Finite Group Databasebeta

← C2×#10594237 #11910256

Subgroups — C2×#10594237 #11910256

Order 1152.

2475 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#885C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5C2×#63971C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8C2×#63912C211yesmaximal, characteristic, complemented
9C2×#63899C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63887C211yesmaximal, characteristic, complemented
13C2×#63871C211yesmaximal, characteristic, complemented
14C2×#63869C211yesmaximal, characteristic, complemented
15C2×#63852C211yesmaximal, characteristic, complemented
16#10594237C2116yesmaximal, direct product factor
17C2×#5684—31nomaximal
18C2×#5667—31nomaximal
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36#64092C2218yescomplemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#886C2218yescomplemented
46C3×#885C2218yescomplemented
47#63978C2218yescomplemented
48#63971C2218yescomplemented
49#63970C2218yescomplemented
50C2×#3724C2211yescharacteristic
51C2×#3724C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56#63964C2218yescomplemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63912C2218yescomplemented
62#63899C2218yescomplemented
63#63891C2218yescomplemented
64#63890C2218yescomplemented
65#63887C2218yescomplemented
66#63871C2218yescomplemented
67#63869C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#123—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#938—31no—
77C2×#930—31no—
78C2×#924—31no—
79#5684—316no—
80#5667—316no—
81C2×#897—31no—
82C2×#896—31no—
83C2×#894—31no—
84C2×#890—31no—
85C2×#886—31no—
86C2×#886—31no—
87C2×#886D311yescharacteristic, complemented
88C2×#885—31no—
89C2×#885D311yescharacteristic, complemented
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—61no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#875—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×#638—42no—
109C2×#638C2314yes—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4×C3⋊D3—42no—
114C2×C4×C3⋊D3C2314yes—
115C2×C3×#67—42no—
116C2×C3×#67—42no—
117C2×C3×#67C2314yes—
118C2×C3×#67C2314yes—
119C22×C3×Dic3—42no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#627—42no—
130C2×#627C2314yes—
131C2×#626—42no—
132C2×#626—42no—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#625—42no—
136C2×#625C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C22⋊C4C2314yes—
142#3757C2314yes—
143#3752C2314yes—
144C4⋊(C3⋊Dic3)C2314yes—
145#3750C2314yes—
146C3×#217C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4×Dic3C2314yes—
154#3724C2314yes—
155#3724C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164C2×#562—91noSylow
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C23×C3×C4—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—61no—
176C22×#67C2×D311yescharacteristic
177C22×#67C2×D311yescharacteristic
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3C2×D311yescharacteristic
181C22×D12—31no—
182C22×D12—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—61no—
188C22×Dic6—31no—
189C22×Dic6—31no—
190C22×Dic6C2×D311yescharacteristic
191C3×#124—38no—
192C3×#123—38no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—21no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4C2×D311yescharacteristic
202C2×C3×C22⋊C4C2×D311yescharacteristic
203C2×C3×C42—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—61no—
209C2×#217C2×D311yescharacteristic
210#946—38no—
211#946—38no—
212#939—38no—
213#939—38no—
214#939—38no—
215#938—38no—
216#930—38no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—61no—
237C2×C4⋊Dic3C2×D311yescharacteristic
238C2×C4⋊Dic3C2×D311yescharacteristic
239#924—38no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—61no—
251C2×C4×Dic3C2×D311yescharacteristic
252#897—38no—
253#896—38no—
254#894—38no—
255#890—38no—
256#886—38no—
257#886—38no—
258#886C2×D318yescomplemented
259#885—38no—
260#885C2×D318yescomplemented
261#884—38no—
262#884—38no—
263#884—38no—
264#883—38no—
265#883—38no—
266#883—38no—
267#883—68no—
268#878—38no—
269#878—38no—
270#878—38no—
271#875—38no—
272#870—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294#638—44no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3C2412yes—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C4×C3⋊D3—44no—
