
169C2×C4×Dic3C2×D311yescharacteristic
170#897—64no—
171C4×D12—64no—
172C3⋊#95—32no—
173C3⋊#95—32no—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—21no—
176C22×C3⋊D3—21no—
177C22×C3⋊D3—21no—
178C22×C3⋊D3—21no—
179C22×C3⋊D3—21no—
180C22×C3⋊D3—21no—
181C22×C3⋊D3C2×Q812yes—
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3C2×Q812yes—
189C32×Q8—44no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—22no—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D412yes—
195C2×C32×C4C2×D412yes—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—22no—
198C2×C3⋊Dic3—22no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3C2×D414yes—
202C4×C3⋊D3—44no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3C2×D412yes—
214C2×C3×Dic3C2×D414yes—
215C2×C3×Dic3C2×D412yes—
216C2×C3×Dic3C2×Q812yes—
217C2×C3×Dic3#4112yes—
218C3×C4×D3—44no—
219C3×Dic6—44no—
220#626—28no—
221C2×C4⋊Q8—31no—
222C2×C22⋊Q8—31no—
223C2×C22⋊Q8—91no—
224C2×C22⋊Q8—91no—
225C2×C22⋊Q8—91no—
226C2×C4×D4—91no—
227#399—92no—
228#399—92no—
229#390—92no—
230#384—92no—
231C4×C4⋊C4—91no—
232C24×C3—31no—
233C23×D3—31no—
234C23×D3—31no—
235C23×D3—61no—
236C23×D3C22×D311yescharacteristic
237C2×C3×Q8—24no—
238C2×C3×Q8—22no—
239C2×C3×Q8—22no—
240C2×C3×Q8—22no—
241C2×C3×Q8—22no—
242C2×C3×Q8—22no—
243C2×C3×Q8—22no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C2×C3×Q8—62no—
247C2×C3×Q8—62no—
248C2×C3×Q8—62no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—62no—
257C22×C3×C4—62no—
258C22×C3×C4—62no—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—34no—
264C2×#67—62no—
265C2×#67—62no—
266C22×Dic3—32no—
267C22×Dic3—32no—
268C22×Dic3—31no—
269C22×Dic3—31no—
270C22×Dic3—61no—
271C22×Dic3—62no—
272C22×Dic3C22×D311yescharacteristic
273C22×Dic3C22×D312yes—
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D311yescharacteristic
277C2×D12—34no—
278C2×D12—62no—
279C2×D12—62no—
280C2×C4×D3—22no—
281C2×C4×D3—22no—
282C2×C4×D3—22no—
283C2×C4×D3—64no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×C4×D3—62no—
290C2×C4×D3—122no—
291C2×C4×D3—122no—
292C2×Dic6—22no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—64no—
297C3×C4⋊C4—64no—
298C3×C4⋊C4—64no—
299C3×C22⋊C4—64no—
300C3×C42—34no—
301#217—64no—
302#217—62no—
303(C2×D3)⋊C4—24no—
304(C2×D3)⋊C4—62no—
305(C2×D3)⋊C4—64no—
306(C2×D3)⋊C4—64no—
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—68no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312(C2×D3)⋊C4—64no—
313C4⋊Dic3—34no—
314C4⋊Dic3—34no—
315C4⋊Dic3—64no—
316C4⋊Dic3—62no—
317C4⋊Dic3—64no—
318C4⋊Dic3#6714yescomplemented
319Dic3⋊C4—24no—
320Dic3⋊C4—24no—
321Dic3⋊C4—24no—
322Dic3⋊C4—64no—
323Dic3⋊C4—64no—
324Dic3⋊C4—64no—
325Dic3⋊C4—64no—
326Dic3⋊C4—68no—
327Dic3⋊C4—62no—
328Dic3⋊C4—64no—
329C4×Dic3—64no—
330C4×Dic3—64no—
331C4×Dic3#6714yes—
332C22×C32C22×D411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C22×D411yescharacteristic
335C22×C32C22×Q811yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C22×C322−1+411yescharacteristic
338C22×C322−1+411yescharacteristic
339C2×C3⋊D3—22no—
340C2×C3⋊D3—22no—
341C2×C3⋊D3—22no—
342C2×C3⋊D3—41no—
343C2×C3⋊D3—41no—
344C2×C3⋊D3—41no—
345C2×C3⋊D3—41no—
346C2×C3×D3—22no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3—41no—
350C2×C3×D3—41no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C32×C4—42no—
354C32×C4#12714yes—
355C3⋊Dic3—24no—
356C3⋊Dic3—41no—
357C3×Dic3—22no—
358C3×Dic3—24no—
359C3×Dic3—42no—
360C3×Dic3—41no—
361C3×Dic3C22⋊Q814yescomplemented
362C22×Q8—31no—
