Finite Group Databasebeta

← C2×#10595341 #11902556

Subgroups — C2×#10595341 #11902556

Order 1152.

3709 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5#10595341C2116yesmaximal, direct product factor
6C2×#63910C212yesmaximal, complemented
7C2×C4×#626C211yesmaximal, characteristic, complemented
8C2×#63897C212yesmaximal, complemented
9C2×#63894C211yesmaximal, characteristic, complemented
10C2×#63883C212yesmaximal, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63853C212yesmaximal, complemented
13C2×#5726—31nomaximal
14C2×#5631—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C2×#3832—28no—
17C2×#3832C2218yescomplemented
18C22×C4⋊(C3⋊D3)C2212yes—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2212yes—
25C22×#626C2211yescharacteristic
26C22×#624C2212yes—
27C22×#624C2212yes—
28C2×#3799—28no—
29C2×#3799C2218yescomplemented
30C3×#946C2218yescomplemented
31C3×#944C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2212yes—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2212yes—
41C2×#3722C2212yes—
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44#63910C22116yescomplemented
45C4×#626C2218yescomplemented
46#63897C22116yescomplemented
47#63894C2218yescomplemented
48#63883C22116yescomplemented
49#63871C2218yescomplemented
50#63853C22116yescomplemented
51C22×#239—31no—
52C22×#239—31no—
53C22×#239—31no—
54C22×#239—61no—
55C22×#235—31no—
56C2×C3×C4⋊Q8—31no—
57C2×C3×C22⋊Q8—31no—
58C2×#946—31no—
59C2×#946D311yescharacteristic, complemented
60C2×#944D311yescharacteristic, complemented
61C2×C4×#67—31no—
62#5726—316no—
63#5631—316no—
64C2×#897—31no—
65C2×#895—32no—
66C2×#894—32no—
67C2×#894—32no—
68C2×#894—32no—
69C2×#893—31no—
70C2×D3×C4⋊C4—32no—
71C2×D3×C4⋊C4—32no—
72C2×#884—32no—
73C2×#883—32no—
74C2×C4×D12—31no—
75C2×C4×D12—31no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3⋊D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C2×C32×Q8—24no—
80C2×C32×Q8C2314yes—
81C22×C32×C4C2312yes—
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84#3832—232no—
85C2×C4⋊(C3⋊D3)—28no—
86C2×C4⋊(C3⋊D3)D418yescomplemented
87C2×C4⋊(C3⋊D3)C2318yes—
88C2×C4⋊(C3⋊D3)C2314yes—
89C2×C4×C3⋊D3—28no—
90C2×C4×C3⋊D3—24no—
91C2×C4×C3⋊D3C2318yes—
92C2×C4×C3⋊D3C2314yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2311yescharacteristic
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3C2314yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6C2314yes—
102C2×#626—28no—
103C2×#626—24no—
104C2×#626C2318yes—
105C2×#626C2314yes—
106C2×#624—28no—
107C2×#624—28no—
108C2×#624C2318yes—
109C2×#624C2318yes—
110#3799—232no—
111C3×(C2×D3)⋊C4C2318yes—
112C3×C4⋊Dic3C2314yes—
113C3×Dic3⋊C4C2318yes—
114C3×Dic3⋊C4C2318yes—
115C3×Dic3⋊C4C2318yes—
116C3×C4×Dic3C2314yes—
117Dic3⋊Dic3C2318yes—
118Dic3⋊Dic3C2314yes—
119#3722C2318yes—
120#3722C2318yes—
121#3722C2314yes—
122(C2×D3)⋊Dic3C2314yes—
123C2×#547—91noSylow
124C22×C3×Q8—21no—
125C22×C3×Q8—31no—
126C22×C3×Q8C2×D311yescharacteristic
127C22×C3×Q8C2×D311yescharacteristic
128C23×C3×C4—31no—
129C22×#67—32no—
130C22×#67—31no—
131C2×#239—38no—
132C2×#239—38no—
133C2×#239—38no—
134C2×#239—68no—
