Finite Group Databasebeta

← C2×#10594923 #11901160

Subgroups — C2×#10594923 #11901160

Order 1152.

3725 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5C2×#63971C212yesmaximal, complemented
6C2×#63958C212yesmaximal, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63910C212yesmaximal, complemented
9C2×#63900C211yesmaximal, characteristic, complemented
10#10594923C2116yesmaximal, direct product factor
11C2×#63896C212yesmaximal, complemented
12C2×#63871C211yesmaximal, characteristic, complemented
13C2×#5629—31nomaximal
14C2×#5608—31nomaximal
15C23×C32×C4C2211yescharacteristic
16C22×#638C2211yescharacteristic
17C22×#638C2211yescharacteristic
18C2×#3828—28no—
19C2×#3828C2218yescomplemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×#634C2211yescharacteristic
24C22×C3×#67C2212yes—
25C22×C3×D12C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#626C2212yes—
28C22×#626C2212yes—
29C22×#624C2212yes—
30C22×D3×Dic3C2212yes—
31C2×#3796—28no—
32C2×#3796C2218yescomplemented
33C2×C3×#217C2212yes—
34C3×#930C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×C4⋊Dic3C2211yescharacteristic
38C3×#924C2218yescomplemented
39C2×C3×Dic3⋊C4C2212yes—
40#63971C22116yescomplemented
41C2×#3724C2212yes—
42C2×Dic3⋊Dic3C2212yes—
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45#63958C22116yescomplemented
46#63916C2218yescomplemented
47#63910C22116yescomplemented
48#63900C2218yescomplemented
49#63896C22116yescomplemented
50#63871C2218yescomplemented
51C22×#239—31no—
52C22×#237—31no—
53C22×#235—31no—
54C22×#235—31no—
55C22×#235—61no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×#121—31no—
58C2×#946—31no—
59C2×#939—32no—
60C2×#938—32no—
61C2×#938—31no—
62C2×#930D311yescharacteristic, complemented
63C2×#924D311yescharacteristic, complemented
64#5629—316no—
65#5608—316no—
66C2×#897—31no—
67C2×#896—32no—
68C2×#895—31no—
69C2×#895—32no—
70C2×D3×C4⋊C4—31no—
71C2×D3×C4⋊C4—31no—
72C2×#884—32no—
73C2×#884—32no—
74C2×#884—32no—
75C2×#878—32no—
76C24×C32C2311yescharacteristic
77C23×C3⋊D3C2311yescharacteristic
78C23×C3⋊D3C2311yescharacteristic
79C23×C3×D3C2312yes—
80C22×C32×C4—24no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2314yes—
83C22×C32×C4C2311yescharacteristic
84C2×#638—24no—
85C2×#638—24no—
86C2×#638C2314yes—
87C2×#638C2314yes—
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90#3828—232no—
91C2×C4⋊(C3⋊D3)—24no—
92C2×C4⋊(C3⋊D3)C2314yes—
93C2×C4×C3⋊D3—24no—
94C2×C4×C3⋊D3D418yescomplemented
95C2×C4×C3⋊D3C2314yes—
96C2×C4×C3⋊D3C2314yes—
97C2×#634—24no—
98C2×#634C2314yes—
99C2×C3×#67—44no—
100C2×C3×#67C2318yes—
101C22×C3×Dic3C2312yes—
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2312yes—
104C2×C3×D12—24no—
105C2×C3×D12C2314yes—
106C2×C3×Dic6—24no—
107C2×C3×Dic6C2314yes—
108C2×#626—28no—
109C2×#626—44no—
110C2×#626C2318yes—
111C2×#626C2318yes—
112C2×#624—44no—
113C2×#624C2318yes—
114C2×D3×Dic3—28no—
115C2×D3×Dic3C2318yes—
116#3796—232no—
117C3×#217C2318yes—
118C3×(C2×D3)⋊C4C2318yes—
119C3×C4⋊Dic3C2314yes—
120C3×C4⋊Dic3C2314yes—
121C3×Dic3⋊C4C2318yes—
122#3724C2318yes—
123Dic3⋊Dic3C2318yes—
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C2×#537—91noSylow
127C22×C3×Q8—31no—
128C22×C3×D4—32no—
129C22×C3×D4—31no—
130C23×C3×C4—21no—
131C23×C3×C4C2×D311yescharacteristic
