Finite Group Databasebeta

← C2×#10594049 #11900086

Subgroups — C2×#10594049 #11900086

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic
2C2×#64090C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#877C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×C4×#627C211yesmaximal, characteristic, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63883C211yesmaximal, characteristic, complemented
11C2×#63880C211yesmaximal, characteristic, complemented
12C2×#63878C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63837C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594049C2116yesmaximal, direct product factor
17C2×#5546—31nomaximal
18C2×#5523—31nomaximal
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#624C2211yescharacteristic
29C22×#624C2211yescharacteristic
30C2×#3804C4116yescomplemented
31C2×#3804C2218yes—
32C22×D3×Dic3C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×C32×C22⋊C4C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38#64090C2218yescomplemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#67⋊C4C2218yescomplemented
48C3×#877C2218yescomplemented
49#67⋊Dic3C2218yescomplemented
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2218yescomplemented
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63952C2218yescomplemented
62C4×#627C2218yescomplemented
63C4×#626C2218yescomplemented
64#63883C2218yescomplemented
65#63880C2218yescomplemented
66#63878C2218yescomplemented
67D3×Dic3⋊C4C2218yescomplemented
68#63837C2218yescomplemented
69#63836C2218yescomplemented
70C22×#237—31no—
71C22×#235—31no—
72C2×C3×C4×D4—31no—
73C2×C3×#117—31no—
74C2×D4×Dic3—31no—
75C2×C4×#67—31no—
76C2×C4×#67—31no—
77C22×C4⋊Dic3—31no—
78C22×Dic3⋊C4—31no—
79C22×Dic3⋊C4—31no—
80#5546—316no—
81#5523—316no—
82C2×#892—31no—
83C2×#892—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—31no—
86C2×D3×C4⋊C4—31no—
87C2×#887—31no—
88C2×#67⋊C4—31no—
89C2×#67⋊C4—31no—
90C2×#67⋊C4—31no—
91C2×#67⋊C4—31no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—61no—
94C2×#67⋊C4D311yescharacteristic, complemented
95C2×#877—31no—
96C2×#877D311yescharacteristic, complemented
97C2×C4×D12—31no—
98C2×C4×D12—31no—
99C2×#872—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C2×C4×Dic6—31no—
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×#638C2×C418yescomplemented
109C2×#638C2314yes—
110C22×C3⋊Dic3—42no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2314yes—
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×C3×#67C2×C418yescomplemented
118C2×C3×#67C2314yes—
119C22×C3×Dic3—42no—
120C22×C3×Dic3C2×C418yescomplemented
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2314yes—
130C2×C3×C4×D3—42no—
131C2×C3×C4×D3C2314yes—
132C2×#627C2×C418yescomplemented
133C2×#627C2314yes—
134C2×#626C2×C418yescomplemented
135C2×#626C2314yes—
136C2×#624—42no—
137C2×#624C2×C418yescomplemented
138C2×#624C2314yes—
139C2×#624C2314yes—
140#3804C2×C4164yescomplemented
141C2×D3×Dic3—42no—
142C2×D3×Dic3C2×C418yescomplemented
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145C32×C22⋊C4C2314yes—
146#3752C2314yes—
147#3750C2314yes—
148C4×C3⋊Dic3C2314yes—
149C3×#217C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2314yes—
155C3×C4×Dic3C2314yes—
156C3×C4×Dic3C2314yes—
157#3724C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163#3722C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165Dic32C2314yes—
166Dic32C2314yes—
167C2×#520—91noSylow
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—61no—
176C22×#67C2×D311yescharacteristic
177C23×Dic3—31no—
178C23×Dic3—31no—
