Finite Group Databasebeta

← C2×#10594254 #11900015

Subgroups — C2×#10594254 #11900015

Order 1152.

4053 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic
2C2×#64090C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×C4×#625C211yesmaximal, characteristic, complemented
13C2×#63879C211yesmaximal, characteristic, complemented
14C2×#63878C211yesmaximal, characteristic, complemented
15C2×#63877C211yesmaximal, characteristic, complemented
16#10594254C2116yesmaximal, direct product factor
17C2×#5545—31nomaximal
18C2×#5486—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×D3×#67C4116yescomplemented
30C2×D3×#67C2218yes—
31C22×#626C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#624C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic, complemented
36C2×C32×C22⋊C4C2211yescharacteristic, complemented
37C2×#3752C2211yescharacteristic, complemented
38C2×#3750C2211yescharacteristic, complemented
39C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
40#64090C2218yescomplemented
41C2×C3×#217C2211yescharacteristic, complemented
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#67⋊C4C2218yescomplemented
48C3×D3×C22⋊C4C2218yescomplemented
49#67⋊Dic3C2218yescomplemented
50C2×#3724C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2218yescomplemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×Dic32C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63952C2218yescomplemented
62#63921C2218yescomplemented
63D3×(C2×D3)⋊C4C2218yescomplemented
64#63904C2218yescomplemented
65C4×#626C2218yescomplemented
66C4×#625C2218yescomplemented
67#63879C2218yescomplemented
68#63878C2218yescomplemented
69#63877C2218yescomplemented
70C23×#67—31no—
71C22×D3×D4—31no—
72C2×C3×C4×D4—31no—
73C22×C3×C22⋊C4—31no—
74C22×#217—31no—
75C2×D4×Dic3—31no—
76C2×C4×#67—31no—
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×C4×#67—31no—
80C2×C4×#67—31no—
81C2×C4×#67—31no—
82C22×(C2×D3)⋊C4—31no—
83C22×(C2×D3)⋊C4—31no—
84#5545—316no—
85C2×#893—31no—
86C2×#892—31no—
87#5486—316no—
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×D3×C22⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4D311yescharacteristic, complemented
99C2×#877—31no—
100C2×#877—31no—
101C2×C4×D12—31no—
102C2×#872—31no—
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3C2×C418yescomplemented
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C22×D32—42no—
113C22×D32—42no—
114C22×D32C2×C418yescomplemented
115C22×D32C2314yes—
116C22×C32×C4C2311yescharacteristic
117C22×C32×C4C2311yescharacteristic
118C2×#638C2×C418yescomplemented
119C2×#638C2314yes—
120C22×C3⋊Dic3—42no—
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2314yescomplemented
125C2×C4×C3⋊D3—42no—
126C2×C4×C3⋊D3C2314yescomplemented
127C2×C3×#67C2×C418yescomplemented
128C2×C3×#67C2314yes—
129C22×C3×Dic3—42no—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2314yescomplemented
136C2×C3×C4×D3—42no—
137C2×C3×C4×D3—42no—
138C2×C3×C4×D3—42no—
139C2×C3×C4×D3C2314yescomplemented
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×C4×D3C2314yescomplemented
142D3×#67C2×C4164yescomplemented
143C2×#626C2×C418yescomplemented
144C2×#626C2314yes—
145C2×#625C2×C418yescomplemented
146C2×#625C2314yes—
147C2×#624—42no—
148C2×#624C2314yescomplemented
