Finite Group Databasebeta

← C2×#10594040 #11902923

Subgroups — C2×#10594040 #11902923

Order 1152.

2993 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic
5C2×#63964C211yesmaximal, characteristic, complemented
6C22×#3722C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×C4×#626C211yesmaximal, characteristic, complemented
9C2×#63874C211yesmaximal, characteristic, complemented
10C2×#63868C211yesmaximal, characteristic, complemented
11C2×#63868C211yesmaximal, characteristic, complemented
12C2×#63865C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594040C2116yesmaximal, direct product factor
17C2×#5556—31nomaximal
18C2×#5527—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C22⋊C4×C3⋊D3C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40C2×C3×C4×Dic3C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×#67⋊C4C2218yescomplemented
43C3×#877C2218yescomplemented
44#63981C2218yes—
45C2×#3724C2211yescharacteristic, complemented
46C2×#3724C2211yescharacteristic, complemented
47C2×#3724C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50#63964C2218yescomplemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2218yescomplemented
58#63961C2218yescomplemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C4×#626C2218yescomplemented
62#63874C2218yescomplemented
63#63868C2218yescomplemented
64#63868C2218yescomplemented
65#63865C2218yescomplemented
66#63853C2218yescomplemented
67#63852C2218yescomplemented
68#63850C2218yescomplemented
69C2×C3×C4×D4—31no—
70C2×C3×#117—31no—
71C2×#937—31no—
72C2×#935—31no—
73C2×#929—31no—
74C2×#929—31no—
75C2×C4×#67—31no—
76C22×(C2×D3)⋊C4—31no—
77C22×(C2×D3)⋊C4—31no—
78C2×#924—31no—
79#5556—316no—
80#5527—316no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#896—31no—
84C2×#896—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#885—31no—
88C2×#883—31no—
89C2×#882—31no—
90C2×#67⋊C4D311yescharacteristic, complemented
91C2×D3×C22⋊C4—31no—
92C2×D3×C22⋊C4—31no—
93C2×D3×C22⋊C4—61no—
94C2×#878—31no—
95C2×#877D311yescharacteristic, complemented
96C2×#876—31no—
97C2×#876—31no—
98C2×#875—31no—
99C2×C4×D12—31no—
100C2×#872—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—24no—
104C23×C3⋊D3—24no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2314yes—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4×C3⋊D3—24no—
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×C4×C3⋊D3C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67C2314yes—
120C22×C3×Dic3—24no—
121C22×C3×Dic3—42no—
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yescomplemented
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×#626—24no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C32×C22⋊C4C2314yes—
140#3757C2314yes—
141#3752C2314yes—
142#3752C2314yes—
143C3×#217C2314yes—
144C3×(C2×D3)⋊C4C2314yescomplemented
145C3×Dic3⋊C4C2314yescomplemented
146C3×Dic3⋊C4C2314yescomplemented
147C3×Dic3⋊C4C2314yescomplemented
148C3×C4×Dic3C2314yescomplemented
149C3×C4×Dic3C2314yescomplemented
150C3×C4×Dic3C2314yescomplemented
151#3724C2314yescomplemented
152#3724C2314yescomplemented
153#3724C2314yescomplemented
154Dic3⋊Dic3C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yescomplemented
163(C2×D3)⋊Dic3C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C24×D3—61no—
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67C2×D311yescharacteristic
175C23×Dic3C2×D311yescharacteristic
176C23×Dic3C2×D311yescharacteristic
177C22×D12—31no—
178C22×D12—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—61no—
184C22×C4×D3—61no—
185C22×C4×D3C2×D311yescharacteristic, complemented
186C22×Dic6—31no—
187C22×Dic6—31no—
188C3×C4×D4—38no—
189C3×#117—38no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C22⋊C4—21no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C42—31no—
199C2×C3×C42—31no—
200C2×C3×C42—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—61no—
206C2×#217C2×D311yescharacteristic
207#937—38no—
208#935—38no—
209#929—38no—
210#929—38no—
211C4×#67—38no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
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—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—38no—
231C2×(C2×D3)⋊C4—38no—
232C2×(C2×D3)⋊C4—61no—
