Finite Group Databasebeta

← C2×#10594200 #11903826

Subgroups — C2×#10594200 #11903826

Order 1152.

2651 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×#885C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic
5C2×Dic3×#67C211yesmaximal, characteristic, complemented
6C2×#63966C211yesmaximal, characteristic, complemented
7C2×#63959C211yesmaximal, characteristic, complemented
8C2×#63907C211yesmaximal, characteristic, complemented
9C2×#63905C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63891C211yesmaximal, characteristic, complemented
12C2×#63881C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594200C2116yesmaximal, direct product factor
17C2×#5681—31nomaximal
18C2×#5559—31nomaximal
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#625C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#885C2218yescomplemented
45C3×#67⋊C4C2218yescomplemented
46#63979C2218yes—
47Dic3×#67C2218yescomplemented
48#63966C2218yescomplemented
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63959C2218yescomplemented
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63907C2218yescomplemented
62#63905C2218yescomplemented
63C4×#626C2218yescomplemented
64#63891C2218yescomplemented
65#63881C2218yescomplemented
66#63852C2218yescomplemented
67Dic3×Dic6C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×C4×D4—31no—
71C2×#947—31no—
72C2×Q8×Dic3—31no—
73C2×#940—31no—
74C2×#940—31no—
75C2×#936—31no—
76C2×D4×Dic3—31no—
77C2×#929—31no—
78C2×#929—31no—
79C2×C4×#67—31no—
80C2×C4×#67—31no—
81#5681—316no—
82#5559—316no—
83C2×#893—31no—
84C2×#887—31no—
85C2×#886—31no—
86C2×#886—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#885D311yescharacteristic, complemented
91C2×#883—31no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—61no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4D311yescharacteristic, complemented
98C2×#875—31no—
99C2×C4×D12—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—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—24no—
116C2×C3×#67—24no—
117C2×C3×#67C2314yes—
118C2×C3×#67C2314yes—
119C22×C3×Dic3—42no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3C2314yes—
129C2×C3×Dic6—24no—
130C2×C3×Dic6C2314yes—
131C2×#627—24no—
132C2×#627C2314yes—
133C2×#626—24no—
134C2×#626—24no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#625—42no—
138C2×#625C2314yes—
139C2×D3×Dic3—42no—
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×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161Dic32C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#559—91noSylow
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C22×C3×D4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—61no—
177C22×#67C2×D311yescharacteristic
178C22×#67C2×D311yescharacteristic
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—61no—
187C22×C4×D3C2×D311yescharacteristic
188C22×Dic6—31no—
189C22×Dic6—31no—
190C22×Dic6C2×D311yescharacteristic
191C3×#124—38no—
192C3×C4×D4—38no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—21no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×C3×C42—31no—
202C2×C3×C42—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—61no—
209C2×#217C2×D311yescharacteristic
210#947—38no—
211Q8×Dic3—38no—
212#940—38no—
213#940—38no—
214#936—38no—
215D4×Dic3—38no—
216#929—38no—
217#929—38no—
218C4×#67—38no—
219C4×#67—38no—
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—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—61no—
230C2×(C2×D3)⋊C4C2×D311yescharacteristic
231C2×(C2×D3)⋊C4C2×D311yescharacteristic
232C2×(C2×D3)⋊C4C2×D311yescharacteristic
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—61no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—61no—
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3C2×D311yescharacteristic
253C2×C4×Dic3C2×D311yescharacteristic
254#893—38no—
255#887—38no—
256#886—38no—
257#886—38no—
258#885—38no—
259#885—38no—
260#885—38no—
261#885C2×D318yescomplemented
262#883—38no—
