Finite Group Databasebeta

← C2×#10594054 #11900449

Subgroups — C2×#10594054 #11900449

Order 1152.

3921 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64087C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C2×#63976C211yesmaximal, characteristic, complemented
8C2×Dic3×#67C211yesmaximal, characteristic, complemented
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×Dic3×D12C211yesmaximal, characteristic, complemented
11C2×#63891C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63884C211yesmaximal, characteristic, complemented
14C2×#63879C211yesmaximal, characteristic, complemented
15C2×#63877C211yesmaximal, characteristic, complemented
16#10594054C2116yesmaximal, direct product factor
17C2×#5586—31nomaximal
18C2×#5547—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3—28no—
32C22×D3×Dic3C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2218yescomplemented
37C22×D3×Dic3C2211yescharacteristic, complemented
38C2×#3795—28no—
39C2×#3795C2218yescomplemented
40C2×C32×C22⋊C4C2211yescharacteristic
41C2×#3757C2211yescharacteristic
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C2×#3750C2211yescharacteristic, complemented
44C2×#3750C2211yescharacteristic, complemented
45#64087C2218yescomplemented
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×C4×Dic3C2211yescharacteristic, complemented
51C3×#882C2218yescomplemented
52C3×#67⋊C4C2218yescomplemented
53#63980C2218yescomplemented
54#63976C2218yescomplemented
55Dic3×#67C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×Dic32C2211yescharacteristic, complemented
64#63896C2218yescomplemented
65Dic3×D12C2218yescomplemented
66#63891C2218yescomplemented
67#63885C2218yescomplemented
68#63884C2218yescomplemented
69#63879C2218yescomplemented
70#63877C2218yescomplemented
71C24×Dic3—31no—
72C22×#237—31no—
73C22×#235—31no—
74C23×C4×D3—31no—
75C2×C3×#120—31no—
76C2×C3×C4×D4—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#937—31no—
82C2×#935—31no—
83C2×D4×Dic3—31no—
84C2×D4×Dic3—31no—
85C2×C4×#67—31no—
86C2×C4×#67—31no—
87#5586—316no—
88#5547—316no—
89C2×#896—31no—
90C2×#894—31no—
91C2×#886—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#882D311yescharacteristic, complemented
95C2×#67⋊C4—31no—
96C2×#67⋊C4D311yescharacteristic, complemented
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—61no—
101C2×#877—31no—
102C2×C4×D12—31no—
103C2×#872—31no—
104C24×C32C2311yescharacteristic
105C23×C3×D3—24no—
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C3⋊Dic3—24no—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2314yes—
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C2×#634—24no—
122C2×#634C2314yescomplemented
123C2×C3×#67—24no—
124C2×C3×#67—24no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3—24no—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—24no—
134C2×C3×D12—24no—
135C2×C3×D12C2314yes—
136C2×C3×D12C2314yes—
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3C2314yescomplemented
139C2×#625—24no—
140C2×#625—24no—
141C2×#625—24no—
142C2×#625C2314yes—
143C2×#625C2314yes—
144C2×#625C2314yescomplemented
145C2×D3×Dic3—24no—
146C2×D3×Dic3—24no—
147C2×D3×Dic3—24no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—232no—
150C2×D3×Dic3D418yescomplemented
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yescomplemented
156#3795—232no—
157C32×C22⋊C4C2314yes—