179C23×Dic3—31no—
180C23×Dic3—31no—
181C23×Dic3—61no—
182C23×Dic3C2×D311yescharacteristic
183C23×Dic3C2×D311yescharacteristic
184C2×#237—316no—
185C2×#237—38no—
186C2×#235—316no—
187C2×#235—38no—
188C22×D12—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—61no—
198C22×C4×D3C2×D311yescharacteristic
199C22×Dic6—31no—
200C22×Dic6—31no—
201C3×C4×D4—38no—
202C3×#117—38no—
203C2×C3×C4⋊C4—31no—
204C2×C3×C4⋊C4—31no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C22⋊C4—21no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C22⋊C4—31no—
209C2×C3×C22⋊C4C2×D311yescharacteristic
210C2×C3×C22⋊C4C2×D311yescharacteristic
211C2×C3×C42—31no—
212C2×C3×C42—31no—
213C2×C3×C42—31no—
214C2×#217—31no—
215C2×#217C2×D311yescharacteristic
216D4×Dic3—38no—
217C4×#67—38no—
218C4×#67—38no—
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—61no—
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—38no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—38no—
242C2×Dic3⋊C4—38no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—61no—
254C2×C4×Dic3C2×D311yescharacteristic
255C2×C4×Dic3C2×D311yescharacteristic
256C2×C4×Dic3C2×D311yescharacteristic
257#892—38no—
258#892—38no—
259D3×C4⋊C4—38no—
260D3×C4⋊C4—38no—
261D3×C4⋊C4—38no—
262#887—38no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#67⋊C4—38no—
266#67⋊C4—38no—
267#67⋊C4—38no—
268#67⋊C4—68no—
269#67⋊C4C2×D318yescomplemented
270#877—38no—
271#877C2×D318yescomplemented
272C4×D12—38no—
273C4×D12—38no—
274#872—38no—
275C4×Dic6—38no—
276C4×Dic6—38no—
277C4×Dic6—38no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32C22×C414yes—
281C23×C32C2412yes—
282C23×C32C2411yescharacteristic
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3C22×C414yes—
286C22×C3⋊D3C2412yes—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3C22×C414yes—
290C22×C3×D3C2412yes—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295#638C22×C4116yescomplemented
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—44no—
299C2×C3⋊Dic3C22×C414yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C4×C3⋊D3—44no—
304C3×#67C22×C4116yescomplemented
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—44no—
310C2×C3×Dic3C22×C414yes—
311C2×C3×Dic3C22×C414yes—
312C2×C3×Dic3C22×C414yes—
313C2×C3×Dic3C22×C4116yescomplemented
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×C4×D3—44no—
322#627C22×C4116yescomplemented
323#626C22×C4116yescomplemented
324#624—44no—
325#624C22×C4116yescomplemented
326D3×Dic3—44no—
327D3×Dic3C22×C4116yescomplemented
328C22×#41—91no—
329#520—916no—
330C2×C4×Q8—91no—
331C2×C4×Q8—91no—
332C2×C4×D4—31no—
333C2×C4×D4—91no—
334C2×C4×D4—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—31no—
339C2×#117—91no—
340C2×#117—91no—
341C22×C4⋊C4—91no—
342C22×C4⋊C4—91no—
343C22×C4⋊C4—91no—
344C24×C3—21no—
345C24×C3—31no—
346C24×C3C22×D311yescharacteristic
347C24×C3C22×D311yescharacteristic
348C23×D3—31no—
349C23×D3—31no—
350C23×D3—61no—
351C23×D3C22×D311yescharacteristic
352C2×C3×D4—38no—
353C2×C3×D4—34no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—38no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—34no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—34no—
366C22×C3×C4—34no—
367C22×C3×C4—122no—
368C22×C3×C4—122no—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—38no—
374C2×#67—38no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—38no—
378C2×#67—34no—
379C2×#67—64no—
380C2×#67—68no—
381C2×#67C4×D318yescomplemented
382C2×#67C22×D314yes—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—38no—