263#883—38no—
264#883—38no—
265#883—38no—
266#883—68no—
267#67⋊C4—38no—
268#67⋊C4C2×D318yescomplemented
269#875—38no—
270C4×D12—38no—
271C4×Dic6—38no—
272C4×Dic6—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—28no—
303C3×#67—28no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—44no—
309C2×C3×Dic3#4114yes—
310C2×C3×Dic3#4114yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×C4×D3—44no—
318C3×Dic6—28no—
319#627—28no—
320#626—28no—
321#626—28no—
322#625—44no—
323D3×Dic3—44no—
324#559—916no—
325C2×#127—91no—
326C2×#124—31no—
327C2×#124—91no—
328C2×#124—91no—
329C2×#124—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×#123—91no—
333C2×#123—91no—
334C2×C4×Q8—91no—
335C2×C4×Q8—91no—
336C2×C4×D4—31no—
337C2×C4×D4—91no—
338C2×C4×D4—91no—
339C2×C4×D4—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—64no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—64no—
355C2×C3×D4—64no—
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—34no—
366C22×C3×C4—122no—
367C22×C3×C4—122no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—24no—
373C2×#67—24no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—64no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67—122no—
386C2×#67—122no—
387C2×#67—124no—
388C2×#67C22×D314yes—
389C2×#67C22×D314yes—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—42no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—122no—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D314yes—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C2×D12—34no—
410C2×D12—34no—
411C2×D12—64no—
412C2×D12—64no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—42no—
417C2×C4×D3—64no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—124no—
422C2×C4×D3C22×D314yes—
423C2×Dic6—24no—
424C2×Dic6—34no—
425C2×Dic6—34no—
426C2×Dic6—64no—
427C2×Dic6—64no—
428C2×Dic6C22×D314yes—
429C3×C4⋊C4—34no—
430C3×C22⋊C4—24no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4C22×D314yes—
436C3×C22⋊C4C22×D314yes—
437C3×C42—34no—
438C3×C42—34no—
439#217—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—34no—
455(C2×D3)⋊C4—64no—
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—64no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—64no—
471Dic3⋊C4C22×D314yes—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3C22×D314yes—
479C4×Dic3C22×D314yes—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—44no—
484C22×C32C2×#4112yes—
485C22×C32C2×#4112yes—
486C22×C32H(5,𝔽2)12yes—
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×Dic3C2×#4114yes—
510C3×Dic3C2×#4114yes—
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—31no—
521C23×C4—91no—
522C23×C4—91no—
523#127—98no—
524#124—38no—
525#124—98no—
526#124—98no—
527#124—98no—
528#123—98no—
529#123—98no—
530#123—98no—
531#123—98no—
532C4×Q8—98no—
533C4×Q8—98no—
534C4×D4—38no—
535C4×D4—98no—
536C4×D4—98no—
537C4×D4—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—91no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4D3211yescharacteristic
556C2×C42—31no—
557C2×C42—31no—
558C2×C42—91no—
559C2×C42—91no—
560C2×C42—91no—
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—68no—
605C3×D4—68no—
606C3×D4—68no—
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—34no—
614C2×C3×C4—34no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—124no—
628C2×C3×C4—124no—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633#67—28no—
634#67—28no—
635#67—68no—
636#67—68no—
637#67—124no—
638#67—124no—
639#67—124no—
640#67—124no—
641#67—128no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—44no—
653C2×Dic3—62no—
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—122no—
663C2×Dic3—122no—
664C2×Dic3—122no—
665C2×Dic3—124no—
666C2×Dic3#23514yes—
667C2×Dic3#23714yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674D12—68no—
675D12—68no—
676C4×D3—44no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—128no—
681Dic6—28no—
682Dic6—68no—
683Dic6—68no—
684C2×C32—42no—
685C2×C32#55914yescomplemented