132C23×C3×C4C2×D311yescharacteristic
133C22×#67—31no—
134C22×#67—31no—
135C22×#67—31no—
136C22×#67—31no—
137C22×#67—32no—
138C22×#67—32no—
139C22×#67—61no—
140C22×#67—61no—
141C22×#67C2×D312yes—
142C23×Dic3—32no—
143C2×#239—38no—
144C2×#239—68no—
145C2×#237—38no—
146C2×#237—68no—
147C2×#235—38no—
148C2×#235—38no—
149C2×#235—68no—
150C2×#235—68no—
151C2×#235—68no—
152C2×#235—616no—
153C22×D12—32no—
154C22×D12—31no—
155C22×D12—31no—
156C22×D12—32no—
157C22×D12—61no—
158C22×D12C2×D311yescharacteristic
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—32no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—32no—
165C22×C4×D3—32no—
166C22×C4×D3—61no—
167C22×C4×D3—61no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—61no—
171C22×Dic6C2×D311yescharacteristic
172C3×C22⋊Q8—38no—
173C3×#121—38no—
174C2×C3×C4⋊C4—32no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4—32no—
179C2×#217—32no—
180C2×#217C2×D312yes—
181#946—38no—
182#939—316no—
183#938—316no—
184#938—38no—
185#930C2×D318yescomplemented
186C2×(C2×D3)⋊C4—32no—
187C2×(C2×D3)⋊C4—32no—
188C2×(C2×D3)⋊C4—32no—
189C2×(C2×D3)⋊C4C2×D312yes—
190C2×C4⋊Dic3—32no—
191C2×C4⋊Dic3C2×D311yescharacteristic
192C2×C4⋊Dic3C2×D311yescharacteristic
193#924C2×D318yescomplemented
194C2×Dic3⋊C4—32no—
195C2×Dic3⋊C4—32no—
196C2×Dic3⋊C4—32no—
197C2×Dic3⋊C4C2×D312yes—
198#897—38no—
199#896—316no—
200#895—38no—
201#895—316no—
202D3×C4⋊C4—38no—
203D3×C4⋊C4—38no—
204#884—316no—
205#884—316no—
206#884—316no—
207#878—316no—
208C23×C32—22no—
209C23×C32—22no—
210C23×C32—22no—
211C23×C32C2412yes—
212C23×C32C2411yescharacteristic
213C22×C3⋊D3—22no—
214C22×C3⋊D3—22no—
215C22×C3⋊D3—22no—
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3C2×D414yes—
219C22×C3⋊D3C2412yes—
220C22×C3⋊D3C2412yes—
221C22×C3×D3—24no—
222C22×C3×D3—24no—
223C22×C3×D3—24no—
224C22×C3×D3C2414yes—
225C2×C32×C4—22no—
226C2×C32×C4—28no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2412yes—
230#638—28no—
231#638—28no—
232C2×C3⋊Dic3—22no—
233C2×C3⋊Dic3C2×D414yes—
234C2×C3⋊Dic3C2412yes—
235C2×C3⋊Dic3C2412yes—
236C4⋊(C3⋊D3)—28no—
237C4×C3⋊D3—28no—
238C4×C3⋊D3C2×D4116yescomplemented
239#634—28no—
240C3×#67—48no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—24no—
243C2×C3×Dic3—24no—
244C2×C3×Dic3C2414yes—
245C2×C3×Dic3C2414yes—
246C2×C3×Dic3C2414yes—
247C3×D12—28no—
248C3×Dic6—28no—
249#626—216no—
250#626—48no—
251#624—48no—
252D3×Dic3—216no—
253C22×#41—91no—
254C22×#41—91no—
255#537—916no—
256C2×C22⋊Q8—31no—
257C2×C22⋊Q8—92no—
258C2×C22⋊Q8—91no—
259C2×#121—31no—
260C2×#121—92no—
261C2×#121—92no—
262C2×#121—92no—
263C2×#121—91no—
264C22×C4⋊C4—91no—
265C24×C3—21no—
266C24×C3—32no—
267C24×C3C22×D311yescharacteristic
268C24×C3C22×D311yescharacteristic
269C23×D3—31no—
270C23×D3—31no—
271C23×D3—31no—
272C23×D3—31no—
273C23×D3—61no—
274C23×D3—61no—
275C23×D3C22×D312yes—
276C2×C3×Q8—34no—
277C2×C3×Q8—64no—
278C2×C3×D4—38no—
279C2×C3×D4—34no—
280C2×C3×D4—64no—
281C2×C3×D4—124no—
282C22×C3×C4—28no—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—24no—
288C22×C3×C4—32no—
289C22×C3×C4—32no—
290C22×C3×C4—32no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D314yes—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D314yes—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C2×#67—34no—