233C2×(C2×D3)⋊C4—61no—
234C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237#924—38no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
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⋊C4C2×D311yescharacteristic, complemented
247C2×Dic3⋊C4C2×D311yescharacteristic, complemented
248C2×Dic3⋊C4C2×D311yescharacteristic, complemented
249C2×C4×Dic3C2×D311yescharacteristic, complemented
250C2×C4×Dic3C2×D311yescharacteristic, complemented
251C2×C4×Dic3C2×D311yescharacteristic, complemented
252#898—38no—
253#898—38no—
254#896—38no—
255#896—38no—
256#894—38no—
257#894—38no—
258#885—38no—
259#883—38no—
260#882—38no—
261#67⋊C4C2×D318yescomplemented
262D3×C22⋊C4—38no—
263D3×C22⋊C4—38no—
264D3×C22⋊C4—68no—
265#878—38no—
266#877C2×D318yescomplemented
267#876—38no—
268#876—38no—
269#875—38no—
270C4×D12—38no—
271#872—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—28no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—28no—
285C22×C3⋊D3—44no—
286C22×C3⋊D3—416no—
287C22×C3⋊D3#4114yes—
288C22×C3⋊D3C2412yes—
289C22×C3⋊D3C2412yes—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3C2412yes—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—28no—
303C4×C3⋊D3—44no—
304C3×#67—28no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—28no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—44no—
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#627—44no—
323#626—28no—
324#626—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—31no—
336C2×C4×D4—91no—
337C2×#117—31no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—34no—
350C23×D3—34no—
351C23×D3—61no—
352C23×D3—64no—
353C23×D3—61no—
354C23×D3—64no—
355C23×D3—64no—
356C23×D3—68no—
357C23×D3—64no—
358C23×D3—64no—
359C23×D3—124no—
360C23×D3—122no—
361C23×D3—122no—
362C23×D3—124no—
363C23×D3C22×D311yescharacteristic
364C2×C3×D4—34no—
365C2×C3×D4—64no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—34no—
376C22×C3×C4—34no—
377C22×C3×C4—34no—
378C22×C3×C4—64no—
379C22×C3×C4—122no—
380C22×C3×C4—122no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—24no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—64no—
389C2×#67—122no—
390C2×#67C22×D314yes—
391C22×Dic3—24no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—42no—
397C22×Dic3—61no—
398C22×Dic3—61no—
399C22×Dic3C22×D314yes—
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D314yes—
408C2×D12—34no—
409C2×D12—34no—
410C2×D12—64no—
411C2×D12—122no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—42no—
417C2×C4×D3—64no—
418C2×C4×D3—64no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—124no—
422C2×C4×D3—122no—
423C2×C4×D3—122no—
424C2×C4×D3—124no—
425C2×C4×D3C22×D314yescomplemented
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—122no—
429C2×Dic6—122no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4C22×D314yes—
437C3×C22⋊C4C22×D314yes—
438C3×C42—34no—
439C3×C42—34no—
440C3×C42—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—34no—
445#217—64no—
446#217C22×D314yes—
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—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—64no—
466(C2×D3)⋊C4—64no—
467(C2×D3)⋊C4C22×D314yescomplemented
468C4⋊Dic3—34no—
469C4⋊Dic3—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⋊C4C22×D314yescomplemented
479Dic3⋊C4C22×D314yescomplemented
480Dic3⋊C4C22×D314yescomplemented
481C4×Dic3C22×D314yescomplemented
482C4×Dic3C22×D314yescomplemented
483C4×Dic3C22×D314yescomplemented
484C22×C32—28no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32C2×#4114yes—
488C22×C32C2×#4112yes—
489C22×C32C2×#4112yes—
490C22×C32H(5,𝔽2)12yes—
491C22×C32C2511yescharacteristic
492C2×C3⋊D3—28no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—416no—
499C2×C3⋊D3—44no—
500C2×C3⋊D3C2×#4114yes—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—44no—
505C32×C4—22no—
506C32×C4—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C25—91no—
517C22×Q8—91no—
518C22×D4—31no—
519C22×D4—91no—
520C22×D4—91no—
521C23×C4—31no—
522C23×C4—31no—
523C23×C4—31no—
524C23×C4—91no—
525C23×C4—91no—
526#126—98no—
527#126—98no—
528#124—98no—
529#123—98no—
530#123—98no—
531#123—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#120—98no—