135C2×#239—68no—
136C2×#239—68no—
137C2×#239—68no—
138C2×#239—616no—
139C2×#235—38no—
140C2×#235—68no—
141C22×D12—31no—
142C22×D12—31no—
143C22×D12—32no—
144C22×D12—31no—
145C22×D12—32no—
146C22×D12—32no—
147C22×D12—61no—
148C22×D12—62no—
149C22×C4×D3—31no—
150C22×C4×D3—32no—
151C22×C4×D3—32no—
152C22×C4×D3—31no—
153C22×C4×D3—32no—
154C22×C4×D3—32no—
155C22×C4×D3—32no—
156C22×C4×D3—32no—
157C22×C4×D3—62no—
158C22×C4×D3—61no—
159C22×C4×D3C2×D311yescharacteristic
160C22×Dic6C2×D311yescharacteristic
161C3×C4⋊Q8—38no—
162C3×C22⋊Q8—38no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—32no—
165C2×C3×C4⋊C4—32no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—32no—
168C2×C3×C42—31no—
169C2×#217—31no—
170#946—38no—
171#946C2×D318yescomplemented
172#944C2×D318yescomplemented
173C4×#67—38no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4C2×D312yes—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—32no—
184C2×C4⋊Dic3C2×D311yescharacteristic
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—32no—
187C2×Dic3⋊C4C2×D312yes—
188C2×Dic3⋊C4C2×D312yes—
189C2×Dic3⋊C4C2×D312yes—
190C2×C4×Dic3C2×D311yescharacteristic
191#897—38no—
192#895—316no—
193#894—316no—
194#894—316no—
195#894—316no—
196#893—38no—
197D3×C4⋊C4—316no—
198D3×C4⋊C4—316no—
199#884—316no—
200#883—316no—
201C4×D12—38no—
202C4×D12—38no—
203C23×C32C2411yescharacteristic
204C22×C3⋊D3—22no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3—22no—
209C22×C3⋊D3C2×D418yes—
210C22×C3⋊D3C2412yes—
211C22×C3⋊D3C2414yes—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3C2412yes—
216C32×Q8—28no—
217C2×C32×C4—24no—
218C2×C32×C4C2×D414yes—
219C2×C32×C4C2414yes—
220C2×C32×C4C2412yes—
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3C2412yes—
223C4⋊(C3⋊D3)—216no—
224C4⋊(C3⋊D3)C2×D4116yescomplemented
225C4×C3⋊D3—216no—
226C4×C3⋊D3—28no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3#4114yescomplemented
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2414yes—
234C2×C3×Dic3C2412yes—
235C2×C3×Dic3C2414yes—
236C2×C3×Dic3C2412yes—
237C3×C4×D3—28no—
238C3×Dic6—28no—
239#626—216no—
240#626—28no—
241#624—216no—
242#624—216no—
243C22×#41—91no—
244C22×#41—91no—
245#547—916no—
246C2×C4⋊Q8—31no—
247C2×#123—92no—
248C2×#123—92no—
249C2×C22⋊Q8—31no—
250C2×C22⋊Q8—91no—
251C2×#121—92no—
252C2×C4×D4—91no—
253C2×C4×D4—91no—
254C22×C4⋊C4—92no—
255C24×C3—31no—
256C23×D3—32no—
257C23×D3—32no—
258C23×D3—31no—
259C23×D3—31no—
260C23×D3—62no—
261C23×D3—61no—
262C23×D3C22×D311yescharacteristic
263C2×C3×Q8—28no—
264C2×C3×Q8—24no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8—34no—
268C2×C3×Q8—64no—
269C2×C3×Q8C22×D314yes—
270C2×C3×Q8C22×D314yes—
271C22×C3×C4—22no—
272C22×C3×C4—21no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—32no—
277C22×C3×C4—31no—
278C22×C3×C4—34no—
279C22×C3×C4—64no—
280C22×C3×C4C22×D312yes—
281C22×C3×C4C22×D312yes—
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C2×#67—38no—
285C2×#67—34no—
286C2×#67—68no—
287C2×#67—64no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—61no—
291C22×Dic3C22×D311yescharacteristic