158#3757C2314yes—
159C4⋊(C3⋊Dic3)C2314yescomplemented
160#3750C2314yescomplemented
161#3750C2314yescomplemented
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yescomplemented
165C3×Dic3⋊C4C2314yescomplemented
166C3×C4×Dic3C2314yescomplemented
167#3724C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yescomplemented
172(C2×D3)⋊Dic3C2314yescomplemented
173(C2×D3)⋊Dic3C2314yescomplemented
174Dic32C2314yescomplemented
175C2×#525—91noSylow
176C25×C3—31no—
177C24×D3C2×D311yescharacteristic
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C23×C3×C4—31no—
183C23×C3×C4—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67C2×D311yescharacteristic
191C22×#67C2×D311yescharacteristic
192C23×Dic3—31no—
193C23×Dic3—31no—
194C23×Dic3—31no—
195C23×Dic3—31no—
196C23×Dic3—31no—
197C23×Dic3—31no—
198C23×Dic3—31no—
199C23×Dic3—38no—
200C23×Dic3—61no—
201C23×Dic3—68no—
202C23×Dic3C2×D311yescharacteristic
203C2×#237—38no—
204C2×#237—68no—
205C2×#235—38no—
206C2×#235—68no—
207C22×D12C2×D311yescharacteristic
208C22×D12C2×D311yescharacteristic
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—31no—
213C22×C4×D3—38no—
214C22×C4×D3—31no—
215C22×C4×D3—68no—
216C22×C4×D3C2×D311yescharacteristic, complemented
217C22×Dic6—31no—
218C22×Dic6—31no—
219C22×Dic6—61no—
220C3×#120—38no—
221C3×C4×D4—38no—
222C2×C3×C4⋊C4—31no—
223C2×C3×C22⋊C4—21no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4C2×D311yescharacteristic
228C2×C3×C22⋊C4C2×D311yescharacteristic
229C2×C3×C42—31no—
230#953—38no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—61no—
239#939—38no—
240#939—38no—
241#939—38no—
242#937—38no—
243#935—38no—
244D4×Dic3—38no—
245D4×Dic3—38no—
246C4×#67—38no—
247C4×#67—38no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4C2×D311yescharacteristic
254C2×(C2×D3)⋊C4C2×D311yescharacteristic
255C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—31no—
258C2×C4⋊Dic3—31no—
259C2×C4⋊Dic3—61no—
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—61no—
268C2×Dic3⋊C4—61no—
269C2×Dic3⋊C4C2×D311yescharacteristic, complemented
270C2×C4×Dic3—31no—
271C2×C4×Dic3—31no—
272C2×C4×Dic3C2×D311yescharacteristic, complemented
273#896—38no—
274#894—38no—
275#886—38no—
276#884—38no—
277#883—38no—
278#882C2×D318yescomplemented
279#67⋊C4—38no—
280#67⋊C4C2×D318yescomplemented
281#878—38no—
282#878—38no—
283#878—38no—
284#878—68no—
285#877—38no—
286C4×D12—38no—
287#872—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32#4114yescomplemented
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3×D3—232no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—28no—
299C22×C3×D3—28no—
300C22×C3×D3—28no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3C2×D414yes—
308C22×C3×D3#4114yescomplemented
309C22×C3×D3C2412yes—
310C22×C3×D3C2412yes—
311C22×C3×D3C2412yes—
312C22×C3×D3C2412yes—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4C2412yes—
316C2×C32×C4C2412yes—
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3—22no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—28no—
321C2×C3⋊Dic3C2×D414yes—
322C2×C3⋊Dic3C2412yes—
323C2×C3⋊Dic3C2412yes—
324C2×C3⋊Dic3C2412yes—
325C2×C3⋊Dic3C2412yes—
326#634—28no—
327C3×#67—28no—
328C3×#67—28no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—28no—
333C2×C3×Dic3C2×D414yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C3×D12—28no—
339C3×D12—28no—
