Finite Group Databasebeta

← C2×#10594058 #11900792

Subgroups — C2×#10594058 #11900792

Order 1152.

3621 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64094C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×#63970C211yesmaximal, characteristic, complemented
9C2×#63915C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×#63904C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
15C2×#63840C211yesmaximal, characteristic, complemented
16#10594058C2116yesmaximal, direct product factor
17C2×#5596—31nomaximal
18C2×#5548—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×#3804—28no—
36C2×#3804C2218yescomplemented
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic
40C2×#3795—28no—
41C2×#3795C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×#3757C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3752C2211yescharacteristic
46C2×C4×C3⋊Dic3C2211yescharacteristic
47#64094C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C3×#884C2218yescomplemented
54C3×#67⋊C4C2218yescomplemented
55#63979C2218yescomplemented
56Dic3×#67C2218yescomplemented
57#63970C2218yescomplemented
58C2×Dic3⋊Dic3C2211yescharacteristic
59C2×Dic3⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64#63915C2218yescomplemented
65#63906C2218yescomplemented
66#63904C2218yescomplemented
67#63886C2218yescomplemented
68#63880C2218yescomplemented
69C4×D3×Dic3C2218yescomplemented
70#63840C2218yescomplemented
71C22×#237—31no—
72C22×#237—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C2×C3×C4×D4—31no—
77C2×#940—31no—
78C2×#940—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#938—31no—
82C2×D4×Dic3—31no—
83C2×#930—31no—
84C2×C4×#67—31no—
85C2×C4×#67—31no—
86C22×C4×Dic3—31no—
87#5596—316no—
88#5548—316no—
89C2×#895—31no—
90C2×#893—31no—
91C2×#888—31no—
92C2×#888—31no—
93C2×#885—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#885—31no—
97C2×#885—61no—
98C2×#884—31no—
99C2×#884D311yescharacteristic, complemented
100C2×#67⋊C4—31no—
101C2×#67⋊C4D311yescharacteristic, complemented
102C2×C4×D12—31no—
103C2×C42×D3—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C2×#638—24no—
112C2×#638C2314yes—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×#634—24no—
117C2×#634C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67—24no—
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yes—
124C22×C3×Dic3—24no—
125C22×C3×Dic3C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—24no—
132C2×C3×D12C2314yes—
133C2×C3×C4×D3—24no—
134C2×C3×C4×D3—24no—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2314yes—
137C2×#627—24no—
138C2×#627C2314yes—
139C2×#626—24no—
140C2×#626—24no—
141C2×#626—24no—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#625—24no—
146C2×#625—24no—
147C2×#625C2314yes—
148C2×#625C2314yes—
149C2×#624—24no—
150C2×#624C2314yes—
151#3804—232no—
152C2×D3×Dic3—24no—
153C2×D3×Dic3—24no—
154C2×D3×Dic3D418yescomplemented
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158#3795—232no—
159C32×C22⋊C4C2314yes—
160#3757C2314yes—
161#3752C2314yes—
162#3752C2314yes—
163C4×C3⋊Dic3C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168C3×C4×Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173Dic32C2314yes—
174Dic32C2314yes—
175C2×#532—91noSylow
176C22×C3×D4—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—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—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—61no—
193C22×#67C2×D311yescharacteristic
194C22×#67C2×D311yescharacteristic
195C22×#67C2×D311yescharacteristic
196C23×Dic3—31no—
197C23×Dic3—31no—
198C23×Dic3—31no—
199C23×Dic3C2×D311yescharacteristic
200C2×#237—38no—
201C2×#237—38no—
202C2×#237—68no—
203C2×#237—68no—
204C2×#235—38no—
205C2×#235—38no—
206C2×#235—68no—