686C2×C32C22×#4111yescharacteristic
687C2×C32C22×#4111yescharacteristic
688C2×C32C2×H(5,𝔽2)11yescharacteristic
689C3⋊D3—42no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—91no—
695C24C2×D3211yescharacteristic
696C2×Q8—34no—
697C2×Q8—64no—
698C2×Q8—94no—
699C2×Q8—184no—
700C2×D4—34no—
701C2×D4—34no—
702C2×D4—64no—
703C2×D4—64no—
704C2×D4—94no—
705C2×D4—94no—
706C2×D4—94no—
707C2×D4—94no—
708C2×D4—184no—
709C2×D4—184no—
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—34no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—94no—
725C22×C4—122no—
726C22×C4—122no—
727C22×C4—362no—
728C22×C4—362no—
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—94no—
742C22⋊C4—94no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4C2×D3214yes—
749C42—34no—
750C42—34no—
751C42—94no—
752C42—94no—
753C42—94no—
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×C3C2×#23512yes—
779C22×C3C2×#23712yes—
780C22×C3#100412yes—
781C22×C3D3×#4112yes—
782C22×C3D3×#4112yes—
783C22×C3#100912yes—
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—34no—
811C3×C4—34no—
812C3×C4—42no—
813C3×C4—42no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830Dic3—122no—
831Dic3C2×#23514yes—
832Dic3C2×#23714yes—
833C32C2×#55911yescharacteristic, 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—68no—
852Q8—188no—
853D4—68no—
854D4—68no—
855D4—188no—
856D4—188no—
857D4—364no—
858D4—364no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—34no—
862C2×C4—34no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
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—124no—
878C2×C4—182no—
879C2×C4—182no—
880C2×C4—182no—
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#555914yescomplemented
895C2×C3#568114yescomplemented
896C2×C3C22×#23511yescharacteristic
897C2×C3C22×#23711yescharacteristic
898C2×C3C2×#100411yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900C2×C3C2×D3×#4111yescharacteristic
901C2×C3C2×#100911yescharacteristic
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—
923C22D3×#23512yes—
924C22D3×#23712yes—
925C22#6431412yes—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—22no—
929C4—34no—
930C4—34no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—182no—
936C4—182no—
937C4—182no—
938C3—21no—
939C3C2×#555911yescharacteristic, complemented
940C3C2×#568111yescharacteristic, complemented
941C2—42no—
942C2—122no—
943C2—122no—
944C2—362no—
945C2#1059420014yesdirect product factor
946C2C2×D3×#23511yescharacteristic
947C2C2×D3×#23711yescharacteristic
948C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63979C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#559
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×#885C2semidirect
3. C2×C3×#67⋊C4C2semidirect
5. C2×Dic3×#67C2semidirect
6. C2×#63966C2semidirect
7. C2×#63959C2semidirect
8. C2×#63907C2semidirect
9. C2×#63905C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63891C2semidirect
12. C2×#63881C2semidirect
13. C2×#63852C2semidirect
14. C2×Dic3×Dic6C2semidirect
15. C2×#63837C2semidirect
16. #10594200C2direct (N × H)
36. #64092C22semidirect
44. C3×#885C22semidirect
45. C3×#67⋊C4C22semidirect
47. Dic3×#67C22semidirect
48. #63966C22semidirect
57. #63959C22semidirect
61. #63907C22semidirect
62. #63905C22semidirect
63. C4×#626C22semidirect
64. #63891C22semidirect
65. #63881C22semidirect
66. #63852C22semidirect
67. Dic3×Dic6C22semidirect
68. #63837C22semidirect
90. C2×#885D3semidirect
97. C2×#67⋊C4D3semidirect
261. #885C2×D3semidirect
268. #67⋊C4C2×D3semidirect
685. C2×C32#559semidirect
833. C32C2×#559semidirect
894. C2×C3#5559semidirect
895. C2×C3#5681semidirect
939. C3C2×#5559semidirect
940. C3C2×#5681semidirect
945. C2#10594200direct (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×#8852
C2×C3×#67⋊C42
C2×#639792
C2×Dic3×#672
C2×#639662
C2×#639592
C2×#639072
C2×#639052
C2×C4×#6262
C2×#638912
C2×#638812
C2×#638522
C2×Dic3×Dic62
C2×#638372
#105942002
C2×#56813
C2×#55593