Finite Group Databasebeta

← C2×#10594885 #11902531

Subgroups — C2×#10594885 #11902531

Order 1152.

3435 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64138C211yesmaximal, characteristic, complemented
4C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×Dic3×#67C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63904C211yesmaximal, characteristic, complemented
9C2×#63888C211yesmaximal, characteristic, complemented
10C2×#63886C211yesmaximal, characteristic, complemented
11#10594885C2116yesmaximal, direct product factor
12C2×#63884C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63851C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16C2×#63839C211yesmaximal, characteristic, complemented
17C2×#5824—31nomaximal
18C2×#5507—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C2×C3×#235—28no—
26C2×C3×#235C2218yescomplemented
27C22×C3×D12C2211yescharacteristic
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×Dic6C2211yescharacteristic
31C22×#627C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×#3804—28no—
36C2×#3804C2218yescomplemented
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic
39C2×#3757C2211yescharacteristic
40#64138C2218yescomplemented
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44C2×#3750C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2218yescomplemented
50#63978C2218yescomplemented
51Dic3×#67C2218yescomplemented
52C2×#3724C2211yescharacteristic
53C2×#3724C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57#63961C2218yescomplemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63#63904C2218yescomplemented
64#63888C2218yescomplemented
65#63886C2218yescomplemented
66#63884C2218yescomplemented
67D3×Dic3⋊C4C2218yescomplemented
68#63851C2218yescomplemented
69#63850C2218yescomplemented
70#63839C2218yescomplemented
71C22×C3×#41—31no—
72C22×#237—31no—
73C22×#235—31no—
74C22×#235D311yescharacteristic, complemented
75C22×C3×C4⋊C4—31no—
76#5824—316no—
77C2×#946—31no—
78C2×#944—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#935—31no—
82C2×#935—31no—
83C2×D4×Dic3—31no—
84C2×#930—31no—
85C2×#929—31no—
86C2×#929—31no—
87C2×#929—31no—
88C2×#929—31no—
89C2×#929—61no—
90C2×C4×#67—31no—
91C2×C4×#67—31no—
92C2×#924—31no—
93C22×Dic3⋊C4—31no—
94C22×Dic3⋊C4D311yescharacteristic, complemented
95C2×#896—31no—
96C2×#896—31no—
97#5507—316no—
98C2×#895—31no—
99C2×#894—31no—
100C2×#894—31no—
101C2×#893—31no—
102C2×D3×C4⋊C4—31no—
103C2×#888—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4—24no—
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2314yes—
112C2×#638—24no—
113C2×#638C2314yes—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C3×#67—24no—
118C2×C3×#67D418yescomplemented
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C22×C3×Dic3—24no—
122C22×C3×Dic3—24no—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C3×#235—232no—
132C2×C3×D12—24no—
133C2×C3×D12C2314yes—
134C2×C3×C4×D3—24no—
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2314yes—
138C2×C3×Dic6—24no—
139C2×C3×Dic6C2314yes—
140C2×#627—24no—
141C2×#627C2314yes—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#624—24no—
147C2×#624C2314yes—
148#3804—232no—
149C2×D3×Dic3—24no—
150C2×D3×Dic3—24no—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153#3757C2314yes—
154#3752C2314yes—
155#3752C2314yes—
156#3750C2314yes—
157#3750C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×Dic3⋊C4C2314yes—
162#3724C2314yes—
163#3724C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166#3722C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171Dic32C2314yes—
172C2×#547—91noSylow
173C2×C3×#41—38no—
174C2×C3×#41—68no—
175C22×C3×Q8—31no—
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C23×C3×C4—21no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C23×C3×C4—31no—
183C23×C3×C4—31no—
184C23×C3×C4C2×D311yescharacteristic
185C23×C3×C4C2×D311yescharacteristic
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—61no—
191C22×#67C2×D311yescharacteristic
192C22×#67C2×D311yescharacteristic
193C23×Dic3—31no—
194C23×Dic3—31no—
195C23×Dic3C2×D311yescharacteristic
196C23×Dic3C2×D311yescharacteristic
197C2×#237—38no—
198C2×#237—68no—
199C2×#235—28no—
200C2×#235—38no—
201C2×#235—68no—
202C2×#235C2×D318yescomplemented
203C22×D12—31no—
204C22×D12—31no—
205C22×D12C2×D311yescharacteristic
206C22×C4×D3—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3C2×D311yescharacteristic
211C22×C4×D3C2×D311yescharacteristic