302C3×#67—44no—
303C3×#67—44no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—44no—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×Dic6—44no—
318#627—44no—
319#626—44no—
320#626—44no—
321#625—44no—
322D3×Dic3—44no—
323D3×Dic3—44no—
324#562—916no—
325C2×#125—91no—
326C2×#124—31no—
327C2×#124—91no—
328C2×#123—31no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×C22⋊Q8—91no—
335C2×C22⋊Q8—91no—
336C2×#121—91no—
337C2×#121—91no—
338C2×#121—91no—
339C2×#121—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—61no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×Q8—34no—
351C2×C3×Q8—122no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—122no—
355C2×C3×D4—122no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—34no—
365C22×C3×C4—122no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—42no—
377C2×#67—42no—
378C2×#67—64no—
379C2×#67—122no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67—124no—
386C2×#67C22×D314yes—
387C2×#67C22×D314yes—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—34no—
395C22×Dic3—34no—
396C22×Dic3—42no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—122no—
401C22×Dic3—122no—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D314yes—
409C2×D12—34no—
410C2×D12—34no—
411C2×D12—122no—
412C2×D12—122no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—64no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—122no—
422C2×C4×D3—124no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—42no—
426C2×Dic6—122no—
427C2×Dic6—122no—
428C2×Dic6C22×D314yes—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C22⋊C4—24no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4C22×D314yes—
438C3×C22⋊C4C22×D314yes—
439C3×C42—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—64no—
445#217C22×D314yes—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—64no—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457(C2×D3)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D314yes—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—64no—
466C4⋊Dic3C22×D314yes—
467C4⋊Dic3C22×D314yes—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—64no—
479C4×Dic3C22×D314yes—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—44no—
484C22×C32H(5,𝔽2)12yes—
485C22×C32H(5,𝔽2)12yes—
486C22×C322−1+412yes—
487C22×C32C2511yescharacteristic
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—44no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—44no—
499C2×C3×D3—44no—
500C32×C4—22no—
501C32×C4—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C22×Q8—31no—
512C22×Q8—91no—
513C22×D4—31no—
514C22×D4—31no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523#125—98no—
524#124—38no—
525#124—98no—
526#123—38no—
527#123—98no—
528#123—98no—
529#123—98no—
530C22⋊Q8—98no—
531C22⋊Q8—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#121—98no—
535#121—98no—
536#121—98no—
537#121—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4D3211yescharacteristic
560C2×C42—31no—
561C23×C3—22no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—21no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3C23×D312yes—
581C23×C3C23×D312yes—
582C23×C3C23×D311yescharacteristic
583C23×C3C23×D311yescharacteristic
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—62no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3C23×D312yes—
603C22×D3C23×D312yes—
604C3×Q8—124no—
605C3×D4—124no—
606C3×D4—124no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—124no—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632#67—44no—
633#67—44no—
634#67—124no—
635#67—124no—
636#67—124no—
637#67—124no—
638#67—124no—
639#67—124no—
640#67—128no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—44no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—122no—
664C2×Dic3—122no—
665C2×Dic3—122no—
666C2×Dic3—124no—
667C2×Dic3—124no—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674D12—124no—
675D12—124no—
676C4×D3—124no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—128no—
681Dic6—44no—
682Dic6—124no—
683Dic6—124no—
684C2×C32—42no—
685C2×C32#56214yescomplemented
686C2×C32C2×H(5,𝔽2)11yescharacteristic
687C2×C32C2×H(5,𝔽2)11yescharacteristic
688C2×C32C2×2−1+411yescharacteristic
689C3⋊D3—42no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—91no—