363C22×Q8D3211yescharacteristic
364C22×D4—91no—
365C23×C4—31no—
366C23×C4—91no—
367C4⋊Q8—64no—
368C22⋊Q8—64no—
369C22⋊Q8—184no—
370C22⋊Q8—184no—
371C22⋊Q8—184no—
372C4×D4—184no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—32no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—92no—
380C2×C4⋊C4—92no—
381C2×C4⋊C4—92no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—92no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—92no—
387C2×C22⋊C4—92no—
388C2×C42—31no—
389C2×C42—92no—
390#95—92no—
391C23×C3—21no—
392C23×C3—32no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3—61no—
397C23×C3—61no—
398C23×C3—61no—
399C23×C3C23×D311yescharacteristic
400C23×C3C23×D311yescharacteristic
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—32no—
408C22×D3—32no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—62no—
412C22×D3—61no—
413C22×D3—61no—
414C22×D3—61no—
415C22×D3—61no—
416C22×D3—61no—
417C22×D3—61no—
418C22×D3—61no—
419C22×D3—61no—
420C22×D3—61no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—121no—
425C22×D3—121no—
426C22×D3—121no—
427C22×D3—121no—
428C22×D3D3×Q812yes—
429C3×Q8—48no—
430C3×Q8—44no—
431C3×Q8—44no—
432C3×Q8—124no—
433C2×C3×C4—24no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—34no—
447C2×C3×C4—32no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—62no—
456C2×C3×C4—61no—
457C2×C3×C4—62no—
458C2×C3×C4—61no—
459C2×C3×C4—62no—
460C2×C3×C4—124no—
461C2×C3×C4D3×D412yes—
462C2×C3×C4D3×D412yes—
463C2×C3×C4D3×D412yes—
464C2×C3×C4D3×D412yes—
465C2×C3×C4C2×#6712yes—
466C2×C3×C4C2×#6712yes—
467#67—68no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—21no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—21no—
476C2×Dic3—22no—
477C2×Dic3—21no—
478C2×Dic3—34no—
479C2×Dic3—34no—
480C2×Dic3—64no—
481C2×Dic3—62no—
482C2×Dic3—62no—
483C2×Dic3—62no—
484C2×Dic3—62no—
485C2×Dic3—62no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—122no—
495C2×Dic3—122no—
496C2×Dic3D3×Q812yes—
497C2×Dic3#23912yes—
498C2×Dic3C2×#6712yes—
499C2×Dic3C2×#6714yes—
500C2×Dic3C2×#6712yes—
501D12—68no—
502C4×D3—44no—
503C4×D3—128no—
504C4×D3—124no—
505C4×D3—124no—
506Dic6—44no—
507C2×C32C2×C22⋊Q811yescharacteristic
508C2×C32C2×#12711yescharacteristic
509C2×C32#53611yescharacteristic
510C2×C32#54711yescharacteristic
511C2×C32#54711yescharacteristic
512C2×C32D4×Q811yescharacteristic
513C2×C32D4×Q811yescharacteristic
514C3⋊D3—42no—
515C3×D3—42no—
516C24—31no—
517C24—91no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—62no—
522C2×Q8—62no—
523C2×Q8—62no—
524C2×D4—94no—
525C2×D4—182no—
526C2×D4—182no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—92no—
536C22×C4—91no—
537C22×C4—182no—
538C22×C4—182no—
539C22×C4—182no—
540C22×C4C2×D3212yes—
541C22×C4C2×D3211yescharacteristic
542C4⋊C4—34no—
543C4⋊C4—64no—
544C4⋊C4—64no—
545C4⋊C4—64no—
546C4⋊C4—94no—
547C4⋊C4—184no—
548C4⋊C4—182no—
549C4⋊C4—184no—
550C4⋊C4—184no—
551C22⋊C4—64no—
552C22⋊C4—184no—
553C22⋊C4—182no—
554C22⋊C4—184no—
555C22⋊C4—182no—
556C22⋊C4—184no—
557C42—34no—
558C42—184no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—121no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×Q811yescharacteristic
578C22×C3C2×D3×Q811yescharacteristic
579C22×C3C2×#23911yescharacteristic
580C22×C3#100711yescharacteristic
581C22×C3#100711yescharacteristic
582C22×C3#100711yescharacteristic
583C22×C3D3×#4111yescharacteristic
584C22×C3#101011yescharacteristic
585C22×C3C22×#6711yescharacteristic
586C22×C3C22×#6711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—64no—