340C3×C4×D3—28no—
341#625—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—91no—
357C2×#121—91no—
358C2×#120—31no—
359C2×#120—91no—
360C2×C4×D4—31no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C2×C4×D4—91no—
364C2×#117—91no—
365C24×C3—21no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3—34no—
369C24×C3—31no—
370C24×C3—31no—
371C24×C3—64no—
372C24×C3—64no—
373C24×C3—64no—
374C24×C3C22×D311yescharacteristic
375C24×C3C22×D311yescharacteristic
376C23×D3—24no—
377C23×D3—24no—
378C23×D3—24no—
379C23×D3C22×D314yes—
380C23×D3C22×D311yescharacteristic
381C23×D3C22×D311yescharacteristic
382C23×D3C22×D311yescharacteristic
383C23×D3C22×D311yescharacteristic
384C2×C3×D4—34no—
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—34no—
388C2×C3×D4—64no—
389C2×C3×D4—64no—
390C2×C3×D4—64no—
391C2×C3×D4—64no—
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—34no—
399C22×C3×C4—34no—
400C22×C3×C4—64no—
401C22×C3×C4—64no—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C2×#67—24no—
407C2×#67—24no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—34no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67C22×D314yes—
421C2×#67C22×D314yes—
422C22×Dic3—24no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—38no—
426C22×Dic3—34no—
427C22×Dic3—34no—
428C22×Dic3—34no—
429C22×Dic3—31no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—34no—
436C22×Dic3—34no—
437C22×Dic3—34no—
438C22×Dic3—34no—
439C22×Dic3—61no—
440C22×Dic3—64no—
441C22×Dic3—61no—
442C22×Dic3—61no—
443C22×Dic3—61no—
444C22×Dic3—64no—
445C22×Dic3—632no—
446C22×Dic3—64no—
447C22×Dic3—64no—
448C22×Dic3—64no—
449C22×Dic3—64no—
450C22×Dic3—64no—
451C22×Dic3—124no—
452C22×Dic3C22×D314yes—
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457#237—632no—
458#235—632no—
459C2×D12—24no—
460C2×D12—24no—
461C2×D12C22×D314yes—
462C2×D12C22×D314yes—
463C2×C4×D3—24no—
464C2×C4×D3—38no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—632no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3—64no—
474C2×C4×D3—64no—
475C2×C4×D3C22×D314yescomplemented
476C2×Dic6—34no—
477C2×Dic6—34no—
478C2×Dic6—64no—
479C2×Dic6—64no—
480C2×Dic6—64no—
481C2×Dic6—124no—
482C3×C4⋊C4—34no—
483C3×C22⋊C4—24no—
484C3×C22⋊C4—34no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4—34no—
487C3×C22⋊C4C22×D314yes—
488C3×C22⋊C4C22×D314yes—
489C3×C42—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(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4C22×D314yes—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D314yescomplemented
506C4⋊Dic3—34no—
507C4⋊Dic3—34no—
508C4⋊Dic3—34no—
509C4⋊Dic3—64no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—64no—
518Dic3⋊C4—64no—
519Dic3⋊C4C22×D314yescomplemented
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3C22×D314yescomplemented
523C22×C32—28no—
524C22×C32—22no—
525C22×C32—22no—
526C22×C32C22×D412yes—
527C22×C32C2×#4112yes—
528C22×C32C2×#4112yes—
529C22×C32C2×#4114yescomplemented
530C22×C32C2511yescharacteristic
531C2×C3×D3—232no—
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—22no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—44no—
545C2×C3×D3—44no—
546C2×C3×D3C22×D414yes—
547C2×C3×D3C2×#4114yescomplemented
548C32×C4—22no—
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×Dic3C22×D414yes—
558C25—31no—
559C2×#41—98no—
560C2×#41—188no—