212C22×Dic6—31no—
213C22×Dic6—31no—
214C22×Dic6C2×D311yescharacteristic
215C2×C3×C4⋊C4—31no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C4⋊C4—31no—
219C2×C3×C4⋊C4—38no—
220C2×#217—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—31no—
226C2×#217—61no—
227#946—38no—
228#944—38no—
229#939—38no—
230#939—38no—
231#935—38no—
232#935—38no—
233D4×Dic3—38no—
234#930—38no—
235#929—38no—
236#929—38no—
237#929—38no—
238#929—38no—
239#929—68no—
240C4×#67—38no—
241C4×#67—38no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—61no—
253C2×(C2×D3)⋊C4—61no—
254C2×C4⋊Dic3—31no—
255C2×C4⋊Dic3—31no—
256#924—38no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—38no—
268C2×Dic3⋊C4—61no—
269C2×Dic3⋊C4—61no—
270C2×Dic3⋊C4C2×D311yescharacteristic
271C2×Dic3⋊C4C2×D311yescharacteristic
272C2×Dic3⋊C4C2×D311yescharacteristic
273C2×Dic3⋊C4C2×D311yescharacteristic
274C2×Dic3⋊C4C2×D318yescomplemented
275C2×C4×Dic3—31no—
276C2×C4×Dic3—31no—
277#896—38no—
278#896—38no—
279#895—38no—
280#894—38no—
281#894—38no—
282#893—38no—
283D3×C4⋊C4—38no—
284#888—38no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32C2×D414yes—
288C23×C32C2412yes—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3C2412yes—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2×D414yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4—28no—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307#638—28no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—22no—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C3×#67—28no—
315C3×#67C2×D4116yescomplemented
316C2×C3×Dic3—22no—
317C2×C3×Dic3—28no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—28no—
322C2×C3×Dic3C2×D414yes—
323C2×C3×Dic3#4114yescomplemented
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C3×D12—28no—
331C3×C4×D3—28no—
332C3×C4×D3—28no—
333C3×Dic6—28no—
334#627—28no—
335#626—28no—
336#626—28no—
337#624—28no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340C22×#41—31no—
341C22×#41—91no—
342#547—916no—
343C2×C4⋊Q8—91no—
344C2×#123—91no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×C22⋊Q8—91no—
349C2×C22⋊Q8—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×C4×D4—91no—
353C2×C4×D4—91no—
354C22×C4⋊C4—31no—
355C22×C4⋊C4—91no—
356C24×C3—21no—
357C24×C3—31no—
358C24×C3—31no—
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—61no—
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C3×#41—632no—
367C2×C3×Q8—34no—
368C2×C3×Q8—64no—
369C2×C3×D4—38no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—64no—
374C2×C3×D4—64no—
375C22×C3×C4—24no—
376C22×C3×C4—24no—
377C22×C3×C4—21no—
378C22×C3×C4—21no—
379C22×C3×C4—24no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—34no—
387C22×C3×C4—34no—
388C22×C3×C4—34no—
389C22×C3×C4—34no—
390C22×C3×C4—44no—
391C22×C3×C4—64no—
392C22×C3×C4—64no—
393C22×C3×C4—64no—
394C22×C3×C4—64no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D314yes—
400C22×C3×C4C22×D314yes—
401C2×#67—24no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—64no—
407C2×#67—64no—
408C2×#67—64no—
409C2×#67—64no—
410C2×#67—64no—
411C2×#67—124no—
412C2×#67#6718yescomplemented
413C2×#67C22×D314yes—
414C2×#67C22×D314yes—
415C22×Dic3—24no—
416C22×Dic3—24no—
417C22×Dic3—31no—
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—34no—
424C22×Dic3—34no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—61no—
428C22×Dic3—64no—
429C22×Dic3—64no—
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D314yes—
435C22×Dic3C22×D314yes—
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438#237—632no—
439#235—232no—
440#235—632no—
441C2×D12—24no—
442C2×D12—34no—
443C2×D12—34no—
444C2×D12—64no—
445C2×D12—64no—
446C2×D12C22×D314yes—
447C2×C4×D3—24no—
448C2×C4×D3—24no—
449C2×C4×D3—34no—
450C2×C4×D3—34no—
451C2×C4×D3—34no—
452C2×C4×D3—34no—
453C2×C4×D3—64no—
454C2×C4×D3—64no—
455C2×C4×D3—64no—
456C2×C4×D3—64no—
457C2×C4×D3C22×D314yes—
458C2×C4×D3C22×D314yes—
459C2×Dic6—24no—
460C2×Dic6—34no—
461C2×Dic6—34no—
462C2×Dic6—64no—
463C2×Dic6—64no—
464C2×Dic6C22×D314yes—
465C3×C4⋊C4—34no—
466C3×C4⋊C4—34no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—34no—
469#217—34no—
470#217—34no—
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—64no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—64no—
487(C2×D3)⋊C4—64no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—64no—
501Dic3⋊C4—64no—
502Dic3⋊C4C22×D314yes—
503Dic3⋊C4C22×D314yes—
