Finite Group Databasebeta

← C2×#10595130 #11900443

Subgroups — C2×#10595130 #11900443

Order 1152.

3973 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×#3805C211yesmaximal, characteristic, complemented
2C23×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#939C211yesmaximal, characteristic, complemented
5C2×C3×#937C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
9C2×#63970C211yesmaximal, characteristic, complemented
10C2×#63969C211yesmaximal, characteristic, complemented
11C2×#63964C211yesmaximal, characteristic, complemented
12#10595130C2116yesmaximal, direct product factor
13C2×#63902C211yesmaximal, characteristic, complemented
14C2×#63893C211yesmaximal, characteristic, complemented
15C2×#63891C211yesmaximal, characteristic, complemented
16C2×#63878C211yesmaximal, characteristic, complemented
17C2×#5606—31nomaximal
18C2×#5586—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic
28C22×#627C2211yescharacteristic, complemented
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C2×#3805—28no—
32C2×#3805C2218yescomplemented
33C22×D3×Dic3—28no—
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C2×#3757C2211yescharacteristic
41C2×#3757C2211yescharacteristic, complemented
42D4×C3⋊Dic3C2218yescomplemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#939C2218yescomplemented
48C3×#937C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53#63976C2218yescomplemented
54#67⋊Dic3C2218yescomplemented
55#67⋊Dic3C2218yescomplemented
56#63970C2218yescomplemented
57#63969C2218yescomplemented
58C2×#3724C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61C2×Dic3⋊Dic3C2211yescharacteristic, complemented
62#63964C2218yescomplemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64C2×(C2×D3)⋊Dic3C2211yescharacteristic
65C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
66C2×Dic32C2211yescharacteristic, complemented
67#63902C2218yescomplemented
68#63893C2218yescomplemented
69#63891C2218yescomplemented
70#63878C2218yescomplemented
71C24×Dic3—31no—
72C22×#237—31no—
73C22×#237—31no—
74C23×C4×D3—31no—
75C2×C3×#121—31no—
76C2×C3×#120—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#939D311yescharacteristic, complemented
80C2×#938—31no—
81C2×#937—31no—
82C2×#937D311yescharacteristic, complemented
83C2×#935—31no—
84C2×D4×Dic3—31no—
85C2×D4×Dic3—31no—
86C2×D4×Dic3—31no—
87C2×D4×Dic3—31no—
88C2×D4×Dic3—61no—
89C2×#924—31no—
90#5606—316no—
91#5586—316no—
92C2×#897—31no—
93C2×#892—31no—
94C2×#886—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#67⋊C4—31no—
98C2×#67⋊C4—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×#878—31no—
102C2×#878—31no—
103C2×#877—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C2×C32×D4—24no—
114C2×C32×D4C2314yes—
115C22×C32×C4C2311yescharacteristic
116C22×C3⋊Dic3—24no—
117C22×C3⋊Dic3—24no—
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2314yes—
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2314yescomplemented
124C2×C3×#67—24no—
125C2×C3×#67—24no—
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yescomplemented
132C22×C3×Dic3—24no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2314yes—
138C22×C3×Dic3C2311yescharacteristic
139C2×#627—24no—
140C2×#627C2314yescomplemented
141C2×#625—24no—
142C2×#625—24no—
143C2×#625C2314yes—
144C2×#625C2314yes—
145#3805—232no—
146C2×D3×Dic3—24no—
147C2×D3×Dic3—24no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—24no—
150C2×D3×Dic3—232no—
151C2×D3×Dic3D418yescomplemented
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yescomplemented