695C24C2×D3211yescharacteristic
696C2×Q8—34no—
697C2×Q8—94no—
698C2×Q8—122no—
699C2×Q8—362no—
700C2×D4—34no—
701C2×D4—34no—
702C2×D4—94no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—94no—
706C2×D4—122no—
707C2×D4—122no—
708C2×D4—362no—
709C2×D4—362no—
710C2×D4—362no—
711C2×D4—362no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—34no—
719C22×C4—94no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—94no—
725C22×C4—122no—
726C22×C4—362no—
727C22×C4—362no—
728C22×C4—362no—
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4C2×D3214yes—
753C42—34no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—44no—
768C22×C3—44no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—84no—
776C22×C3—124no—
777C22×C3—124no—
778C22×C3#100412yes—
779C22×C3#100412yes—
780C22×C3#100912yes—
781C22×C3#100912yes—
782C22×C3#101012yes—
783C22×C3#101012yes—
784C22×C3C24×D311yescharacteristic
785C22×C3C24×D311yescharacteristic
786C2×D3—22no—
787C2×D3—22no—
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—44no—
793C2×D3—44no—
794C2×D3—64no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—128no—
804C2×D3—124no—
805C2×D3—124no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—122no—
831Dic3—122no—
832Dic3—122no—
833C32C2×#56211yescharacteristic, complemented, Sylow
834C23—22no—
835C23—22no—
836C23—22no—
837C23—32no—
838C23—32no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—92no—
846C23—182no—
847C23—182no—
848C23—182no—
849C23C22×D3212yes—
850C23C22×D3211yescharacteristic
851Q8—124no—
852Q8—364no—
853D4—124no—
854D4—124no—
855D4—364no—
856D4—364no—
857D4—364no—
858D4—364no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—92no—
876C2×C4—124no—
877C2×C4—182no—
878C2×C4—182no—
879C2×C4—182no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4—364no—
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—24no—
889C2×C3—42no—
890C2×C3—42no—
891C2×C3—82no—
892C2×C3—122no—
893C2×C3—122no—
894C2×C3#566714yescomplemented
895C2×C3#568414yescomplemented
896C2×C3C2×#100411yescharacteristic
897C2×C3C2×#100411yescharacteristic
898C2×C3C2×#100911yescharacteristic
899C2×C3C2×#100911yescharacteristic
900C2×C3C2×#101011yescharacteristic
901C2×C3C2×#101011yescharacteristic
902D3—42no—
903D3—42no—
904D3—124no—
905D3—122no—
906D3—122no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—44no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—124no—
918C22—124no—
919C22—182no—
920C22—182no—
921C22—182no—
922C22—364no—
923C22#6430712yes—
924C22#6430912yes—
925C22#6431412yes—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—22no—
929C4—62no—
930C4—62no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—182no—
936C4—182no—
937C4—182no—
938C3—21no—
939C3C2×#566711yescharacteristic, complemented
940C3C2×#568411yescharacteristic, complemented
941C2—42no—
942C2—122no—
943C2—122no—
944C2—362no—
945C2#1059423714yesdirect product factor
946C2C2×#6430711yescharacteristic
947C2C2×#6430911yescharacteristic
948C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#885C2semidirect
4. C2×#63978C2semidirect
5. C2×#63971C2semidirect
6. C2×#63970C2semidirect
7. C2×#63964C2semidirect
8. C2×#63912C2semidirect
9. C2×#63899C2semidirect
10. C2×#63891C2semidirect
11. C2×#63890C2semidirect
12. C2×#63887C2semidirect
13. C2×#63871C2semidirect
14. C2×#63869C2semidirect
15. C2×#63852C2semidirect
16. #10594237C2direct (N × H)
36. #64092C22semidirect
45. C3×#886C22semidirect
46. C3×#885C22semidirect
47. #63978C22semidirect
48. #63971C22semidirect
49. #63970C22semidirect
56. #63964C22semidirect
61. #63912C22semidirect
62. #63899C22semidirect
63. #63891C22semidirect
64. #63890C22semidirect
65. #63887C22semidirect
66. #63871C22semidirect
67. #63869C22semidirect
68. #63852C22semidirect
87. C2×#886D3semidirect
89. C2×#885D3semidirect
258. #886C2×D3semidirect
260. #885C2×D3semidirect
685. C2×C32#562semidirect
833. C32C2×#562semidirect
894. C2×C3#5667semidirect
895. C2×C3#5684semidirect
939. C3C2×#5667semidirect
940. C3C2×#5684semidirect
945. C2#10594237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640922
C2×C3×#8862
C2×C3×#8852
C2×#639782
C2×#639712
C2×#639702
C2×#639642
C2×#639122
C2×#638992
C2×#638912
C2×#638902
C2×#638872
C2×#638712
C2×#638692
C2×#638522
#105942372
C2×#56843
C2×#56673