561C22×Q8—91no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—91no—
567C22×D4—91no—
568C22×D4—91no—
569C23×C4—31no—
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—188no—
579#123—98no—
580#123—98no—
581C22⋊Q8—98no—
582C22⋊Q8—98no—
583#121—98no—
584#121—98no—
585#120—38no—
586#120—98no—
587C4×D4—38no—
588C4×D4—98no—
589C4×D4—98no—
590C4×D4—98no—
591#117—98no—
592C2×C4⋊C4—31no—
593C2×C4⋊C4—91no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4—91no—
603C2×C22⋊C4—91no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4D3211yescharacteristic
608C2×C42—31no—
609C2×C42—91no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—21no—
616C23×C3—24no—
617C23×C3—34no—
618C23×C3—34no—
619C23×C3—32no—
620C23×C3—32no—
621C23×C3—32no—
622C23×C3—32no—
623C23×C3—42no—
624C23×C3—42no—
625C23×C3—68no—
626C23×C3—68no—
627C23×C3—632no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3—68no—
631C23×C3—62no—
632C23×C3—62no—
633C23×C3—62no—
634C23×C3—62no—
635C23×C3—62no—
636C23×C3—62no—
637C23×C3—62no—
638C23×C3—62no—
639C23×C3#23514yescomplemented
640C23×C3#23714yescomplemented
641C23×C3C23×D312yes—
642C23×C3C23×D312yes—
643C23×C3C23×D311yescharacteristic
644C23×C3C23×D311yescharacteristic
645C22×D3—232no—
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—28no—
651C22×D3—28no—
652C22×D3—28no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3D3×D414yes—
660C22×D3#23714yescomplemented
661C22×D3C23×D312yes—
662C22×D3C23×D312yes—
663C22×D3C23×D312yes—
664C22×D3C23×D312yes—
665C3×D4—68no—
666C3×D4—68no—
667C3×D4—68no—
668C3×D4—68no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—34no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—42no—
681C2×C3×C4—42no—
682C2×C3×C4—68no—
683C2×C3×C4—68no—
684C2×C3×C4—62no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D312yes—
689C2×C3×C4C23×D312yes—
690C2×C3×C4C23×D312yes—
691#67—28no—
692#67—28no—
693#67—68no—
694#67—68no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—68no—
699C2×Dic3—22no—
700C2×Dic3—22no—
701C2×Dic3—22no—
702C2×Dic3—28no—
703C2×Dic3—34no—
704C2×Dic3—34no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—316no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—64no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—68no—
720C2×Dic3—68no—
721C2×Dic3—68no—
722C2×Dic3—68no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—68no—
730C2×Dic3—68no—
731C2×Dic3—128no—
732C2×Dic3—122no—
733C2×Dic3—122no—
734C2×Dic3—122no—
735C2×Dic3D3×D414yes—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740D12—28no—
741D12—28no—
742C4×D3—28no—
743C4×D3—316no—
744C4×D3—68no—
745C4×D3—68no—
746C4×D3—68no—
747C4×D3—68no—
748Dic6—68no—
749Dic6—68no—
750Dic6—128no—
751C2×C32—24no—
752C2×C32#52514yescomplemented
753C2×C32C23×D411yescharacteristic
754C2×C32C22×#4111yescharacteristic
755C2×C32C22×#4111yescharacteristic
756C3×D3—24no—
757C3×D3—24no—
758C3×D3—42no—
759C3×D3—42no—
760C24—31no—
761C24—31no—
762C24—34no—
763C24—31no—
764C24—31no—
765C24—64no—
766C24—64no—
767C24—64no—
768C24C2×D3211yescharacteristic
769#41—1832no—
770C2×Q8—94no—
771C2×Q8—184no—
772C2×D4—34no—
773C2×D4—34no—
774C2×D4—34no—
775C2×D4—34no—
776C2×D4—64no—
777C2×D4—64no—
778C2×D4—64no—
779C2×D4—64no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—184no—
784C2×D4—184no—
785C2×D4—184no—
786C22×C4—31no—