157#3757C2314yes—
158#3757C2314yescomplemented
159C4⋊(C3⋊Dic3)C2314yescomplemented
160C4×C3⋊Dic3C2314yescomplemented
161C3×#217C2314yes—
162C3×#217C2314yescomplemented
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167#3724C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174Dic32C2314yescomplemented
175C2×#525—91noSylow
176C25×C3—31no—
177C24×D3C2×D311yescharacteristic
178C22×C3×D4—21no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4C2×D311yescharacteristic
184C22×C3×D4C2×D311yescharacteristic
185C23×C3×C4—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67C2×D311yescharacteristic
191C22×#67C2×D311yescharacteristic
192C22×#67C2×D311yescharacteristic
193C22×#67C2×D311yescharacteristic, complemented
194C23×Dic3—31no—
195C23×Dic3—31no—
196C23×Dic3—31no—
197C23×Dic3—31no—
198C23×Dic3—31no—
199C23×Dic3—31no—
200C23×Dic3—31no—
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—38no—
204C23×Dic3—61no—
205C23×Dic3—61no—
206C23×Dic3—68no—
207C23×Dic3C2×D311yescharacteristic
208C2×#237—38no—
209C2×#237—38no—
210C2×#237—68no—
211C2×#237—68no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—38no—
217C22×C4×D3—31no—
218C22×C4×D3—68no—
219C22×Dic6—31no—
220C22×Dic6—31no—
221C3×#121—38no—
222C3×#120—38no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229#953—38no—
230C2×#217—31no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—61no—
238C2×#217—61no—
239C2×#217C2×D311yescharacteristic
240C2×#217C2×D311yescharacteristic, complemented
241#939—38no—
242#939C2×D318yescomplemented
243#938—38no—
244#937—38no—
245#937C2×D318yescomplemented
246#935—38no—
247D4×Dic3—38no—
248D4×Dic3—38no—
249D4×Dic3—38no—
250D4×Dic3—38no—
251D4×Dic3—68no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4C2×D311yescharacteristic
256C2×(C2×D3)⋊C4C2×D311yescharacteristic
257C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
258C2×C4⋊Dic3—31no—
259C2×C4⋊Dic3—31no—
260C2×C4⋊Dic3—31no—
261C2×C4⋊Dic3—31no—
262C2×C4⋊Dic3—31no—
263C2×C4⋊Dic3—61no—
264#924—38no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×C4×Dic3—31no—
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—61no—
276#897—38no—
277#892—38no—
278#886—38no—
279#883—38no—
280#883—38no—
281#67⋊C4—38no—
282#67⋊C4—38no—
283#67⋊C4—38no—
284#67⋊C4—38no—
285#878—38no—
286#878—38no—
287#877—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2412yes—
296C23×C32C2411yescharacteristic
297C22×C3×D3—232no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—28no—
303C22×C3×D3—28no—
304C22×C3×D3—28no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3C2×D414yes—
309C22×C3×D3#4114yescomplemented
310C22×C3×D3C2412yes—
311C22×C3×D3C2412yes—
312C22×C3×D3C2412yes—
313C32×D4—28no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316C2×C3⋊Dic3—22no—
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—28no—
320C2×C3⋊Dic3—28no—
321C2×C3⋊Dic3C2×D414yes—
322C2×C3⋊Dic3C2412yes—
323C2×C3⋊Dic3C2412yes—
324C2×C3⋊Dic3C2412yes—
325C2×C3⋊Dic3C2412yes—
326C3×#67—28no—
327C3×#67—28no—
328C3×#67—28no—
329C3×#67—28no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—22no—
333C2×C3×Dic3—22no—
334C2×C3×Dic3—28no—
335C2×C3×Dic3C2×D414yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2412yes—
341#627—28no—
342#625—28no—
343#625—28no—
344D3×Dic3—28no—
345D3×Dic3—28no—
346D3×Dic3—28no—
347D3×Dic3—28no—
348D3×Dic3C2×D4116yescomplemented
349C22×#41—91no—
350C24×C4—91no—
351#525—916no—
352C2×#123—91no—
353C2×#123—91no—
354C2×C22⋊Q8—91no—
355C2×C22⋊Q8—91no—
356C2×#121—31no—
357C2×#121—91no—