535C4×D4—38no—
536C4×D4—98no—
537#117—38no—
538#117—98no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—98no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—98no—
562C2×C22⋊C4D3211yescharacteristic
563C2×C42—31no—
564C2×C42—31no—
565C2×C42—31no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—21no—
572C23×C3—24no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3#23514yes—
580C23×C3#23514yes—
581C23×C3C23×D312yes—
582C23×C3C23×D312yes—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—34no—
589C22×D3—34no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—64no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—68no—
598C22×D3—68no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—616no—
606C22×D3—64no—
607C22×D3—68no—
608C22×D3—68no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—128no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—1216no—
621C22×D3—1216no—
622C22×D3—128no—
623C22×D3—1232no—
624C22×D3C23×D312yes—
625C3×D4—68no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—42no—
640C2×C3×C4—42no—
641C2×C3×C4—68no—
642C2×C3×C4—62no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—124no—
650C2×C3×C4—124no—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655#67—28no—
656#67—68no—
657#67—124no—
658C2×Dic3—28no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—44no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—122no—
678C2×Dic3—122no—
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D312yes—
686D12—68no—
687D12—124no—
688C4×D3—44no—
689C4×D3—68no—
690C4×D3—68no—
691C4×D3—128no—
692C4×D3—124no—
693C4×D3—124no—
694C4×D3—128no—
695Dic6—124no—
696Dic6—124no—
697C2×C32—24no—
698C2×C32#55114yescomplemented
699C2×C32C22×#4111yescharacteristic
700C2×C32C22×#4111yescharacteristic
701C2×C32C2×H(5,𝔽2)11yescharacteristic
702C3⋊D3—24no—
703C3⋊D3—42no—
704C3×D3—42no—
705C24—31no—
706C24—91no—
707C24—91no—
708C24—94no—
709C24—184no—
710C24—184no—
711C24—362no—
712C24C2×D3211yescharacteristic
713C2×Q8—94no—
714C2×Q8—362no—
715C2×D4—34no—
716C2×D4—64no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—184no—
720C2×D4—362no—
721C22×C4—34no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—34no—
730C22×C4—34no—
731C22×C4—64no—
732C22×C4—91no—
733C22×C4—91no—
734C22×C4—94no—
735C22×C4—94no—
736C22×C4—122no—
737C22×C4—122no—
738C22×C4—184no—
739C22×C4—362no—
740C22×C4C2×D3211yescharacteristic
741C22×C4C2×D3211yescharacteristic
742C4⋊C4—34no—
743C4⋊C4—34no—
744C4⋊C4—34no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C22⋊C4—34no—
751C22⋊C4—34no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4C2×D3214yes—
764C42—34no—
765C42—34no—
766C42—34no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—28no—
772C22×C3—28no—
773C22×C3—22no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—48no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—124no—
785C22×C3C2×#23514yes—
786C22×C3C2×#23514yes—
787C22×C3C2×#23512yes—
788C22×C3C2×#23512yes—
789C22×C3#100412yes—
790C22×C3D3×#4112yes—
791C22×C3D3×#4112yes—
792C22×C3#100912yes—
793C22×C3C24×D311yescharacteristic
794C22×C3C24×D311yescharacteristic
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—34no—
799C2×D3—34no—
800C2×D3—44no—
801C2×D3—64no—
802C2×D3—64no—
803C2×D3—64no—
804C2×D3—616no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—68no—
810C2×D3—68no—
811C2×D3—64no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—1216no—
821C2×D3—1216no—
822C2×D3—1232no—
823C2×D3—128no—
824C2×D3—124no—
825C2×D3—124no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—62no—
837C3×C4—62no—
838C3×C4—62no—
839Dic3—22no—
840Dic3—22no—
841Dic3—22no—
842Dic3—22no—
843Dic3—22no—
844Dic3—22no—
845Dic3—22no—
846Dic3—62no—
847Dic3—62no—
848Dic3—62no—
849Dic3—62no—
850Dic3—122no—
851Dic3—122no—
852C32C2×#55111yescharacteristic, complemented, Sylow
853C23—22no—
854C23—22no—
855C23—32no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—94no—
860C23—92no—
861C23—92no—
862C23—188no—
863C23—182no—
864C23—182no—
865C23—188no—
866C23—182no—
867C23—182no—
868C23—182no—
869C23—364no—
870C23—3616no—
871C23#379814yes—
872C23C22×D3212yes—
873C23C22×D3211yescharacteristic
874Q8—364no—
875D4—68no—
876D4—188no—