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2×C418yescomplemented
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yescomplemented
153C32×C22⋊C4C2314yescomplemented
154#3752C2314yescomplemented
155#3750C2314yescomplemented
156C4×C3⋊Dic3C2314yescomplemented
157C3×#217C2314yescomplemented
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162C3×C4×Dic3C2314yescomplemented
163#3724C2314yescomplemented
164Dic3⋊Dic3C2314yescomplemented
165#3722C2314yescomplemented
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
169(C2×D3)⋊Dic3C2314yescomplemented
170(C2×D3)⋊Dic3C2314yescomplemented
171Dic32C2314yescomplemented
172Dic32C2314yescomplemented
173C2×#518—91noSylow
174C25×C3—31no—
175C24×D3—31no—
176C24×D3—31no—
177C24×D3C2×D311yescharacteristic
178C22×C3×D4—31no—
179C23×C3×C4—31no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C23×C3×C4—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—316no—
188C22×#67—38no—
189C22×#67—31no—
190C22×#67—61no—
191C22×#67C2×D311yescharacteristic
192C23×Dic3—31no—
193C23×Dic3—31no—
194C23×Dic3—31no—
195C23×Dic3—31no—
196C23×Dic3—61no—
197C23×Dic3C2×D311yescharacteristic, complemented
198C2×D3×D4—316no—
199C2×D3×D4—38no—
200C22×D12—31no—
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3—61no—
208C22×C4×D3C2×D311yescharacteristic, complemented
209C22×C4×D3C2×D311yescharacteristic, complemented
210C22×C4×D3C2×D311yescharacteristic, complemented
211C3×C4×D4—38no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C22⋊C4—21no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4—31no—
218C2×C3×C22⋊C4—38no—
219C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
220C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
221C2×C3×C42—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—31no—
226C2×#217—31no—
227C2×#217—38no—
228C2×#217C2×D311yescharacteristic, complemented
229D4×Dic3—38no—
230C4×#67—38no—
231C4×#67—38no—
232C4×#67—38no—
233C4×#67—38no—
234C4×#67—38no—
235C4×#67—38no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—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—38no—
247C2×(C2×D3)⋊C4—61no—
248C2×(C2×D3)⋊C4C2×D311yescharacteristic
249C2×(C2×D3)⋊C4C2×D311yescharacteristic
250C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
251C2×C4⋊Dic3—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—61no—
258C2×Dic3⋊C4C2×D311yescharacteristic, complemented
259C2×C4×Dic3—31no—
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262C2×C4×Dic3—31no—
263C2×C4×Dic3—31no—
264C2×C4×Dic3—31no—
265C2×C4×Dic3—61no—
266C2×C4×Dic3C2×D311yescharacteristic, complemented
267#893—38no—
268#892—38no—
269#67⋊C4—38no—
270#67⋊C4—38no—
271#67⋊C4—38no—
272#67⋊C4—38no—
273#67⋊C4—38no—
274#67⋊C4—68no—
275#67⋊C4C2×D318yescomplemented
276D3×C22⋊C4—38no—
277D3×C22⋊C4—38no—
278D3×C22⋊C4—38no—
279D3×C22⋊C4C2×D318yescomplemented
280#877—38no—
281#877—38no—
282C4×D12—38no—
283#872—38no—
284C23×C32—22no—
285C23×C32—22no—
286C23×C32C22×C414yes—
287C23×C32C2412yes—
288C23×C32C2411yescharacteristic
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3C22×C414yes—
292C22×C3⋊D3C2412yes—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—416no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3C22×C414yes—
303C22×C3×D3C22×C414yes—
304C22×C3×D3C22×C414yes—