386C22×Dic3—34no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—34no—
392C22×Dic3—34no—
393C22×Dic3—34no—
394C22×Dic3—42no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—64no—
398C22×Dic3—61no—
399C22×Dic3—122no—
400C22×Dic3—122no—
401C22×Dic3—122no—
402C22×Dic3—124no—
403C22×Dic3C4×D318yescomplemented
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D314yes—
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D314yes—
413#237—364no—
414#235—364no—
415C2×D12—38no—
416C2×D12—34no—
417C2×C4×D3—38no—
418C2×C4×D3—34no—
419C2×C4×D3—38no—
420C2×C4×D3—38no—
421C2×C4×D3—34no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—34no—
425C2×C4×D3—34no—
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—42no—
429C2×C4×D3—64no—
430C2×C4×D3—122no—
431C2×C4×D3—122no—
432C2×C4×D3—122no—
433C2×C4×D3—122no—
434C2×C4×D3—124no—
435C2×C4×D3—122no—
436C2×C4×D3C22×D314yes—
437C2×Dic6—38no—
438C2×Dic6—38no—
439C2×Dic6—34no—
440C2×Dic6—34no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—34no—
444C3×C22⋊C4—24no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4C22×D314yes—
448C3×C22⋊C4C22×D314yes—
449C3×C42—34no—
450C3×C42—34no—
451C3×C42—34no—
452#217—34no—
453#217C22×D314yes—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—64no—
460(C2×D3)⋊C4C22×D314yes—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—64no—
476Dic3⋊C4C22×D314yes—
477Dic3⋊C4C22×D314yes—
478Dic3⋊C4C22×D314yes—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—34no—
484C4×Dic3—34no—
485C4×Dic3—64no—
486C4×Dic3C22×D314yes—
487C4×Dic3C22×D314yes—
488C4×Dic3C22×D314yes—
489C22×C32—28no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32C23×C414yes—
493C22×C32C23×C412yes—
494C22×C32H(5,𝔽2)12yes—
495C22×C322−1+412yes—
496C22×C32C2511yescharacteristic
497C2×C3⋊D3—28no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3C23×C414yes—
501C2×C3×D3—28no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3C23×C414yes—
505C32×C4—22no—
506C32×C4—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3⋊Dic3C23×C414yes—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3C23×C414yes—
515C3×Dic3C23×C414yes—
516C3×Dic3C23×C414yes—
517C2×#41—98no—
518C2×#41—916no—
519C22×Q8—91no—
520C22×D4—31no—
521C22×D4—91no—
522C22×D4—91no—
523C23×C4—31no—
524C23×C4—31no—
525C23×C4—31no—
526C23×C4—91no—
527C23×C4—91no—
528C23×C4—91no—
529C23×C4—91no—
530C23×C4—91no—
531C23×C4—91no—
532C4×Q8—98no—
533C4×Q8—98no—
534C4×D4—38no—
535C4×D4—98no—
536C4×D4—98no—
537C4×D4—98no—
538C4×D4—98no—
539C4×D4—98no—
540#117—38no—
541#117—98no—
542#117—98no—
543C2×C4⋊C4—31no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—98no—
547C2×C4⋊C4—98no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—91no—
550C2×C4⋊C4—91no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—91no—
553C2×C4⋊C4—91no—
554C2×C4⋊C4—98no—
555C2×C4⋊C4—91no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4D3211yescharacteristic
562C2×C42—31no—
563C2×C42—31no—
564C2×C42—31no—
565C2×C42—91no—
566C2×C42—91no—
567C2×C42—91no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—21no—
574C23×C3—24no—
575C23×C3—34no—
576C23×C3—32no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3C2×C4×D314yes—
582C23×C3C2×C4×D314yes—
583C23×C3C23×D312yes—
584C23×C3C23×D312yes—
585C23×C3C23×D311yescharacteristic
586C23×C3C23×D311yescharacteristic
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—34no—
590C22×D3—34no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3C2×C4×D314yes—
602C22×D3C23×D312yes—
603C3×D4—316no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—34no—