877D4—364no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—68no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—124no—
899C2×C4—188no—
900C2×C4—182no—
901C2×C4—182no—
902C2×C4—364no—
903C2×C4C22×D3212yes—
904C2×C4C22×D3212yes—
905C2×C3—24no—
906C2×C3—24no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—24no—
911C2×C3—44no—
912C2×C3—122no—
913C2×C3#552714yescomplemented
914C2×C3#555614yescomplemented
915C2×C3C22×#23511yescharacteristic
916C2×C3C22×#23511yescharacteristic
917C2×C3C2×#100411yescharacteristic
918C2×C3C2×D3×#4111yescharacteristic
919C2×C3C2×D3×#4111yescharacteristic
920C2×C3C2×#100911yescharacteristic
921D3—42no—
922D3—68no—
923D3—64no—
924D3—64no—
925D3—124no—
926D3—122no—
927D3—122no—
928C22—22no—
929C22—22no—
930C22—28no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—94no—
935C22—124no—
936C22—182no—
937C22—182no—
938C22—188no—
939C22—182no—
940C22—182no—
941C22—182no—
942C22—3616no—
943C22—364no—
944C22C2×#379814yes—
945C22C2×#379812yes—
946C22#6431212yes—
947C22#6431412yes—
948C22C23×D3211yescharacteristic
949C4—22no—
950C4—22no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—62no—
955C4—62no—
956C4—62no—
957C4—62no—
958C4—182no—
959C4—182no—
960C3—21no—
961C3C2×#552711yescharacteristic, complemented
962C3C2×#555611yescharacteristic, complemented
963C2—24no—
964C2—122no—
965C2—184no—
966C2—362no—
967C2#1059404014yesdirect product factor
968C2C22×#379811yescharacteristic
969C2C2×#6431211yescharacteristic
970C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63981C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#551
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×C22⋊C4×C3⋊D3C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C2×C3×#877C2semidirect
5. C2×#63964C2semidirect
6. C22×#3722C2semidirect
7. C2×#63961C2semidirect
8. C2×C4×#626C2semidirect
9. C2×#63874C2semidirect
10. C2×#63868C2semidirect
11. C2×#63868C2semidirect
12. C2×#63865C2semidirect
13. C2×#63853C2semidirect
14. C2×#63852C2semidirect
15. C2×#63850C2semidirect
16. #10594040C2direct (N × H)
25. C22×C3×C4×D3C22semidirect
26. C22×#627C22semidirect
33. C22⋊C4×C3⋊D3C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C2×C3×C4×Dic3C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C3×#67⋊C4C22semidirect
43. C3×#877C22semidirect
45. C2×#3724C22semidirect
46. C2×#3724C22semidirect
47. C2×#3724C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. #63964C22semidirect
57. C2×#3722C22semidirect
58. #63961C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C4×#626C22semidirect
62. #63874C22semidirect
63. #63868C22semidirect
64. #63868C22semidirect
65. #63865C22semidirect
66. #63853C22semidirect
67. #63852C22semidirect
68. #63850C22semidirect
90. C2×#67⋊C4D3semidirect
95. C2×#877D3semidirect
132. C2×C3×C4×D3C23semidirect
134. C2×#627C23semidirect
144. C3×(C2×D3)⋊C4C23semidirect
145. C3×Dic3⋊C4C23semidirect
146. C3×Dic3⋊C4C23semidirect
147. C3×Dic3⋊C4C23semidirect
148. C3×C4×Dic3C23semidirect
149. C3×C4×Dic3C23semidirect
150. C3×C4×Dic3C23semidirect
151. #3724C23semidirect
152. #3724C23semidirect
153. #3724C23semidirect
154. Dic3⋊Dic3C23semidirect
155. Dic3⋊Dic3C23semidirect
162. (C2×D3)⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
185. C22×C4×D3C2×D3semidirect
234. C2×(C2×D3)⋊C4C2×D3semidirect
246. C2×Dic3⋊C4C2×D3semidirect
247. C2×Dic3⋊C4C2×D3semidirect
248. C2×Dic3⋊C4C2×D3semidirect
249. C2×C4×Dic3C2×D3semidirect
250. C2×C4×Dic3C2×D3semidirect
251. C2×C4×Dic3C2×D3semidirect
261. #67⋊C4C2×D3semidirect
266. #877C2×D3semidirect
425. C2×C4×D3C22×D3semidirect
467. (C2×D3)⋊C4C22×D3semidirect
478. Dic3⋊C4C22×D3semidirect
479. Dic3⋊C4C22×D3semidirect
480. Dic3⋊C4C22×D3semidirect
481. C4×Dic3C22×D3semidirect
482. C4×Dic3C22×D3semidirect
483. C4×Dic3C22×D3semidirect
698. C2×C32#551semidirect
852. C32C2×#551semidirect
913. C2×C3#5527semidirect
914. C2×C3#5556semidirect
961. C3C2×#5527semidirect
962. C3C2×#5556semidirect
967. C2#10594040direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×C3×#67⋊C42
C2×C3×#8772
C2×#639812
C2×#639642
C22×#37222
C2×#639612
C2×C4×#6262
C2×#638742
C2×#638682
C2×#638652
C2×#638532
C2×#638522
C2×#638502
#105940402
C2×#55563
C2×#55273