358C2×#120—31no—
359C2×#120—91no—
360C2×C4×D4—91no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C2×C4×D4—91no—
364C2×#117—91no—
365C24×C3—21no—
366C24×C3—21no—
367C24×C3—31no—
368C24×C3—31no—
369C24×C3—34no—
370C24×C3—31no—
371C24×C3—64no—
372C24×C3—64no—
373C24×C3—64no—
374C24×C3C22×D311yescharacteristic
375C24×C3C22×D311yescharacteristic
376C24×C3C22×D311yescharacteristic
377C24×C3C22×D311yescharacteristic
378C23×D3—24no—
379C23×D3—24no—
380C23×D3—24no—
381C23×D3C22×D311yescharacteristic
382C23×D3C22×D314yes—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C2×C3×D4—28no—
386C2×C3×D4—24no—
387C2×C3×D4—24no—
388C2×C3×D4—24no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—34no—
392C2×C3×D4—34no—
393C2×C3×D4—64no—
394C2×C3×D4—64no—
395C2×C3×D4—64no—
396C2×C3×D4—64no—
397C2×C3×D4C22×D314yes—
398C2×C3×D4C22×D314yes—
399C22×C3×C4—21no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—31no—
405C22×C3×C4—34no—
406C22×C3×C4—64no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—24no—
410C2×#67—24no—
411C2×#67—24no—
412C2×#67—24no—
413C2×#67—34no—
414C2×#67—34no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67C22×D314yes—
422C2×#67C22×D314yes—
423C2×#67C22×D314yes—
424C2×#67C22×D314yescomplemented
425C22×Dic3—24no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—38no—
429C22×Dic3—34no—
430C22×Dic3—34no—
431C22×Dic3—34no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—31no—
436C22×Dic3—31no—
437C22×Dic3—31no—
438C22×Dic3—34no—
439C22×Dic3—34no—
440C22×Dic3—34no—
441C22×Dic3—34no—
442C22×Dic3—34no—
443C22×Dic3—34no—
444C22×Dic3—61no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—61no—
448C22×Dic3—64no—
449C22×Dic3—64no—
450C22×Dic3—64no—
451C22×Dic3—64no—
452C22×Dic3—632no—
453C22×Dic3—64no—
454C22×Dic3—64no—
455C22×Dic3—64no—
456C22×Dic3—64no—
457C22×Dic3—64no—
458C22×Dic3—64no—
459C22×Dic3—124no—
460C22×Dic3—124no—
461C22×Dic3C22×D314yes—
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D311yescharacteristic
467#237—632no—
468#237—632no—
469C2×C4×D3—38no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—632no—
476C2×C4×D3—64no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—64no—
480C2×Dic6—34no—
481C2×Dic6—34no—
482C2×Dic6—64no—
483C2×Dic6—64no—
484C3×C4⋊C4—34no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4—34no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490#217—34no—
491#217—34no—
492#217—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—64no—
498#217—64no—
499#217C22×D314yes—
500#217C22×D314yescomplemented
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D314yes—
506(C2×D3)⋊C4C22×D314yescomplemented
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—34no—
510C4⋊Dic3—34no—
511C4⋊Dic3—34no—
512C4⋊Dic3—64no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4C22×D314yescomplemented
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—34no—
523C4×Dic3—64no—
524C22×C32—22no—
525C22×C32—28no—
526C22×C32—22no—
527C22×C32—22no—
528C22×C32—22no—
529C22×C32—22no—
530C22×C32—44no—
531C22×C32C22×D412yes—
532C22×C32C2×#4112yes—
533C22×C32C2×#4112yes—
534C22×C32C2×#4114yescomplemented
535C22×C32C2511yescharacteristic
536C2×C3×D3—232no—
537C2×C3×D3—28no—
538C2×C3×D3—28no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—44no—
547C2×C3×D3C22×D414yes—
548C2×C3×D3C2×#4114yescomplemented
549C32×C4—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3⋊Dic3C22×D414yes—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3C22×D414yes—
559C25—31no—
560C2×#41—98no—