298C2×#67—34no—
299C2×#67—34no—
300C2×#67—34no—
301C2×#67—38no—
302C2×#67—38no—
303C2×#67—44no—
304C2×#67—64no—
305C2×#67—64no—
306C2×#67—68no—
307C2×#67—64no—
308C2×#67—64no—
309C2×#67—64no—
310C2×#67—64no—
311C2×#67—68no—
312C2×#67—68no—
313C2×#67—124no—
314C2×#67C22×D318yes—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—38no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—68no—
323C22×Dic3C22×D312yes—
324C22×Dic3C22×D312yes—
325C22×Dic3C22×D312yes—
326#239—632no—
327#237—632no—
328#235—632no—
329#235—632no—
330#235—664no—
331C2×D12—24no—
332C2×D12—38no—
333C2×D12—34no—
334C2×D12—34no—
335C2×D12—38no—
336C2×D12—64no—
337C2×D12—64no—
338C2×D12—64no—
339C2×D12—68no—
340C2×D12—68no—
341C2×D12—124no—
342C2×D12C22×D314yes—
343C2×C4×D3—38no—
344C2×C4×D3—38no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—38no—
348C2×C4×D3—34no—
349C2×C4×D3—34no—
350C2×C4×D3—38no—
351C2×C4×D3—38no—
352C2×C4×D3—68no—
353C2×C4×D3—64no—
354C2×C4×D3—64no—
355C2×C4×D3—68no—
356C2×C4×D3—68no—
357C2×C4×D3—64no—
358C2×C4×D3—64no—
359C2×C4×D3—124no—
360C2×C4×D3—124no—
361C2×Dic6—24no—
362C2×Dic6—34no—
363C2×Dic6—34no—
364C2×Dic6—64no—
365C2×Dic6—64no—
366C2×Dic6—64no—
367C2×Dic6—68no—
368C2×Dic6C22×D314yes—
369C3×C4⋊C4—34no—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—38no—
372C3×C22⋊C4—38no—
373C3×C22⋊C4—38no—
374#217—38no—
375#217C22×D318yes—
376(C2×D3)⋊C4—38no—
377(C2×D3)⋊C4—38no—
378(C2×D3)⋊C4—38no—
379(C2×D3)⋊C4C22×D318yes—
380C4⋊Dic3—38no—
381C4⋊Dic3C22×D314yes—
382C4⋊Dic3C22×D314yes—
383Dic3⋊C4—38no—
384Dic3⋊C4—38no—
385Dic3⋊C4—38no—
386Dic3⋊C4C22×D318yes—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—44no—
391C22×C32C22×D412yes—
392C22×C32H(5,𝔽2)12yes—
393C22×C322−1+412yes—
394C22×C32C2511yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—28no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—22no—
399C2×C3⋊D3—22no—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—44no—
402C2×C3⋊D3C22×D414yes—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—24no—
406C2×C3×D3—48no—
407C32×C4—22no—
408C32×C4C22×D414yes—
409C3⋊Dic3—22no—
410C3⋊Dic3C22×D414yes—
411C3×Dic3—24no—
412C3×Dic3—24no—
413C3×Dic3—24no—
414C2×#41—98no—
415C2×#41—98no—
416C2×#41—188no—
417C2×#41—188no—
418C22×Q8—31no—
419C22×Q8—91no—
420C22×D4—32no—
421C22×D4—31no—
422C22×D4—92no—
423C22×D4—92no—
424C22×D4—91no—
425C22×D4—91no—
426C22×D4—91no—
427C23×C4—92no—
428C23×C4—92no—
429C23×C4—91no—
430C23×C4—91no—
431C23×C4D3211yescharacteristic
432C22⋊Q8—38no—
433C22⋊Q8—916no—
434C22⋊Q8—98no—
435#121—38no—
436#121—916no—
437#121—916no—
438#121—916no—
439#121—98no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—98no—
444C2×C4⋊C4—92no—
445C2×C4⋊C4—92no—
446C2×C22⋊C4—32no—
447C2×C22⋊C4—32no—
448C2×C22⋊C4—92no—
449C2×C22⋊C4—92no—
450C23×C3—24no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—21no—
459C23×C3—34no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—64no—
463C23×C3—64no—
464C23×C3—64no—
465C23×C3C23×D312yes—
466C23×C3C23×D312yes—
467C23×C3C23×D311yescharacteristic
468C23×C3C23×D311yescharacteristic
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—24no—
472C22×D3—34no—
473C22×D3—34no—
474C22×D3—32no—
475C22×D3—32no—
476C22×D3—32no—
477C22×D3—32no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—62no—