305C22×C3×D3C22×C4116yescomplemented
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×D32—416no—
310C2×D32—44no—
311C2×D32—44no—
312C2×D32C22×C4116yescomplemented
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316C2×C32×C4C2412yes—
317#638C22×C4116yescomplemented
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—44no—
321C2×C3⋊Dic3C22×C414yes—
322C2×C3⋊Dic3C2412yes—
323C2×C3⋊Dic3C2412yes—
324C2×C3⋊Dic3C2412yes—
325C4×C3⋊D3—44no—
326C3×#67C22×C4116yescomplemented
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—44no—
332C2×C3×Dic3C22×C414yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C3×C4×D3—44no—
339C3×C4×D3—44no—
340C3×C4×D3—44no—
341#626C22×C4116yescomplemented
342#625C22×C4116yescomplemented
343#624—44no—
344D3×Dic3—44no—
345D3×Dic3C22×C4116yescomplemented
346C23×D4—91no—
347#518—916no—
348C2×C4×D4—31no—
349C2×C4×D4—91no—
350C2×C4×D4—91no—
351C2×C4×D4—91no—
352C2×C4×D4—91no—
353C2×C4×D4—91no—
354C2×C4×D4—91no—
355C2×C4×D4—91no—
356C2×#117—91no—
357C2×#117—91no—
358C22×C22⋊C4—31no—
359C22×C22⋊C4—91no—
360C22×C22⋊C4—91no—
361C22×C22⋊C4—91no—
362C24×C3—21no—
363C24×C3—31no—
364C24×C3—31no—
365C24×C3—31no—
366C24×C3—38no—
367C24×C3—34no—
368C24×C3—122no—
369C24×C3—122no—
370C24×C3C22×D311yescharacteristic
371C24×C3C22×D311yescharacteristic
372C23×D3—31no—
373C23×D3—31no—
374C23×D3—38no—
375C23×D3—38no—
376C23×D3—34no—
377C23×D3—34no—
378C23×D3—42no—
379C23×D3—42no—
380C23×D3—61no—
381C23×D3—122no—
382C23×D3—122no—
383C23×D3—122no—
384C23×D3—122no—
385C23×D3C4×D318yescomplemented
386C23×D3C22×D311yescharacteristic
387C23×D3C22×D311yescharacteristic
388C23×D3C22×D311yescharacteristic
389C23×D3C22×D314yes—
390C2×C3×D4—38no—
391C2×C3×D4—34no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C22×C3×C4—34no—
401C22×C3×C4—34no—
402C22×C3×C4—34no—
403C22×C3×C4—122no—
404C22×C3×C4—122no—
405C22×C3×C4—122no—
406C22×C3×C4—122no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C22×D311yescharacteristic
410C22×C3×C4C22×D311yescharacteristic
411C2×#67—38no—
412C2×#67—38no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—38no—
416C2×#67—38no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—364no—
420C2×#67—38no—
421C2×#67—34no—
422C2×#67—64no—
423C2×#67—68no—
424C2×#67C4×D318yescomplemented
425C2×#67C22×D314yes—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—38no—
429C22×Dic3—34no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—34no—
435C22×Dic3—34no—
436C22×Dic3—34no—
437C22×Dic3—42no—
438C22×Dic3—61no—
439C22×Dic3—61no—
440C22×Dic3—64no—
441C22×Dic3—61no—
442C22×Dic3—122no—
443C22×Dic3—122no—
444C22×Dic3—122no—
445C22×Dic3—124no—
446C22×Dic3C22×D311yescharacteristic
447C22×Dic3C22×D311yescharacteristic
448C22×Dic3C22×D311yescharacteristic
449C22×Dic3C22×D311yescharacteristic
450C22×Dic3C22×D311yescharacteristic
451C22×Dic3C22×D314yescomplemented
452D3×D4—364no—
453C2×D12—38no—
454C2×D12—34no—
455C2×C4×D3—38no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—34no—
462C2×C4×D3—42no—
463C2×C4×D3—42no—
464C2×C4×D3—42no—
465C2×C4×D3—64no—
466C2×C4×D3—122no—
467C2×C4×D3—122no—
468C2×C4×D3—122no—
469C2×C4×D3—122no—
470C2×C4×D3—124no—
471C2×C4×D3—122no—
472C2×C4×D3C22×D314yescomplemented
473C2×C4×D3C22×D314yescomplemented
474C2×C4×D3C22×D314yescomplemented