611C2×C3×C4—34no—
612C2×C3×C4—34no—
613C2×C3×C4—316no—
614C2×C3×C4—32no—
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—316no—
634#67—316no—
635#67—316no—
636#67—616no—
637#67C2×C4×D3116yescomplemented
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—34no—
643C2×Dic3—34no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—316no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—44no—
652C2×Dic3—64no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—64no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—122no—
662C2×Dic3—124no—
663C2×Dic3—124no—
664C2×Dic3—124no—
665C2×Dic3—128no—
666C2×Dic3C2×C4×D314yes—
667C2×Dic3C2×C4×D314yes—
668C2×Dic3C2×C4×D314yes—
669C2×Dic3C2×C4×D3116yescomplemented
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677D12—316no—
678C4×D3—316no—
679C4×D3—316no—
680C4×D3—316no—
681C4×D3—44no—
682C4×D3—124no—
683C4×D3—124no—
684C4×D3—124no—
685C4×D3—124no—
686C4×D3—128no—
687C4×D3—124no—
688Dic6—316no—
689Dic6—316no—
690C2×C32—24no—
691C2×C32#52014yescomplemented
692C2×C32C24×C411yescharacteristic
693C2×C32C2×H(5,𝔽2)11yescharacteristic
694C2×C32C2×2−1+411yescharacteristic
695C3⋊D3—24no—
696C3×D3—24no—
697C24—31no—
698C24—91no—
699C24C2×D3211yescharacteristic
700#41—964no—
701C2×Q8—94no—
702C2×Q8—98no—
703C2×D4—34no—
704C2×D4—38no—
705C2×D4—94no—
706C2×D4—98no—
707C2×D4—94no—
708C2×D4—98no—
709C22×C4—34no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—38no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—34no—
719C22×C4—34no—
720C22×C4—94no—
721C22×C4—98no—
722C22×C4—94no—
723C22×C4—94no—
724C22×C4—98no—
725C22×C4—94no—
726C22×C4—91no—
727C22×C4—91no—
728C22×C4—91no—
729C22×C4—94no—
730C22×C4—94no—
731C22×C4—122no—
732C22×C4—122no—
733C22×C4—362no—
734C22×C4—362no—
735C22×C4—362no—
736C22×C4—362no—
737C22×C4C2×D3211yescharacteristic
738C22×C4C2×D3211yescharacteristic
739C4⋊C4—34no—
740C4⋊C4—34no—
741C4⋊C4—34no—
742C4⋊C4—94no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C22⋊C4—34no—
750C22⋊C4—34no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4C2×D3214yes—
755C42—34no—
756C42—34no—
757C42—34no—
758C42—94no—
759C42—94no—
760C42—94no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—28no—
766C22×C3—28no—
767C22×C3—22no—
768C22×C3—24no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—21no—
772C22×C3—34no—
773C22×C3—42no—
774C22×C3—48no—
775C22×C3—42no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—68no—
779C22×C3C22×C4×D314yes—
780C22×C3C22×C4×D314yes—
781C22×C3C22×C4×D312yes—
782C22×C3C22×C4×D312yes—
783C22×C3#100412yes—
784C22×C3#100912yes—
785C22×C3#101012yes—
786C22×C3#101012yes—
787C22×C3C24×D311yescharacteristic
788C22×C3C24×D311yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—28no—
792C2×D3—34no—
793C2×D3—34no—
794C2×D3—64no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—68no—
800C2×D3—68no—
801C2×D3—122no—
802C2×D3—128no—
803C2×D3—122no—
804C2×D3C22×C4×D314yes—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—34no—
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—34no—
823Dic3—34no—
824Dic3—64no—
825Dic3—64no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—122no—
831Dic3C22×C4×D314yes—
832Dic3C22×C4×D314yes—
833Dic3C22×C4×D314yes—
834C32C2×#52011yescharacteristic, complemented, Sylow
835C23—22no—
836C23—22no—
837C23—34no—
838C23—32no—
839C23—62no—
840C23—62no—
841C23—94no—
842C23—92no—
843C23—182no—
844C23—182no—
845C23C4×D3214yes—
846C23C22×D3212yes—
847C23C22×D3211yescharacteristic
848Q8—916no—
849D4—316no—
850D4—916no—