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D312yes—
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296#239—632no—
297#239—632no—
298#239—632no—
299#239—664no—
300#235—632no—
301C2×D12—38no—
302C2×D12—38no—
303C2×D12—34no—
304C2×D12—34no—
305C2×D12—34no—
306C2×D12—38no—
307C2×D12—38no—
308C2×D12—38no—
309C2×D12—68no—
310C2×D12—64no—
311C2×D12—68no—
312C2×D12—68no—
313C2×D12—68no—
314C2×D12—616no—
315C2×D12—64no—
316C2×D12—68no—
317C2×C4×D3—24no—
318C2×C4×D3—34no—
319C2×C4×D3—38no—
320C2×C4×D3—38no—
321C2×C4×D3—34no—
322C2×C4×D3—38no—
323C2×C4×D3—38no—
324C2×C4×D3—38no—
325C2×C4×D3—38no—
326C2×C4×D3—68no—
327C2×C4×D3—64no—
328C2×C4×D3—68no—
329C2×C4×D3—68no—
330C2×C4×D3—68no—
331C2×C4×D3—68no—
332C2×C4×D3—68no—
333C2×C4×D3—616no—
334C2×C4×D3—68no—
335C2×C4×D3—64no—
336C2×C4×D3—64no—
337C2×C4×D3—68no—
338C2×C4×D3C22×D314yes—
339C2×Dic6—24no—
340C2×Dic6C22×D314yes—
341C3×C4⋊C4—38no—
342C3×C4⋊C4—38no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—38no—
345C3×C22⋊C4—38no—
346C3×C42—34no—
347#217—34no—
348(C2×D3)⋊C4—34no—
349(C2×D3)⋊C4—38no—
350(C2×D3)⋊C4—34no—
351(C2×D3)⋊C4—38no—
352(C2×D3)⋊C4—38no—
353(C2×D3)⋊C4—34no—
354(C2×D3)⋊C4—38no—
355(C2×D3)⋊C4C22×D318yes—
356C4⋊Dic3—34no—
357C4⋊Dic3—38no—
358C4⋊Dic3C22×D314yes—
359Dic3⋊C4—34no—
360Dic3⋊C4—38no—
361Dic3⋊C4C22×D318yes—
362Dic3⋊C4C22×D318yes—
363Dic3⋊C4C22×D318yes—
364C4×Dic3C22×D314yes—
365C22×C32C22×D412yes—
366C22×C32C2×#4112yes—
367C22×C322−1+412yes—
368C22×C32C2511yescharacteristic
369C2×C3⋊D3—22no—
370C2×C3⋊D3—216no—
371C2×C3⋊D3—24no—
372C2×C3⋊D3—24no—
373C2×C3⋊D3—22no—
374C2×C3⋊D3—22no—
375C2×C3⋊D3—44no—
376C2×C3⋊D3C22×D418yes—
377C2×C3×D3—22no—
378C2×C3×D3—22no—
379C2×C3×D3—22no—
380C2×C3×D3—44no—
381C32×C4—24no—
382C32×C4C22×D414yes—
383C3⋊Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—24no—
386C3×Dic3—24no—
387C3×Dic3—22no—
388C3×Dic3C2×#4114yescomplemented
389C2×#41—98no—
390C2×#41—98no—
391C2×#41—188no—
392C2×#41—188no—
393C22×Q8—31no—
394C22×Q8D3211yescharacteristic
395C22×D4—91no—
396C22×D4—92no—
397C22×D4—91no—
398C22×D4—92no—
399C23×C4—31no—
400C23×C4—92no—
401C23×C4—92no—
402C23×C4—92no—
403C23×C4—91no—
404C4⋊Q8—38no—
405#123—916no—
406#123—916no—
407C22⋊Q8—38no—
408C22⋊Q8—98no—
409#121—916no—
410C4×D4—98no—
411C4×D4—98no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—916no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—92no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—92no—
421C2×C22⋊C4—91no—
422C2×C22⋊C4—92no—
423C2×C22⋊C4—91no—
424C2×C42—31no—
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—62no—
428C23×C3—62no—
429C23×C3—62no—
430C23×C3C23×D311yescharacteristic
431C23×C3C23×D311yescharacteristic
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—22no—
435C22×D3—38no—
436C22×D3—38no—
437C22×D3—34no—
438C22×D3—34no—
439C22×D3—32no—
440C22×D3—32no—
441C22×D3—68no—
442C22×D3—64no—
443C22×D3—62no—
444C22×D3—64no—
445C22×D3—64no—
446C22×D3—64no—
447C22×D3—64no—
448C22×D3—64no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—62no—
455C22×D3—124no—
456C22×D3—124no—
457C22×D3—122no—
458C22×D3—122no—
459C22×D3C23×D312yes—