475C3×C4⋊C4—34no—
476C3×C22⋊C4—24no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—34no—
481C3×C22⋊C4C22×D314yescomplemented
482C3×C22⋊C4C22×D314yescomplemented
483C3×C42—34no—
484#217—34no—
485#217—34no—
486#217—34no—
487#217—34no—
488#217—34no—
489#217C22×D314yescomplemented
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—64no—
500(C2×D3)⋊C4C22×D314yes—
501(C2×D3)⋊C4C22×D314yes—
502(C2×D3)⋊C4C22×D314yescomplemented
503C4⋊Dic3—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—64no—
510Dic3⋊C4C22×D314yescomplemented
511C4×Dic3—34no—
512C4×Dic3—34no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—64no—
518C4×Dic3C22×D314yescomplemented
519C22×C32—28no—
520C22×C32—22no—
521C22×C32—22no—
522C22×C32C23×C414yes—
523C22×C32C23×C412yes—
524C22×C32H(5,𝔽2)12yes—
525C22×C32H(5,𝔽2)12yes—
526C22×C32C2511yescharacteristic
527C2×C3⋊D3—28no—
528C2×C3⋊D3—22no—
529C2×C3⋊D3—22no—
530C2×C3⋊D3C23×C414yes—
531C2×C3×D3—28no—
532C2×C3×D3—28no—
533C2×C3×D3—28no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—416no—
541C2×C3×D3C23×C414yes—
542C2×C3×D3C23×C414yes—
543C2×C3×D3C23×C414yes—
544D32—416no—
545C32×C4—22no—
546C32×C4—22no—
547C3⋊Dic3—22no—
548C3⋊Dic3—22no—
549C3⋊Dic3C23×C414yes—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3C23×C414yes—
555C25—31no—
556C25—91no—
557C22×D4—31no—
558C22×D4—91no—
559C22×D4—98no—
560C22×D4—916no—
561C22×D4—91no—
562C22×D4—91no—
563C23×C4—31no—
564C23×C4—31no—
565C23×C4—31no—
566C23×C4—31no—
567C23×C4—91no—
568C23×C4—91no—
569C23×C4—91no—
570C23×C4—91no—
571C23×C4—91no—
572C4×D4—38no—
573C4×D4—98no—
574C4×D4—98no—
575C4×D4—98no—
576C4×D4—98no—
577C4×D4—98no—
578C4×D4—98no—
579C4×D4—98no—
580#117—98no—
581#117—98no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—91no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4—91no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—38no—
591C2×C22⋊C4—98no—
592C2×C22⋊C4—98no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C22⋊C4—91no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4—98no—
600C2×C22⋊C4—91no—
601C2×C22⋊C4D3211yescharacteristic, complemented
602C2×C42—31no—
603C2×C42—91no—
604C2×C42—91no—
605C2×C42—91no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—21no—
612C23×C3—24no—
613C23×C3—34no—
614C23×C3—34no—
615C23×C3—34no—
616C23×C3—32no—
617C23×C3—32no—
618C23×C3—32no—
619C23×C3—316no—
620C23×C3—42no—
621C23×C3—42no—
622C23×C3—62no—
623C23×C3—62no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—124no—
629C23×C3—124no—
630C23×C3—1216no—
631C23×C3C2×C4×D314yes—
632C23×C3C2×C4×D314yes—
633C23×C3C23×D312yes—
634C23×C3C23×D312yes—
635C23×C3C23×D311yescharacteristic
636C23×C3C23×D311yescharacteristic
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—34no—
644C22×D3—34no—
645C22×D3—32no—
646C22×D3—32no—
647C22×D3—316no—
648C22×D3—316no—
649C22×D3—416no—
650C22×D3—44no—
651C22×D3—44no—
652C22×D3—64no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—1216no—
665C22×D3—1216no—
666C22×D3C2×C4×D314yes—
667C22×D3C2×C4×D314yes—
668C22×D3C2×C4×D314yes—
669C22×D3C2×C4×D3116yescomplemented
670C22×D3C23×D312yes—
671C22×D3C23×D312yes—
672C22×D3C23×D312yes—
673C3×D4—316no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—34no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—42no—