787C22×C4—34no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—34no—
792C22×C4—64no—
793C22×C4—64no—
794C22×C4—94no—
795C22×C4—98no—
796C22×C4—94no—
797C22×C4—94no—
798C22×C4—94no—
799C22×C4—94no—
800C22×C4—91no—
801C22×C4—94no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—184no—
806C22×C4—184no—
807C22×C4—1832no—
808C22×C4—184no—
809C22×C4—184no—
810C22×C4—184no—
811C22×C4C2×D3211yescharacteristic
812C22×C4C2×D3211yescharacteristic
813C4⋊C4—34no—
814C4⋊C4—94no—
815C4⋊C4—94no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—94no—
819C22⋊C4—34no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4C2×D3214yes—
829C42—34no—
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—42no—
845C22×C3—48no—
846C22×C3—42no—
847C22×C3—632no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—68no—
853C22×C3—68no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—124no—
861C22×C3—124no—
862C22×C3C2×#23512yes—
863C22×C3C2×#23514yescomplemented
864C22×C3C2×D3×D412yes—
865C22×C3C2×D3×D412yes—
866C22×C3C2×#23712yes—
867C22×C3C2×#23712yes—
868C22×C3C2×#23714yescomplemented
869C22×C3D3×#4112yes—
870C22×C3C24×D311yescharacteristic
871C22×C3C24×D311yescharacteristic
872C2×D3—232no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—28no—
878C2×D3—28no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—44no—
886C2×D3—44no—
887C2×D3C2×D3×D414yes—
888C2×D3C2×#23714yescomplemented
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—34no—
894C3×C4—42no—
895C3×C4—42no—
896C3×C4—62no—
897C3×C4—62no—
898C3×C4—62no—
899Dic3—22no—
900Dic3—22no—
901Dic3—22no—
902Dic3—34no—
903Dic3—34no—
904Dic3—64no—
905Dic3—62no—
906Dic3—62no—
907Dic3—62no—
908Dic3—62no—
909Dic3—62no—
910Dic3—62no—
911Dic3—122no—
912Dic3—122no—
913Dic3—122no—
914Dic3C2×D3×D414yes—
915C32C2×#52511yescharacteristic, complemented, Sylow
916C23—22no—
917C23—22no—
918C23—34no—
919C23—34no—
920C23—32no—
921C23—32no—
922C23—32no—
923C23—32no—
924C23—68no—
925C23—68no—
926C23—632no—
927C23—62no—
928C23—62no—
929C23—68no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23#379514yescomplemented
939C23C22×D3212yes—
940C23C22×D3211yescharacteristic
941Q8—188no—
942D4—68no—
943D4—68no—
944D4—68no—
945D4—68no—
946D4—188no—
947D4—188no—
948D4—188no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—34no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—68no—
957C2×C4—68no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—62no—
961C2×C4—916no—
962C2×C4—94no—
963C2×C4—92no—
964C2×C4—92no—
965C2×C4—92no—
966C2×C4—92no—
967C2×C4—188no—
968C2×C4—188no—
969C2×C4—188no—
970C2×C4—188no—
971C2×C4—188no—
972C2×C4—182no—
973C2×C4—182no—
974C2×C4—182no—
975C2×C4C22×D3212yes—
976C2×C4C22×D3212yes—
977C2×C3—24no—
978C2×C3—24no—
979C2×C3—24no—
980C2×C3—21no—
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—44no—
984C2×C3—64no—
985C2×C3—64no—
986C2×C3—122no—
987C2×C3—122no—
988C2×C3#554714yescomplemented
989C2×C3#558614yescomplemented
990C2×C3C22×#23511yescharacteristic
991C2×C3C22×D3×D411yescharacteristic
992C2×C3C22×D3×D411yescharacteristic
993C2×C3C22×#23711yescharacteristic
994C2×C3C22×#23711yescharacteristic
995C2×C3C2×D3×#4111yescharacteristic
996D3—24no—
997D3—24no—
998D3—42no—
999D3—42no—
1000C22—28no—
1001C22—22no—
1002C22—22no—
1003C22—34no—
1004C22—34no—
1005C22—632no—
1006C22—68no—
1007C22—68no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—124no—