561C2×#41—188no—
562C22×Q8—91no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4D3211yescharacteristic
570C23×C4—31no—
571C23×C4—91no—
572C23×C4—91no—
573C23×C4—91no—
574C23×C4—91no—
575C23×C4—91no—
576C23×C4—98no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4—188no—
580#123—98no—
581#123—98no—
582C22⋊Q8—98no—
583C22⋊Q8—98no—
584#121—38no—
585#121—98no—
586#120—38no—
587#120—98no—
588C4×D4—98no—
589C4×D4—98no—
590C4×D4—98no—
591C4×D4—98no—
592#117—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C42—91no—
610C2×C42—91no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—24no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—22no—
619C23×C3—22no—
620C23×C3—22no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—21no—
625C23×C3—24no—
626C23×C3—34no—
627C23×C3—34no—
628C23×C3—32no—
629C23×C3—32no—
630C23×C3—32no—
631C23×C3—42no—
632C23×C3—42no—
633C23×C3—42no—
634C23×C3—42no—
635C23×C3—68no—
636C23×C3—68no—
637C23×C3—632no—
638C23×C3—62no—
639C23×C3—62no—
640C23×C3—62no—
641C23×C3—68no—
642C23×C3—62no—
643C23×C3—62no—
644C23×C3—62no—
645C23×C3—62no—
646C23×C3#23714yescomplemented
647C23×C3#23714yescomplemented
648C23×C3C23×D312yes—
649C23×C3C23×D312yes—
650C23×C3C23×D312yes—
651C23×C3C23×D312yes—
652C23×C3C23×D311yescharacteristic
653C23×C3C23×D311yescharacteristic
654C22×D3—232no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—28no—
660C22×D3—28no—
661C22×D3—28no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3D3×D414yes—
666C22×D3#23714yescomplemented
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—216no—
671C3×D4—28no—
672C3×D4—28no—
673C3×D4—68no—
674C3×D4—68no—
675C3×D4—68no—
676C3×D4—68no—
677C2×C3×C4—24no—
678C2×C3×C4—22no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—34no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—68no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694#67—28no—
695#67—28no—
696#67—28no—
697#67—28no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—68no—
702C2×Dic3—22no—
703C2×Dic3—22no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—28no—
707C2×Dic3—34no—
708C2×Dic3—34no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—316no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—64no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—68no—
724C2×Dic3—68no—
725C2×Dic3—68no—
726C2×Dic3—68no—
727C2×Dic3—68no—
728C2×Dic3—68no—
729C2×Dic3—68no—
730C2×Dic3—62no—
731C2×Dic3—62no—
732C2×Dic3—62no—
733C2×Dic3—62no—
734C2×Dic3—62no—
735C2×Dic3—62no—
736C2×Dic3—68no—
737C2×Dic3—128no—
738C2×Dic3—128no—
739C2×Dic3—122no—
740C2×Dic3—122no—
741C2×Dic3—122no—
742C2×Dic3D3×D414yes—
743C2×Dic3C23×D312yes—
744C2×Dic3C23×D312yes—
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D312yes—
748C4×D3—316no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—68no—
753Dic6—68no—
754Dic6—68no—
755C2×C32—24no—
756C2×C32—42no—
757C2×C32#52514yescomplemented
758C2×C32C23×D411yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C2×C32C22×#4111yescharacteristic
761C3×D3—24no—
762C3×D3—24no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—34no—
767C24—31no—
768C24—64no—
769C24—64no—
770C24—64no—
771C24C2×D3211yescharacteristic
772C24C2×D3211yescharacteristic
773#41—1832no—
774C2×Q8—94no—
775C2×Q8—184no—
776C2×D4—24no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—34no—
780C2×D4—34no—
781C2×D4—64no—
782C2×D4—64no—
783C2×D4—64no—
784C2×D4—64no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—184no—
788C2×D4—184no—
789C2×D4C2×D3214yes—
790C22×C4—31no—