485C22×D3—64no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3—62no—
491C22×D3—62no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3C23×D314yes—
497C3×Q8—68no—
498C3×D4—68no—
499C3×D4—128no—
500C2×C3×C4—24no—
501C2×C3×C4—216no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—28no—
505C2×C3×C4—28no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—24no—
509C2×C3×C4—34no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—64no—
513C2×C3×C4—64no—
514C2×C3×C4—64no—
515C2×C3×C4D3×D414yes—
516C2×C3×C4D3×D414yes—
517C2×C3×C4C23×D312yes—
518C2×C3×C4C23×D312yes—
519C2×C3×C4C23×D312yes—
520C2×C3×C4C23×D312yes—
521#67—48no—
522#67—616no—
523#67—68no—
524#67—68no—
525#67—68no—
526#67—68no—
527#67—616no—
528#67—616no—
529#67—128no—
530C2×Dic3—24no—
531C2×Dic3—24no—
532C2×Dic3—24no—
533C2×Dic3—34no—
534C2×Dic3—34no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—64no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—616no—
543C2×Dic3—64no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3C23×D314yes—
547C2×Dic3C23×D314yes—
548C2×Dic3C23×D314yes—
549D12—28no—
550D12—68no—
551D12—68no—
552D12—616no—
553D12—616no—
554D12—128no—
555C4×D3—316no—
556C4×D3—316no—
557C4×D3—616no—
558C4×D3—616no—
559C4×D3—616no—
560C4×D3—68no—
561C4×D3—68no—
562C4×D3—128no—
563C4×D3—128no—
564Dic6—28no—
565Dic6—68no—
566Dic6—68no—
567Dic6—616no—
568C2×C32—42no—
569C2×C32#53714yescomplemented
570C2×C32C23×D411yescharacteristic
571C2×C32C2×H(5,𝔽2)11yescharacteristic
572C2×C32C2×2−1+411yescharacteristic
573C3⋊D3—24no—
574C3⋊D3—42no—
575C3×D3—44no—
576C24—32no—
577C24—91no—
578C24—91no—
579C24C2×D3211yescharacteristic
580#41—1832no—
581#41—1832no—
582C2×Q8—34no—
583C2×Q8—64no—
584C2×Q8—94no—
585C2×Q8—184no—
586C2×D4—38no—
587C2×D4—34no—
588C2×D4—64no—
589C2×D4—98no—
590C2×D4—98no—
591C2×D4—94no—
592C2×D4—94no—
593C2×D4—94no—
594C2×D4—124no—
595C2×D4—184no—
596C2×D4—188no—
597C2×D4—184no—
598C2×D4—184no—
599C2×D4—364no—
600C22×C4—24no—
601C22×C4—32no—
602C22×C4—32no—
603C22×C4—32no—
604C22×C4—98no—
605C22×C4—98no—
606C22×C4—91no—
607C22×C4—94no—
608C22×C4—98no—
609C22×C4—91no—
610C22×C4—94no—
611C22×C4—188no—
612C22×C4—184no—
613C22×C4—364no—
614C22×C4C2×D3214yes—
615C22×C4C2×D3211yescharacteristic
616C22×C4C2×D3211yescharacteristic
617C4⋊C4—34no—
618C4⋊C4—34no—
619C4⋊C4—38no—
620C4⋊C4—98no—
621C4⋊C4—98no—
622C22⋊C4—38no—
623C22⋊C4—38no—
624C22⋊C4—98no—
625C22⋊C4—98no—
626C22×C3—24no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—48no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—64no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—128no—
646C22×C3C2×D3×D412yes—
647C22×C3C2×D3×D412yes—
648C22×C3#100412yes—
649C22×C3#100712yes—
650C22×C3#100912yes—
651C22×C3#101012yes—
652C22×C3C24×D311yescharacteristic
653C22×C3C24×D311yescharacteristic
654C2×D3—24no—
655C2×D3—24no—
656C2×D3—24no—
657C2×D3—34no—
658C2×D3—34no—
659C2×D3—48no—
660C2×D3—64no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—68no—
666C2×D3—68no—
667C2×D3—64no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—122no—
675C2×D3—122no—
676C2×D3—128no—
677C2×D3—122no—
678C2×D3—122no—
679C2×D3—128no—
680C2×D3—124no—
681C2×D3—124no—
682C3×C4—24no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—24no—
686C3×C4—64no—