207C2×#235—68no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12C2×D311yescharacteristic
212C22×C4×D3—31no—
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3C2×D311yescharacteristic
218C22×C4×D3C2×D311yescharacteristic
219C22×Dic6—31no—
220C22×Dic6—31no—
221C22×Dic6—31no—
222C22×Dic6—31no—
223C22×Dic6—61no—
224C3×#121—38no—
225C3×C4×D4—38no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—21no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4C2×D311yescharacteristic
232C2×C3×C22⋊C4C2×D311yescharacteristic
233C2×C3×C42—31no—
234C2×#217—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—61no—
239#940—38no—
240#940—38no—
241#939—38no—
242#939—38no—
243#938—38no—
244D4×Dic3—38no—
245#930—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)⋊C4—31no—
254C2×(C2×D3)⋊C4—61no—
255C2×(C2×D3)⋊C4—61no—
256C2×(C2×D3)⋊C4C2×D311yescharacteristic
257C2×(C2×D3)⋊C4C2×D311yescharacteristic
258C2×C4⋊Dic3—31no—
259C2×C4⋊Dic3—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4C2×D311yescharacteristic
263C2×Dic3⋊C4C2×D311yescharacteristic
264C2×C4×Dic3—31no—
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267C2×C4×Dic3—31no—
268C2×C4×Dic3—31no—
269C2×C4×Dic3—31no—
270C2×C4×Dic3—38no—
271C2×C4×Dic3—61no—
272C2×C4×Dic3C2×D311yescharacteristic
273#895—38no—
274#893—38no—
275#888—38no—
276#888—38no—
277#885—38no—
278#885—38no—
279#885—38no—
280#885—38no—
281#885—68no—
282#884—38no—
283#884C2×D318yescomplemented
284#67⋊C4—38no—
285#67⋊C4C2×D318yescomplemented
286C4×D12—38no—
287C42×D3—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3C2×D414yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312C2×C32×C4C2412yes—
313#638—28no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2×D414yes—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320#634—28no—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—28no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—28no—
327C2×C3×Dic3C2×D414yes—
328C2×C3×Dic3#4114yescomplemented
329C2×C3×Dic3#4114yescomplemented
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C3×D12—28no—
336C3×C4×D3—28no—
337C3×C4×D3—28no—
338#627—28no—
339#626—28no—
340#626—28no—
341#626—28no—
342#625—28no—
343#625—28no—
344#624—28no—
345D3×Dic3—28no—
346D3×Dic3—28no—
347D3×Dic3C2×D4116yescomplemented
348C22×#41—91no—
349C22×#41—91no—
350#532—916no—
351C2×C4⋊Q8—91no—
352C2×#127—91no—
353C2×#124—91no—
354C2×#124—91no—
355C2×#121—31no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×C4×D4—31no—
360C2×C4×D4—91no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C22×C42—91no—
364C24×C3—21no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3C22×D311yescharacteristic
369C24×C3C22×D311yescharacteristic
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—61no—
373C23×D3C22×D311yescharacteristic
374C23×D3C22×D311yescharacteristic
375C23×D3C22×D311yescharacteristic
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—64no—
381C2×C3×D4—64no—
382C2×C3×D4—64no—
383C2×C3×D4—64no—
384C22×C3×C4—21no—
385C22×C3×C4—21no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—34no—
392C22×C3×C4—34no—
393C22×C3×C4—34no—
394C22×C3×C4—64no—
395C22×C3×C4—64no—
396C22×C3×C4—64no—
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C2×#67—24no—
402C2×#67—24no—
403C2×#67—24no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—64no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—64no—
423C2×#67—124no—
424C2×#67C22×D314yes—
425C2×#67C22×D314yes—
426C2×#67C22×D314yes—
427C22×Dic3—24no—
428C22×Dic3—31no—
429C22×Dic3—31no—
430C22×Dic3—38no—
431C22×Dic3—34no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—31no—
436C22×Dic3—34no—
437C22×Dic3—34no—
438C22×Dic3—61no—
439C22×Dic3—61no—
440C22×Dic3—61no—
441C22×Dic3—64no—
442C22×Dic3—64no—