595C2×D3—62no—
596C2×D3—62no—
597C2×D3—62no—
598C2×D3—62no—
599C2×D3—62no—
600C2×D3—62no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3—122no—
604C2×D3—122no—
605C2×D3—122no—
606C2×D3—122no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—121no—
614C2×D3—121no—
615C3×C4—24no—
616C3×C4—34no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—64no—
621C3×C4—62no—
622C3×C4—121no—
623C3×C4—122no—
624C3×C4#94014yes—
625C3×C4#94014yes—
626Dic3—22no—
627Dic3—24no—
628Dic3—42no—
629Dic3—41no—
630Dic3—64no—
631Dic3—64no—
632Dic3—124no—
633Dic3—122no—
634Dic3—121no—
635Dic3—121no—
636Dic3#94614yescomplemented
637C32#254211yescharacteristic, complemented, Sylow
638C23—32no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—92no—
646C23—181no—
647C23—181no—
648C23—181no—
649C23—181no—
650C23—181no—
651C23—181no—
652C23C22×D3211yescharacteristic
653Q8—44no—
654Q8—124no—
655D4—188no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—34no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—62no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—94no—
675C2×C4—124no—
676C2×C4—182no—
677C2×C4—182no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4—364no—
682C2×C4D3×#6712yes—
683C2×C4D3×#6712yes—
684C2×C4#381112yes—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—122no—
693C2×C3D3×C22⋊Q811yescharacteristic
694C2×C3#562811yescharacteristic
695C2×C3#563111yescharacteristic
696C2×C3#563211yescharacteristic
697C2×C3#572611yescharacteristic
698C2×C3#572611yescharacteristic
699C2×C3#572711yescharacteristic
700C2×C3#572711yescharacteristic
701C2×C3C2×#94011yescharacteristic
702C2×C3C2×#94011yescharacteristic
703C2×C3C2×#94611yescharacteristic
704C2×C3Q8×#6711yescharacteristic
705C2×C3#581611yescharacteristic
706C2×C3#582411yescharacteristic
707D3—42no—
708D3—124no—
709D3—122no—
710D3—122no—
711C22—62no—
712C22—62no—
713C22—62no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—182no—
719C22—182no—
720C22—182no—
721C22—361no—
722C22—361no—
723C22—361no—
724C22—361no—
725C22#6431511yescharacteristic
726C22#6431611yescharacteristic
727C22D32×Q811yescharacteristic
728C22D3×#23911yescharacteristic
729C22C2×D3×#6711yescharacteristic
730C22C2×D3×#6711yescharacteristic
731C22C2×#381111yescharacteristic
732C4—34no—
733C4—42no—
734C4—64no—
735C4—62no—
736C4—121no—
737C4—122no—
738C4—184no—
739C4—361no—
740C4#6397914yes—
741C3—21no—
742C3#8278011yescharacteristic, complemented
743C3#8325911yescharacteristic, complemented
744C2—122no—
745C2—362no—
746C2#1059534111yescharacteristic
747C2#1059535811yescharacteristic
748C2#1059536111yescharacteristic
749C2#1059539711yescharacteristic
750C2#1059540311yescharacteristic
751C2D3×#94611yescharacteristic
752C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC22×#626C22
hypercenterC22×Q8D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×#944C2semidirect
5. C2×#63871C2semidirect
6. C2×#63856C2semidirect
8. #10591303C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591244C2semidirect
11. #10591203C2semidirect
50. C2×#946D3semidirect
51. C2×#944D3semidirect
91. C2×#626Q8semidirect
93. C4⋊(C3⋊Dic3)D4semidirect
96. C3×C4⋊Dic3D4semidirect
318. C4⋊Dic3#67semidirect
361. C3×Dic3C22⋊Q8semidirect
636. Dic3#946semidirect
637. C32#2542semidirect
742. C3#82780semidirect
743. C3#83259semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C2×C3×#9462
C2×C3×#9442
C2×C4×#6262
C2×#638712
C2×#638562
#105913842
#105913032
Dic3×C4⋊Dic32
#105912442
#105912032
#832593
#827803