851D4—916no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—34no—
855C2×C4—34no—
856C2×C4—316no—
857C2×C4—34no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—916no—
870C2×C4—916no—
871C2×C4—94no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4—182no—
878C2×C4—182no—
879C2×C4—364no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4—364no—
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C3—24no—
886C2×C3—24no—
887C2×C3—24no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—44no—
892C2×C3—64no—
893C2×C3#552314yescomplemented
894C2×C3#554614yescomplemented
895C2×C3C23×C4×D311yescharacteristic
896C2×C3C23×C4×D311yescharacteristic
897C2×C3C2×#100411yescharacteristic
898C2×C3C2×#100911yescharacteristic
899C2×C3C2×#101011yescharacteristic
900C2×C3C2×#101011yescharacteristic
901D3—24no—
902D3—64no—
903D3—64no—
904D3—124no—
905C22—28no—
906C22—22no—
907C22—22no—
908C22—34no—
909C22—68no—
910C22—62no—
911C22—62no—
912C22—94no—
913C22—188no—
914C22—182no—
915C22—182no—
916C22C2×C4×D3214yes—
917C22C2×C4×D3212yes—
918C22#6430912yes—
919C22#6431412yes—
920C22C23×D3211yescharacteristic
921C4—22no—
922C4—22no—
923C4—34no—
924C4—34no—
925C4—34no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—94no—
931C4—182no—
932C4—182no—
933C3—21no—
934C3C2×#552311yescharacteristic, complemented
935C3C2×#554611yescharacteristic, complemented
936C2—24no—
937C2—64no—
938C2—184no—
939C2#1059404914yesdirect product factor
940C2C22×C4×D3211yescharacteristic
941C2C2×#6430911yescharacteristic
942C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#3804C2
cosocleC22×C32C25
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64090C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×C3×#877C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C22×Dic3⋊Dic3C2semidirect
7. C2×#63952C2semidirect
8. C2×C4×#627C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63883C2semidirect
11. C2×#63880C2semidirect
12. C2×#63878C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63837C2semidirect
15. C2×#63836C2semidirect
16. #10594049C2direct (N × H)
30. C2×#3804C4semidirect
38. #64090C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×#877C22semidirect
49. #67⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
61. #63952C22semidirect
62. C4×#627C22semidirect
63. C4×#626C22semidirect
64. #63883C22semidirect
65. #63880C22semidirect
66. #63878C22semidirect
67. D3×Dic3⋊C4C22semidirect
68. #63837C22semidirect
69. #63836C22semidirect
94. C2×#67⋊C4D3semidirect
96. C2×#877D3semidirect
108. C2×#638C2×C4semidirect
117. C2×C3×#67C2×C4semidirect
120. C22×C3×Dic3C2×C4semidirect
132. C2×#627C2×C4semidirect
134. C2×#626C2×C4semidirect
137. C2×#624C2×C4semidirect
140. #3804C2×C4semidirect
142. C2×D3×Dic3C2×C4semidirect
269. #67⋊C4C2×D3semidirect
271. #877C2×D3semidirect
295. #638C22×C4semidirect
304. C3×#67C22×C4semidirect
313. C2×C3×Dic3C22×C4semidirect
322. #627C22×C4semidirect
323. #626C22×C4semidirect
325. #624C22×C4semidirect
327. D3×Dic3C22×C4semidirect
381. C2×#67C4×D3semidirect
403. C22×Dic3C4×D3semidirect
637. #67C2×C4×D3semidirect
669. C2×Dic3C2×C4×D3semidirect
691. C2×C32#520semidirect
834. C32C2×#520semidirect
893. C2×C3#5523semidirect
894. C2×C3#5546semidirect
934. C3C2×#5523semidirect
935. C3C2×#5546semidirect
939. C2#10594049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C2×#640902
C2×C3×#67⋊C42
C2×C3×#8772
C2×#67⋊Dic32
C22×Dic3⋊Dic32
C2×#639522
C2×C4×#6272
C2×C4×#6262
C2×#638832
C2×#638802
C2×#638782
C2×D3×Dic3⋊C42
C2×#638372
C2×#638362
#105940492
C2×#55463
C2×#55233