460C3×Q8—216no—
461C3×Q8—28no—
462C3×Q8—28no—
463C3×Q8—68no—
464C2×C3×C4—28no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—24no—
470C2×C3×C4—34no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—34no—
474C2×C3×C4—34no—
475C2×C3×C4—32no—
476C2×C3×C4—62no—
477C2×C3×C4—64no—
478C2×C3×C4—64no—
479C2×C3×C4—62no—
480C2×C3×C4—68no—
481C2×C3×C4D3×D414yes—
482C2×C3×C4D3×D414yes—
483C2×C3×C4C23×D314yes—
484C2×C3×C4C23×D314yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C23×D312yes—
487#67—616no—
488#67—68no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—24no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—62no—
496C2×Dic3—64no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3#23914yescomplemented
500C2×Dic3C23×D312yes—
501C2×Dic3C23×D314yes—
502C2×Dic3C23×D314yes—
503C2×Dic3C23×D312yes—
504C2×Dic3C23×D312yes—
505D12—316no—
506D12—316no—
507D12—616no—
508D12—616no—
509D12—616no—
510D12—632no—
511D12—68no—
512D12—616no—
513C4×D3—28no—
514C4×D3—616no—
515C4×D3—616no—
516C4×D3—616no—
517C4×D3—616no—
518C4×D3—616no—
519C4×D3—632no—
520C4×D3—616no—
521C4×D3—68no—
522C4×D3—68no—
523C4×D3—616no—
524Dic6—28no—
525C2×C32#54714yescomplemented
526C2×C32C23×D411yescharacteristic
527C2×C32C22×#4111yescharacteristic
528C2×C32C2×2−1+411yescharacteristic
529C3⋊D3—28no—
530C3⋊D3—42no—
531C3×D3—42no—
532C24—31no—
533C24—92no—
534C24—91no—
535#41—1832no—
536#41—1832no—
537C2×Q8—24no—
538C2×Q8—34no—
539C2×Q8—64no—
540C2×Q8C2×D3214yes—
541C2×D4—94no—
542C2×D4—98no—
543C2×D4—94no—
544C2×D4—98no—
545C2×D4—98no—
546C2×D4—188no—
547C2×D4—184no—
548C2×D4—188no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—32no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—34no—
555C22×C4—64no—
556C22×C4—98no—
557C22×C4—98no—
558C22×C4—91no—
559C22×C4—98no—
560C22×C4—94no—
561C22×C4—188no—
562C22×C4—188no—
563C22×C4—188no—
564C22×C4—184no—
565C22×C4C2×D3212yes—
566C22×C4C2×D3211yescharacteristic
567C4⋊C4—38no—
568C4⋊C4—38no—
569C4⋊C4—34no—
570C4⋊C4—38no—
571C4⋊C4—94no—
572C4⋊C4—98no—
573C22⋊C4—38no—
574C22⋊C4—98no—
575C22⋊C4—94no—
576C22⋊C4—98no—
577C22⋊C4—94no—
578C42—34no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—21no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—124no—
587C22×C3C2×D3×D412yes—
588C22×C3C2×D3×D412yes—
589C22×C3C2×#23912yes—
590C22×C3#100712yes—
591C22×C3#100712yes—
592C22×C3D3×#4112yes—
593C22×C3C24×D311yescharacteristic
594C22×C3C24×D311yescharacteristic
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—38no—
599C2×D3—38no—
600C2×D3—44no—
601C2×D3—68no—
602C2×D3—64no—
603C2×D3—64no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—616no—
607C2×D3—616no—
608C2×D3—64no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—62no—
615C2×D3—1216no—
616C2×D3—124no—
617C2×D3—124no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—128no—
621C2×D3—124no—
622C2×D3—124no—
623C3×C4—28no—
624C3×C4—24no—
625C3×C4—24no—
626C3×C4—24no—
627C3×C4—34no—
628C3×C4—62no—
629C3×C4—64no—
630C3×C4—64no—
631C3×C4—62no—
632C3×C4C2×D3×D414yes—
633C3×C4C2×D3×D414yes—
634Dic3—24no—
635Dic3—22no—
636Dic3—22no—