1019C22—124no—
1020C22C2×#379512yes—
1021C22C2×#379514yescomplemented
1022C22D32×D412yes—
1023C22D3×#23712yes—
1024C22C23×D3211yescharacteristic
1025C4—22no—
1026C4—22no—
1027C4—34no—
1028C4—62no—
1029C4—62no—
1030C4—62no—
1031C4—94no—
1032C4—182no—
1033C4—182no—
1034C4—182no—
1035C3—21no—
1036C3C2×#554711yescharacteristic, complemented
1037C3C2×#558611yescharacteristic, complemented
1038C2—24no—
1039C2—64no—
1040C2—64no—
1041C2—122no—
1042C2—122no—
1043C2#1059405414yesdirect product factor
1044C2C22×#379511yescharacteristic
1045C2C2×D32×D411yescharacteristic
1046C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
2. C22×#3795C2semidirect
3. C2×#64087C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63980C2semidirect
7. C2×#63976C2semidirect
8. C2×Dic3×#67C2semidirect
9. C2×#63896C2semidirect
10. C2×Dic3×D12C2semidirect
11. C2×#63891C2semidirect
12. C2×#63885C2semidirect
13. C2×#63884C2semidirect
14. C2×#63879C2semidirect
15. C2×#63877C2semidirect
16. #10594054C2direct (N × H)
21. C22×#634C22semidirect
27. C22×C3×C4×D3C22semidirect
30. C22×#625C22semidirect
36. C22×D3×Dic3C22semidirect
37. C22×D3×Dic3C22semidirect
39. C2×#3795C22semidirect
42. C2×C4⋊(C3⋊Dic3)C22semidirect
43. C2×#3750C22semidirect
44. C2×#3750C22semidirect
45. #64087C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×C4×Dic3C22semidirect
51. C3×#882C22semidirect
52. C3×#67⋊C4C22semidirect
53. #63980C22semidirect
54. #63976C22semidirect
55. Dic3×#67C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×Dic32C22semidirect
64. #63896C22semidirect
65. Dic3×D12C22semidirect
66. #63891C22semidirect
67. #63885C22semidirect
68. #63884C22semidirect
69. #63879C22semidirect
70. #63877C22semidirect
94. C2×#882D3semidirect
96. C2×#67⋊C4D3semidirect
122. C2×#634C23semidirect
138. C2×C3×C4×D3C23semidirect
144. C2×#625C23semidirect
150. C2×D3×Dic3D4semidirect
155. C2×D3×Dic3C23semidirect
159. C4⋊(C3⋊Dic3)C23semidirect
160. #3750C23semidirect
161. #3750C23semidirect
164. C3×(C2×D3)⋊C4C23semidirect
165. C3×Dic3⋊C4C23semidirect
166. C3×C4×Dic3C23semidirect
167. #3724C23semidirect
168. Dic3⋊Dic3C23semidirect
171. (C2×D3)⋊Dic3C23semidirect
172. (C2×D3)⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. Dic32C23semidirect
216. C22×C4×D3C2×D3semidirect
255. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×Dic3⋊C4C2×D3semidirect
272. C2×C4×Dic3C2×D3semidirect
278. #882C2×D3semidirect
280. #67⋊C4C2×D3semidirect
290. C23×C32#41semidirect
308. C22×C3×D3#41semidirect
348. D3×Dic3C2×D4semidirect
475. C2×C4×D3C22×D3semidirect
505. (C2×D3)⋊C4C22×D3semidirect
519. Dic3⋊C4C22×D3semidirect
522. C4×Dic3C22×D3semidirect
529. C22×C32C2×#41semidirect
547. C2×C3×D3C2×#41semidirect
639. C23×C3#235semidirect
640. C23×C3#237semidirect
660. C22×D3#237semidirect
752. C2×C32#525semidirect
863. C22×C3C2×#235semidirect
868. C22×C3C2×#237semidirect
888. C2×D3C2×#237semidirect
915. C32C2×#525semidirect
938. C23#3795semidirect
988. C2×C3#5547semidirect
989. C2×C3#5586semidirect
1021. C22C2×#3795semidirect
1036. C3C2×#5547semidirect
1037. C3C2×#5586semidirect
1043. C2#10594054direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C22×#37952
C2×#640872
C2×C3×#8822
C2×C3×#67⋊C42
C2×#639802
C2×#639762
C2×Dic3×#672
C2×#638962
C2×Dic3×D122
C2×#638912
C2×#638852
C2×#638842
C2×#638792
C2×#638772
#105940542
C2×#55863
C2×#55473