687C2×C3×C4—42no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—124no—
693C2×C3×C4—124no—
694C2×C3×C4—124no—
695C2×C3×C4—124no—
696C2×C3×C4C23×D312yes—
697C2×C3×C4C23×D312yes—
698C2×C3×C4C23×D312yes—
699C2×C3×C4C23×D312yes—
700#67—316no—
701#67—316no—
702#67—316no—
703#67—316no—
704#67—316no—
705#67—616no—
706#67C2×C4×D3116yescomplemented
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—34no—
712C2×Dic3—34no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—316no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—44no—
721C2×Dic3—64no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—64no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—122no—
731C2×Dic3—124no—
732C2×Dic3—124no—
733C2×Dic3—124no—
734C2×Dic3—128no—
735C2×Dic3C2×C4×D314yes—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741D12—316no—
742C4×D3—316no—
743C4×D3—44no—
744C4×D3—44no—
745C4×D3—44no—
746C4×D3—124no—
747C4×D3—124no—
748C4×D3—124no—
749C4×D3—124no—
750C4×D3—128no—
751C4×D3—124no—
752C2×C32—24no—
753C2×C32#51814yescomplemented
754C2×C32C24×C411yescharacteristic
755C2×C32C2×H(5,𝔽2)11yescharacteristic
756C2×C32C2×H(5,𝔽2)11yescharacteristic
757C3⋊D3—24no—
758C3×D3—24no—
759C3×D3—24no—
760C3×D3—24no—
761C24—31no—
762C24—31no—
763C24—31no—
764C24—34no—
765C24—38no—
766C24—94no—
767C24—98no—
768C24—91no—
769C24—122no—
770C24—122no—
771C24—362no—
772C24—362no—
773C24C2×D3211yescharacteristic
774C2×D4—34no—
775C2×D4—38no—
776C2×D4—94no—
777C2×D4—98no—
778C2×D4—964no—
779C2×D4—94no—
780C2×D4—98no—
781C2×D4—94no—
782C2×D4—98no—
783C22×C4—31no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—34no—
789C22×C4—34no—
790C22×C4—34no—
791C22×C4—34no—
792C22×C4—94no—
793C22×C4—94no—
794C22×C4—98no—
795C22×C4—94no—
796C22×C4—91no—
797C22×C4—91no—
798C22×C4—91no—
799C22×C4—94no—
800C22×C4—94no—
801C22×C4—122no—
802C22×C4—122no—
803C22×C4—122no—
804C22×C4—122no—
805C22×C4—362no—
806C22×C4—362no—
807C22×C4—362no—
808C22×C4—362no—
809C22×C4C2×D3211yescharacteristic
810C22×C4C2×D3211yescharacteristic
811C4⋊C4—34no—
812C4⋊C4—94no—
813C4⋊C4—94no—
814C4⋊C4—94no—
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—34no—
818C22⋊C4—34no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4C2×D3214yescomplemented
827C42—34no—
828C42—94no—
829C42—94no—
830C42—94no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—28no—
836C22×C3—28no—
837C22×C3—22no—
838C22×C3—24no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—34no—
843C22×C3—34no—
844C22×C3—34no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—48no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—68no—
855C22×C3—68no—
856C22×C3—68no—
857C22×C3—1216no—
858C22×C3C22×C4×D314yes—
859C22×C3C22×C4×D314yes—
860C22×C3C22×C4×D312yes—
861C22×C3C22×C4×D312yes—
862C22×C3#100412yes—
863C22×C3#100412yes—
864C22×C3#100412yes—
865C22×C3#100912yes—
866C22×C3C24×D311yescharacteristic
867C22×C3C24×D311yescharacteristic
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—28no—
875C2×D3—28no—
876C2×D3—28no—
877C2×D3—34no—
878C2×D3—34no—
879C2×D3—416no—
880C2×D3—64no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—68no—
886C2×D3—68no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—128no—
890C2×D3—1216no—
891C2×D3—1216no—
892C2×D3C22×C4×D314yes—