791C22×C4—34no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—64no—
797C22×C4—94no—
798C22×C4—98no—
799C22×C4—94no—
800C22×C4—94no—
801C22×C4—94no—
802C22×C4—94no—
803C22×C4—91no—
804C22×C4—94no—
805C22×C4—94no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—91no—
809C22×C4—184no—
810C22×C4—1832no—
811C22×C4—184no—
812C22×C4—184no—
813C22×C4—184no—
814C22×C4—184no—
815C22×C4—184no—
816C22×C4C2×D3211yescharacteristic
817C4⋊C4—34no—
818C4⋊C4—94no—
819C4⋊C4—94no—
820C4⋊C4—94no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—34no—
827C22⋊C4—34no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4—94no—
832C22⋊C4—94no—
833C42—94no—
834C42—94no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—28no—
840C22×C3—28no—
841C22×C3—24no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—22no—
847C22×C3—22no—
848C22×C3—22no—
849C22×C3—22no—
850C22×C3—22no—
851C22×C3—24no—
852C22×C3—21no—
853C22×C3—34no—
854C22×C3—34no—
855C22×C3—42no—
856C22×C3—42no—
857C22×C3—48no—
858C22×C3—42no—
859C22×C3—42no—
860C22×C3—48no—
861C22×C3—44no—
862C22×C3—44no—
863C22×C3—632no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3—68no—
869C22×C3—68no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—124no—
874C22×C3C2×D3×D412yes—
875C22×C3C2×D3×D412yes—
876C22×C3C2×#23712yes—
877C22×C3C2×#23712yes—
878C22×C3C2×#23712yes—
879C22×C3C2×#23714yescomplemented
880C22×C3C2×#23714yescomplemented
881C22×C3D3×#4112yes—
882C22×C3C24×D311yescharacteristic
883C22×C3C24×D311yescharacteristic
884C2×D3—232no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—28no—
890C2×D3—28no—
891C2×D3—22no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—44no—
895C2×D3C2×D3×D414yes—
896C2×D3C2×#23714yescomplemented
897C3×C4—24no—
898C3×C4—22no—
899C3×C4—22no—
900C3×C4—34no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905Dic3—22no—
906Dic3—22no—
907Dic3—22no—
908Dic3—22no—
909Dic3—34no—
910Dic3—34no—
911Dic3—64no—
912Dic3—62no—
913Dic3—62no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—122no—
919Dic3—122no—
920Dic3—122no—
921Dic3C2×D3×D414yes—
922C32C2×#52511yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—34no—
929C23—34no—
930C23—32no—
931C23—32no—
932C23—32no—
933C23—68no—
934C23—68no—
935C23—632no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—68no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23#380514yescomplemented
945C23C22×D3212yes—
946C23C22×D3212yes—
947C23C22×D3211yescharacteristic
948Q8—188no—
949D4—28no—
950D4—68no—
951D4—68no—
952D4—68no—
953D4—68no—
954D4—188no—
955D4—188no—
956C2×C4—22no—
957C2×C4—34no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—68no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—916no—
969C2×C4—94no—
970C2×C4—92no—
971C2×C4—92no—
972C2×C4—92no—
973C2×C4—92no—
974C2×C4—188no—
975C2×C4—188no—
976C2×C4—188no—
977C2×C4—188no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4—182no—
981C2×C4—182no—
982C2×C4—182no—
983C2×C4C22×D3212yes—
984C2×C3—24no—
985C2×C3—24no—
986C2×C3—24no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—44no—
991C2×C3—44no—
992C2×C3—42no—
993C2×C3—42no—
994C2×C3—64no—
995C2×C3—64no—
996C2×C3—122no—
997C2×C3#558614yescomplemented
998C2×C3#560614yescomplemented
999C2×C3C22×D3×D411yescharacteristic
1000C2×C3C22×D3×D411yescharacteristic
1001C2×C3C22×#23711yescharacteristic
1002C2×C3C22×#23711yescharacteristic
1003C2×C3C22×#23711yescharacteristic
1004C2×C3C2×D3×#4111yescharacteristic
1005D3—24no—
1006D3—24no—
1007D3—42no—
1008C22—28no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—22no—