687C3×C4—64no—
688C3×C4—64no—
689C3×C4C2×D3×D414yes—
690C3×C4C2×D3×D414yes—
691Dic3—24no—
692Dic3—24no—
693Dic3—24no—
694Dic3—34no—
695Dic3—34no—
696Dic3—64no—
697Dic3—64no—
698Dic3—62no—
699Dic3—62no—
700C32C2×#53711yescharacteristic, complemented, Sylow
701C23—22no—
702C23—22no—
703C23—22no—
704C23—34no—
705C23—64no—
706C23—64no—
707C23—64no—
708C23—94no—
709C23—92no—
710C23—92no—
711C23—182no—
712C23—182no—
713C23—182no—
714C23—182no—
715C23—182no—
716C23C22×D3212yes—
717C23C22×D3211yescharacteristic
718Q8—68no—
719Q8—188no—
720D4—68no—
721D4—128no—
722D4—188no—
723D4—1816no—
724D4—188no—
725D4—188no—
726D4—368no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—34no—
730C2×C4—34no—
731C2×C4—34no—
732C2×C4—64no—
733C2×C4—64no—
734C2×C4—64no—
735C2×C4—94no—
736C2×C4—92no—
737C2×C4—916no—
738C2×C4—92no—
739C2×C4—1816no—
740C2×C4—182no—
741C2×C4—188no—
742C2×C4—368no—
743C2×C4#381114yes—
744C2×C4C22×D3212yes—
745C2×C4C22×D3212yes—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—24no—
750C2×C3—44no—
751C2×C3—42no—
752C2×C3—42no—
753C2×C3—124no—
754C2×C3#560814yescomplemented
755C2×C3#562914yescomplemented
756C2×C3C22×D3×D411yescharacteristic
757C2×C3C22×D3×D411yescharacteristic
758C2×C3C2×#100411yescharacteristic
759C2×C3C2×#100711yescharacteristic
760C2×C3C2×#100911yescharacteristic
761C2×C3C2×#101011yescharacteristic
762D3—44no—
763D3—64no—
764D3—64no—
765D3—124no—
766D3—124no—
767D3—122no—
768D3—122no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—44no—
773C22—64no—
774C22—64no—
775C22—64no—
776C22—94no—
777C22—128no—
778C22—182no—
779C22—182no—
780C22—188no—
781C22—182no—
782C22—182no—
783C22—182no—
784C22—364no—
785C22#6429712yes—
786C22#6430712yes—
787C22C2×#381112yes—
788C22C23×D3211yescharacteristic
789C4—22no—
790C4—64no—
791C4—64no—
792C4—64no—
793C4—94no—
794C4—182no—
795C4C2×#381114yes—
796C3—21no—
797C3C2×#560811yescharacteristic, complemented
798C3C2×#562911yescharacteristic, complemented
799C2—42no—
800C2—124no—
801C2—184no—
802C2—362no—
803C2#1059492314yesdirect product factor
804C2C2×#6429711yescharacteristic
805C2C2×#6430711yescharacteristic
806C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C22×#3796C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×#924C2semidirect
5. C2×#63971C2semidirect
6. C2×#63958C2semidirect
7. C2×#63916C2semidirect
8. C2×#63910C2semidirect
9. C2×#63900C2semidirect
10. #10594923C2direct (N × H)
11. C2×#63896C2semidirect
12. C2×#63871C2semidirect
19. C2×#3828C22semidirect
32. C2×#3796C22semidirect
34. C3×#930C22semidirect
38. C3×#924C22semidirect
40. #63971C22semidirect
45. #63958C22semidirect
46. #63916C22semidirect
47. #63910C22semidirect
48. #63900C22semidirect
49. #63896C22semidirect
50. #63871C22semidirect
62. C2×#930D3semidirect
63. C2×#924D3semidirect
94. C2×C4×C3⋊D3D4semidirect
185. #930C2×D3semidirect
193. #924C2×D3semidirect
238. C4×C3⋊D3C2×D4semidirect
569. C2×C32#537semidirect
700. C32C2×#537semidirect
754. C2×C3#5608semidirect
755. C2×C3#5629semidirect
797. C3C2×#5608semidirect
798. C3C2×#5629semidirect
803. C2#10594923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C22×#37962
C2×C3×#9302
C2×C3×#9242
C2×#639712
C2×#639582
C2×#639162
C2×#639102
C2×#639002
#105949232
C2×#638962
C2×#638712
C2×#56293
C2×#56083