504Dic3⋊C4C22×D314yes—
505Dic3⋊C4C22×D314yes—
506C4×Dic3—34no—
507C4×Dic3—34no—
508C22×C32—28no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32C22×D414yes—
512C22×C32C22×D412yes—
513C22×C32C2×#4112yes—
514C22×C322−1+412yes—
515C22×C32C2511yescharacteristic
516C2×C3⋊D3—22no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—44no—
520C2×C3×D3—28no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—44no—
527C2×C3×D3C22×D414yes—
528C32×C4—22no—
529C32×C4—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3C22×D414yes—
538C3×Dic3C2×#4114yescomplemented
539C2×#41—38no—
540C2×#41—68no—
541C2×#41—98no—
542C2×#41—188no—
543C22×Q8—31no—
544C22×Q8—91no—
545C22×D4—31no—
546C22×D4—31no—
547C22×D4—31no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C23×C4—31no—
552C23×C4—31no—
553C23×C4—31no—
554C23×C4—31no—
555C23×C4—91no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4D3211yescharacteristic
559C4⋊Q8—98no—
560#123—98no—
561#123—98no—
562#123—98no—
563#123—98no—
564C22⋊Q8—98no—
565C22⋊Q8—98no—
566#121—98no—
567#121—98no—
568C4×D4—98no—
569C4×D4—98no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—31no—
574C2×C4⋊C4—38no—
575C2×C4⋊C4—98no—
576C2×C4⋊C4—91no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C22⋊C4—91no—
583C2×C22⋊C4—91no—
584C2×C22⋊C4—91no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C42—91no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—21no—
597C23×C3—24no—
598C23×C3—34no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—42no—
602C23×C3—42no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3D3×D414yes—
609C23×C3C2×#6714yes—
610C23×C3C23×D312yes—
611C23×C3C23×D312yes—
612C23×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—32no—
620C22×D3—32no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3C2×#6714yes—
632C22×D3C23×D312yes—
633C22×D3C23×D312yes—
634C3×Q8—68no—
635C3×D4—316no—
636C3×D4—68no—
637C3×D4—68no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—28no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—28no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—34no—
647C2×C3×C4—34no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—42no—
655C2×C3×C4—42no—
656C2×C3×C4—48no—
657C2×C3×C4—68no—
658C2×C3×C4—68no—
659C2×C3×C4—68no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—68no—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669#67—28no—
670#67—68no—
671#67—68no—
672#67—68no—
673#67—68no—
674#67—128no—
675#67C2×#67116yescomplemented
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—22no—
679C2×Dic3—28no—
680C2×Dic3—22no—
681C2×Dic3—28no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—32no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—68no—
692C2×Dic3—62no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—68no—
699C2×Dic3—122no—
700C2×Dic3—122no—
701C2×Dic3—122no—
702C2×Dic3#23514yescomplemented
703C2×Dic3C2×#6714yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12—28no—
711D12—68no—
712D12—68no—
713C4×D3—28no—
714C4×D3—28no—
715C4×D3—68no—
716C4×D3—68no—
717C4×D3—68no—
718C4×D3—68no—
719Dic6—28no—
720Dic6—68no—
721Dic6—68no—
722C2×C32—24no—
723C2×C32#54714yescomplemented
724C2×C32C23×D411yescharacteristic
725C2×C32C22×#4111yescharacteristic
726C2×C32C2×2−1+411yescharacteristic
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—91no—
733C24C2×D3211yescharacteristic
734#41—632no—
735#41—1832no—
736C2×Q8—34no—
737C2×Q8—64no—
738C2×Q8—94no—
739C2×Q8—184no—
740C2×D4—34no—
741C2×D4—38no—
742C2×D4—34no—
743C2×D4—34no—
744C2×D4—64no—
745C2×D4—64no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—184no—
750C2×D4—184no—
751C2×D4—184no—
752C22×C4—24no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—34no—
756C22×C4—34no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—34no—
763C22×C4—64no—
764C22×C4—64no—
765C22×C4—64no—
766C22×C4—64no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—94no—
770C22×C4—91no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—184no—
774C22×C4—184no—
775C22×C4—184no—
776C22×C4C2×D3214yes—
777C22×C4C2×D3211yescharacteristic
778C22×C4C2×D3211yescharacteristic
779C4⋊C4—34no—
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C42—94no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—28no—
803C22×C3—28no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—24no—
808C22×C3—21no—
809C22×C3—34no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—48no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—68no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—124no—