893C2×D3C22×C4×D314yes—
894C2×D3C22×C4×D314yes—
895C3×C4—22no—
896C3×C4—22no—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—34no—
900C3×C4—42no—
901C3×C4—42no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906Dic3—22no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—34no—
911Dic3—34no—
912Dic3—64no—
913Dic3—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—122no—
919Dic3C22×C4×D314yes—
920C32C2×#51811yescharacteristic, complemented, Sylow
921C23—22no—
922C23—22no—
923C23—34no—
924C23—34no—
925C23—34no—
926C23—32no—
927C23—32no—
928C23—32no—
929C23—316no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—916no—
937C23—94no—
938C23—92no—
939C23—124no—
940C23—124no—
941C23—1216no—
942C23—182no—
943C23—182no—
944C23—364no—
945C23—364no—
946C23—3616no—
947C23C4×D3214yes—
948C23C22×D3212yes—
949C23C22×D3211yescharacteristic
950D4—316no—
951D4—916no—
952D4—916no—
953D4—916no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—916no—
967C2×C4—94no—
968C2×C4—92no—
969C2×C4—92no—
970C2×C4—92no—
971C2×C4—124no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—124no—
975C2×C4—182no—
976C2×C4—182no—
977C2×C4—364no—
978C2×C4—364no—
979C2×C4—364no—
980C2×C4—364no—
981C2×C4C22×D3212yes—
982C2×C4C22×D3212yes—
983C2×C3—24no—
984C2×C3—24no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—44no—
990C2×C3—64no—
991C2×C3—64no—
992C2×C3—64no—
993C2×C3#548614yescomplemented
994C2×C3#554514yescomplemented
995C2×C3C23×C4×D311yescharacteristic
996C2×C3C23×C4×D311yescharacteristic
997C2×C3C2×#100411yescharacteristic
998C2×C3C2×#100411yescharacteristic
999C2×C3C2×#100411yescharacteristic
1000C2×C3C2×#100911yescharacteristic
1001D3—24no—
1002D3—24no—
1003D3—24no—
1004D3—64no—
1005D3—64no—
1006D3—124no—
1007C22—22no—
1008C22—22no—
1009C22—28no—
1010C22—34no—
1011C22—34no—
1012C22—34no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—68no—
1020C22—68no—
1021C22—68no—
1022C22—94no—
1023C22—1216no—
1024C22—182no—
1025C22—182no—
1026C22—188no—
1027C22—3616no—
1028C22C2×C4×D3214yes—
1029C22C2×C4×D3212yes—
1030C22#6431312yes—
1031C22#6431412yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—22no—
1035C4—34no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—62no—
1040C4—94no—
1041C4—182no—
1042C4—182no—
1043C3—21no—
1044C3C2×#548611yescharacteristic, complemented
1045C3C2×#554511yescharacteristic, complemented
1046C2—24no—
1047C2—64no—
1048C2—64no—
1049C2—64no—
1050C2—184no—
1051C2#1059425414yesdirect product factor
1052C2C22×C4×D3211yescharacteristic
1053C2C2×#6431311yescharacteristic
1054C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutatorC2×C32C24×C4
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×D3×#67C2
cosocleC22×C32C25
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#518
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×D3×C22⋊C4C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C22×(C2×D3)⋊Dic3C2semidirect
7. C2×#63952C2semidirect
8. C2×#63921C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63904C2semidirect
11. C2×C4×#626C2semidirect
12. C2×C4×#625C2semidirect
13. C2×#63879C2semidirect
14. C2×#63878C2semidirect
15. C2×#63877C2semidirect
16. #10594254C2direct (N × H)
22. C23×C3⋊Dic3C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C23×C3×Dic3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