637Dic3—24no—
638Dic3—64no—
639Dic3—62no—
640Dic3—62no—
641Dic3C2×#23914yescomplemented
642C32C2×#54711yescharacteristic, complemented, Sylow
643C23—32no—
644C23—62no—
645C23—62no—
646C23—62no—
647C23—98no—
648C23—94no—
649C23—92no—
650C23—184no—
651C23—184no—
652C23—182no—
653C23—182no—
654C23—182no—
655C23C22×D3211yescharacteristic
656Q8—28no—
657Q8—68no—
658D4—916no—
659D4—1816no—
660D4—188no—
661D4—1816no—
662C2×C4—24no—
663C2×C4—34no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—34no—
667C2×C4—32no—
668C2×C4—34no—
669C2×C4—62no—
670C2×C4—64no—
671C2×C4—62no—
672C2×C4—64no—
673C2×C4—68no—
674C2×C4—92no—
675C2×C4—1816no—
676C2×C4—1816no—
677C2×C4—1816no—
678C2×C4—182no—
679C2×C4—188no—
680C2×C4#381114yes—
681C2×C4C22×D3214yes—
682C2×C4C22×D3212yes—
683C2×C3—24no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—122no—
688C2×C3#563114yescomplemented
689C2×C3#572614yescomplemented
690C2×C3C22×D3×D411yescharacteristic
691C2×C3C22×D3×D411yescharacteristic
692C2×C3C22×#23911yescharacteristic
693C2×C3C2×#100711yescharacteristic
694C2×C3C2×#100711yescharacteristic
695C2×C3C2×D3×#4111yescharacteristic
696D3—42no—
697D3—68no—
698D3—68no—
699D3—128no—
700D3—124no—
701D3—122no—
702D3—122no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—98no—
707C22—124no—
708C22—1816no—
709C22—184no—
710C22—184no—
711C22—182no—
712C22—182no—
713C22—182no—
714C22—364no—
715C22#6431612yes—
716C22D3×#23912yes—
717C22C2×#381112yes—
718C22C23×D3211yescharacteristic
719C4—24no—
720C4—34no—
721C4—62no—
722C4—64no—
723C4—62no—
724C4—64no—
725C4—182no—
726C4C2×#381114yes—
727C3—21no—
728C3C2×#563111yescharacteristic, complemented
729C3C2×#572611yescharacteristic, complemented
730C2—122no—
731C2—188no—
732C2—362no—
733C2#1059534114yesdirect product factor
734C2C2×#6431611yescharacteristic
735C2C2×D3×#23911yescharacteristic
736C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×#3799C2semidirect
3. C2×C3×#946C2semidirect
4. C2×C3×#944C2semidirect
5. #10595341C2direct (N × H)
6. C2×#63910C2semidirect
7. C2×C4×#626C2semidirect
8. C2×#63897C2semidirect
9. C2×#63894C2semidirect
10. C2×#63883C2semidirect
11. C2×#63871C2semidirect
12. C2×#63853C2semidirect
17. C2×#3832C22semidirect
29. C2×#3799C22semidirect
30. C3×#946C22semidirect
31. C3×#944C22semidirect
44. #63910C22semidirect
45. C4×#626C22semidirect
46. #63897C22semidirect
47. #63894C22semidirect
48. #63883C22semidirect
49. #63871C22semidirect
50. #63853C22semidirect
59. C2×#946D3semidirect
60. C2×#944D3semidirect
86. C2×C4⋊(C3⋊D3)D4semidirect
171. #946C2×D3semidirect
172. #944C2×D3semidirect
224. C4⋊(C3⋊D3)C2×D4semidirect
231. C2×C3×Dic3#41semidirect
388. C3×Dic3C2×#41semidirect
499. C2×Dic3#239semidirect
525. C2×C32#547semidirect
641. Dic3C2×#239semidirect
642. C32C2×#547semidirect
688. C2×C3#5631semidirect
689. C2×C3#5726semidirect
728. C3C2×#5631semidirect
729. C3C2×#5726semidirect
733. C2#10595341direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×#37992
C2×C3×#9462
C2×C3×#9442
#105953412
C2×#639102
C2×C4×#6262
C2×#638972
C2×#638942
C2×#638832
C2×#638712
C2×#638532
C2×#57263
C2×#56313