820C22×C3C2×#23512yes—
821C22×C3C2×D3×D414yes—
822C22×C3C2×D3×D412yes—
823C22×C3#100712yes—
824C22×C3D3×#4112yes—
825C22×C3#101012yes—
826C22×C3C22×#6714yes—
827C22×C3C22×#6712yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—28no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—44no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—124no—
847C2×D3—124no—
848C2×D3—244no—
849C2×D3C22×#6714yes—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—34no—
855C3×C4—34no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—122no—
873Dic3—122no—
874Dic3—122no—
875Dic3C2×#23514yescomplemented
876Dic3C22×#6714yes—
877C32C2×#54711yescharacteristic, complemented, Sylow
878C23—22no—
879C23—22no—
880C23—34no—
881C23—32no—
882C23—32no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—92no—
889C23—182no—
890C23—182no—
891C23—182no—
892C23D3×#6714yes—
893C23C22×D3212yes—
894C23C22×D3211yescharacteristic
895Q8—68no—
896Q8—188no—
897D4—316no—
898D4—68no—
899D4—68no—
900D4—188no—
901D4—188no—
902D4—188no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—28no—
906C2×C4—34no—
907C2×C4—34no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—68no—
915C2×C4—68no—
916C2×C4—68no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—68no—
922C2×C4—92no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—188no—
926C2×C4—188no—
927C2×C4—188no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4C22×D3212yes—
932C2×C4C22×D3212yes—
933C2×C3—24no—
934C2×C3—24no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—24no—
938C2×C3—21no—
939C2×C3—44no—
940C2×C3—64no—
941C2×C3—122no—
942C2×C3#550714yescomplemented
943C2×C3#582414yescomplemented
944C2×C3C22×#23511yescharacteristic
945C2×C3C22×D3×D411yescharacteristic
946C2×C3C2×#100711yescharacteristic
947C2×C3C2×D3×#4111yescharacteristic
948C2×C3C2×#101011yescharacteristic
949C2×C3C23×#6711yescharacteristic
950D3—24no—
951D3—42no—
952D3—122no—
953D3—122no—
954D3—242no—
955C22—22no—
956C22—22no—
957C22—28no—
958C22—34no—
959C22—62no—
960C22—62no—
961C22—68no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—124no—
966C22—182no—
967C22—182no—
968C22—182no—
969C22—364no—
970C22#6429712yes—
971C22D3×#23512yes—
972C22C2×D3×#6714yes—
973C22C2×D3×#6712yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—22no—
977C4—34no—
978C4—34no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—182no—
984C4—182no—
985C4—182no—
986C3—21no—
987C3C2×#550711yescharacteristic, complemented
988C3C2×#582411yescharacteristic, complemented
989C2—24no—
990C2—64no—
991C2—122no—
992C2—362no—
993C2#1059488514yesdirect product factor
994C2C2×#6429711yescharacteristic
995C2C2×D3×#23511yescharacteristic
996C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#547
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×#3804C2semidirect
3. C2×#64138C2semidirect
4. C22×C3×Dic3⋊C4C2semidirect
5. C2×#63978C2semidirect
6. C2×Dic3×#67C2semidirect
7. C2×#63961C2semidirect
8. C2×#63904C2semidirect
9. C2×#63888C2semidirect
10. C2×#63886C2semidirect
11. #10594885C2direct (N × H)
12. C2×#63884C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63851C2semidirect
15. C2×#63850C2semidirect
16. C2×#63839C2semidirect
26. C2×C3×#235C22semidirect
36. C2×#3804C22semidirect
40. #64138C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. #63978C22semidirect
51. Dic3×#67C22semidirect
57. #63961C22semidirect
63. #63904C22semidirect
64. #63888C22semidirect
65. #63886C22semidirect
66. #63884C22semidirect
67. D3×Dic3⋊C4C22semidirect
68. #63851C22semidirect
69. #63850C22semidirect
70. #63839C22semidirect
74. C22×#235D3semidirect
94. C22×Dic3⋊C4D3semidirect
118. C2×C3×#67D4semidirect
202. C2×#235C2×D3semidirect
274. C2×Dic3⋊C4C2×D3semidirect
315. C3×#67C2×D4semidirect
323. C2×C3×Dic3#41semidirect
412. C2×#67#67semidirect
538. C3×Dic3C2×#41semidirect
675. #67C2×#67semidirect
702. C2×Dic3#235semidirect
723. C2×C32#547semidirect
875. Dic3C2×#235semidirect
877. C32C2×#547semidirect
942. C2×C3#5507semidirect
943. C2×C3#5824semidirect
987. C3C2×#5507semidirect
988. C3C2×#5824semidirect
993. C2#10594885direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×#38042
C2×#641382
C22×C3×Dic3⋊C42
C2×#639782
C2×Dic3×#672
C2×#639612
C2×#639042
C2×#638882
C2×#638862
#105948852
C2×#638842
C2×D3×Dic3⋊C42
C2×#638512
C2×#638502
C2×#638392
C2×#58243
C2×#55073