29. C2×D3×#67C4semidirect
33. C22×#624C22semidirect
35. C22×D3×Dic3C22semidirect
36. C2×C32×C22⋊C4C22semidirect
37. C2×#3752C22semidirect
38. C2×#3750C22semidirect
39. C2×C4×C3⋊Dic3C22semidirect
40. #64090C22semidirect
41. C2×C3×#217C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#67⋊C4C22semidirect
48. C3×D3×C22⋊C4C22semidirect
49. #67⋊Dic3C22semidirect
50. C2×#3724C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×#3722C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×Dic32C22semidirect
60. C2×Dic32C22semidirect
61. #63952C22semidirect
62. #63921C22semidirect
63. D3×(C2×D3)⋊C4C22semidirect
64. #63904C22semidirect
65. C4×#626C22semidirect
66. C4×#625C22semidirect
67. #63879C22semidirect
68. #63878C22semidirect
69. #63877C22semidirect
94. C2×#67⋊C4D3semidirect
98. C2×D3×C22⋊C4D3semidirect
107. C23×C3×D3C2×C4semidirect
114. C22×D32C2×C4semidirect
118. C2×#638C2×C4semidirect
124. C22×C3⋊Dic3C23semidirect
126. C2×C4×C3⋊D3C23semidirect
127. C2×C3×#67C2×C4semidirect
135. C22×C3×Dic3C23semidirect
139. C2×C3×C4×D3C23semidirect
140. C2×C3×C4×D3C23semidirect
141. C2×C3×C4×D3C23semidirect
142. D3×#67C2×C4semidirect
143. C2×#626C2×C4semidirect
145. C2×#625C2×C4semidirect
148. C2×#624C23semidirect
150. C2×D3×Dic3C2×C4semidirect
152. C2×D3×Dic3C23semidirect
153. C32×C22⋊C4C23semidirect
154. #3752C23semidirect
155. #3750C23semidirect
156. C4×C3⋊Dic3C23semidirect
157. C3×#217C23semidirect
160. C3×(C2×D3)⋊C4C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. C3×C4×Dic3C23semidirect
163. #3724C23semidirect
164. Dic3⋊Dic3C23semidirect
165. #3722C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
170. (C2×D3)⋊Dic3C23semidirect
171. Dic32C23semidirect
172. Dic32C23semidirect
197. C23×Dic3C2×D3semidirect
208. C22×C4×D3C2×D3semidirect
209. C22×C4×D3C2×D3semidirect
210. C22×C4×D3C2×D3semidirect
219. C2×C3×C22⋊C4C2×D3semidirect
220. C2×C3×C22⋊C4C2×D3semidirect
228. C2×#217C2×D3semidirect
250. C2×(C2×D3)⋊C4C2×D3semidirect
258. C2×Dic3⋊C4C2×D3semidirect
266. C2×C4×Dic3C2×D3semidirect
275. #67⋊C4C2×D3semidirect
279. D3×C22⋊C4C2×D3semidirect
305. C22×C3×D3C22×C4semidirect
312. C2×D32C22×C4semidirect
317. #638C22×C4semidirect
326. C3×#67C22×C4semidirect
341. #626C22×C4semidirect
342. #625C22×C4semidirect
345. D3×Dic3C22×C4semidirect
385. C23×D3C4×D3semidirect
424. C2×#67C4×D3semidirect
451. C22×Dic3C22×D3semidirect
472. C2×C4×D3C22×D3semidirect
473. C2×C4×D3C22×D3semidirect
474. C2×C4×D3C22×D3semidirect
481. C3×C22⋊C4C22×D3semidirect
482. C3×C22⋊C4C22×D3semidirect
489. #217C22×D3semidirect
502. (C2×D3)⋊C4C22×D3semidirect
510. Dic3⋊C4C22×D3semidirect
518. C4×Dic3C22×D3semidirect
601. C2×C22⋊C4D32semidirect
669. C22×D3C2×C4×D3semidirect
706. #67C2×C4×D3semidirect
753. C2×C32#518semidirect
826. C22⋊C4C2×D32semidirect
920. C32C2×#518semidirect
993. C2×C3#5486semidirect
994. C2×C3#5545semidirect
1044. C3C2×#5486semidirect
1045. C3C2×#5545semidirect
1051. C2#10594254direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C2×#640902
C2×C3×#67⋊C42
C2×C3×D3×C22⋊C42
C2×#67⋊Dic32
C22×(C2×D3)⋊Dic32
C2×#639522
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#639042
C2×C4×#6262
C2×C4×#6252
C2×#638792
C2×#638782
C2×#638772
#105942542
C2×#55453
C2×#54863