1013C22—22no—
1014C22—34no—
1015C22—34no—
1016C22—44no—
1017C22—632no—
1018C22—68no—
1019C22—68no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—124no—
1028C22D32×D412yes—
1029C22D3×#23712yes—
1030C22C2×#380512yes—
1031C22C2×#380514yescomplemented
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—34no—
1035C4—62no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—94no—
1040C4—182no—
1041C4—182no—
1042C4—182no—
1043C3—21no—
1044C3C2×#558611yescharacteristic, complemented
1045C3C2×#560611yescharacteristic, complemented
1046C2—24no—
1047C2—42no—
1048C2—64no—
1049C2—64no—
1050C2—122no—
1051C2#1059513014yesdirect product factor
1052C2C2×D32×D411yescharacteristic
1053C2C2×D3×#23711yescharacteristic
1054C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3805C2semidirect
2. C23×D3×Dic3C2semidirect
3. C2×D4×C3⋊Dic3C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#937C2semidirect
6. C2×#63976C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×#67⋊Dic3C2semidirect
9. C2×#63970C2semidirect
10. C2×#63969C2semidirect
11. C2×#63964C2semidirect
12. #10595130C2direct (N × H)
13. C2×#63902C2semidirect
14. C2×#63893C2semidirect
15. C2×#63891C2semidirect
16. C2×#63878C2semidirect
22. C23×C3⋊Dic3C22semidirect
26. C22×C3×#67C22semidirect
28. C22×#627C22semidirect
32. C2×#3805C22semidirect
38. C22×D3×Dic3C22semidirect
39. C22×D3×Dic3C22semidirect
41. C2×#3757C22semidirect
42. D4×C3⋊Dic3C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C2×C4×C3⋊Dic3C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#939C22semidirect
48. C3×#937C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. #63976C22semidirect
54. #67⋊Dic3C22semidirect
55. #67⋊Dic3C22semidirect
56. #63970C22semidirect
57. #63969C22semidirect
58. C2×#3724C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
62. #63964C22semidirect
65. C2×(C2×D3)⋊Dic3C22semidirect
66. C2×Dic32C22semidirect
67. #63902C22semidirect
68. #63893C22semidirect
69. #63891C22semidirect
70. #63878C22semidirect
79. C2×#939D3semidirect
82. C2×#937D3semidirect
123. C22×C3⋊Dic3C23semidirect
131. C2×C3×#67C23semidirect
140. C2×#627C23semidirect
151. C2×D3×Dic3D4semidirect
156. C2×D3×Dic3C23semidirect
158. #3757C23semidirect
159. C4⋊(C3⋊Dic3)C23semidirect
160. C4×C3⋊Dic3C23semidirect
162. C3×#217C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. #3724C23semidirect
168. Dic3⋊Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. Dic32C23semidirect
193. C22×#67C2×D3semidirect
240. C2×#217C2×D3semidirect
242. #939C2×D3semidirect
245. #937C2×D3semidirect
257. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
293. C23×C32#41semidirect
309. C22×C3×D3#41semidirect
348. D3×Dic3C2×D4semidirect
424. C2×#67C22×D3semidirect
500. #217C22×D3semidirect
506. (C2×D3)⋊C4C22×D3semidirect
518. Dic3⋊C4C22×D3semidirect
534. C22×C32C2×#41semidirect
548. C2×C3×D3C2×#41semidirect
646. C23×C3#237semidirect
647. C23×C3#237semidirect
666. C22×D3#237semidirect
757. C2×C32#525semidirect
879. C22×C3C2×#237semidirect
880. C22×C3C2×#237semidirect
896. C2×D3C2×#237semidirect
922. C32C2×#525semidirect
944. C23#3805semidirect
997. C2×C3#5586semidirect
998. C2×C3#5606semidirect
1031. C22C2×#3805semidirect
1044. C3C2×#5586semidirect
1045. C3C2×#5606semidirect
1051. C2#10595130direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C23×D3×Dic32
C2×D4×C3⋊Dic32
C2×C3×#9392
C2×C3×#9372
C2×#639762
C2×#67⋊Dic32
C2×#639702
C2×#639692
C2×#639642
#105951302
C2×#639022
C2×#638932
C2×#638912
C2×#638782
C2×#56063
C2×#55863