443C22×Dic3C22×D314yes—
444C22×Dic3C22×D311yescharacteristic
445C22×Dic3C22×D311yescharacteristic
446C22×Dic3C22×D311yescharacteristic
447C22×Dic3C22×D311yescharacteristic
448C22×Dic3C22×D311yescharacteristic
449#237—632no—
450#237—632no—
451#235—632no—
452#235—632no—
453C2×D12—24no—
454C2×D12—34no—
455C2×D12—34no—
456C2×D12—34no—
457C2×D12—64no—
458C2×D12—64no—
459C2×D12—64no—
460C2×D12C22×D314yes—
461C2×C4×D3—24no—
462C2×C4×D3—24no—
463C2×C4×D3—38no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—64no—
470C2×C4×D3—64no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3C22×D314yes—
474C2×C4×D3C22×D314yes—
475C2×Dic6—34no—
476C2×Dic6—34no—
477C2×Dic6—34no—
478C2×Dic6—34no—
479C2×Dic6—64no—
480C2×Dic6—64no—
481C2×Dic6—64no—
482C2×Dic6—64no—
483C2×Dic6—64no—
484C2×Dic6—124no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4—34no—
487C3×C22⋊C4—24no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4C22×D314yes—
491C3×C22⋊C4C22×D314yes—
492C3×C42—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)⋊C4—34no—
504(C2×D3)⋊C4—64no—
505(C2×D3)⋊C4—64no—
506(C2×D3)⋊C4C22×D314yes—
507(C2×D3)⋊C4C22×D314yes—
508C4⋊Dic3—34no—
509C4⋊Dic3—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—34no—
515C4×Dic3—34no—
516C4×Dic3—34no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—64no—
521C4×Dic3C22×D314yes—
522C22×C32—22no—
523C22×C32—22no—
524C22×C32—22no—
525C22×C32—44no—
526C22×C32C22×D412yes—
527C22×C32C2×#4112yes—
528C22×C32C2×#4112yes—
529C22×C32C2511yescharacteristic
530C2×C3⋊D3—22no—
531C2×C3⋊D3—22no—
532C2×C3⋊D3—22no—
533C2×C3⋊D3—44no—
534C2×C3×D3—28no—
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—44no—
544C2×C3×D3—44no—
545C2×C3×D3C22×D414yes—
546C32×C4—22no—
547C32×C4—22no—
548C3⋊Dic3—22no—
549C3⋊Dic3—22no—
550C3⋊Dic3C22×D414yes—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3C22×D414yes—
554C3×Dic3C2×#4114yescomplemented
555C3×Dic3C2×#4114yescomplemented
556C2×#41—98no—
557C2×#41—98no—
558C2×#41—188no—
559C2×#41—188no—
560C22×Q8—91no—
561C22×Q8—91no—
562C22×D4—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—91no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C23×C4—31no—
573C23×C4—31no—
574C23×C4—31no—
575C23×C4—91no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C4⋊Q8—98no—
580#127—98no—
581#124—98no—
582#124—98no—
583#121—38no—
584#121—98no—
585#121—98no—
586#121—98no—
587C4×D4—38no—
588C4×D4—98no—
589C4×D4—98no—
590C4×D4—98no—
591C2×C4⋊C4—31no—
592C2×C4⋊C4—31no—
593C2×C4⋊C4—91no—
594C2×C4⋊C4—91no—
595C2×C22⋊C4—31no—
596C2×C22⋊C4—31no—
597C2×C22⋊C4—91no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4—91no—
600C2×C22⋊C4—91no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4D3211yescharacteristic
603C2×C42—31no—
604C2×C42—98no—
605C2×C42—91no—
606C2×C42—91no—
607C2×C42—91no—
608C23×C3—22no—
609C23×C3—22no—
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—21no—
616C23×C3—34no—
617C23×C3—32no—
618C23×C3—32no—
619C23×C3—32no—
620C23×C3—42no—
621C23×C3—42no—
622C23×C3—42no—
623C23×C3—62no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3—62no—
631C23×C3C23×D312yes—
632C23×C3C23×D312yes—
633C23×C3C23×D311yescharacteristic
634C23×C3C23×D311yescharacteristic
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—122no—
653C22×D3—122no—
654C22×D3—122no—
655C22×D3D3×D414yes—
656C22×D3C23×D312yes—
657C22×D3C23×D312yes—
658C22×D3C23×D312yes—
659C3×D4—68no—
660C3×D4—68no—
661C3×D4—68no—
662C3×D4—68no—
663C2×C3×C4—22no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—34no—
670C2×C3×C4—34no—
671C2×C3×C4—34no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—32no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—42no—
678C2×C3×C4—42no—
679C2×C3×C4—68no—
680C2×C3×C4—68no—
681C2×C3×C4—68no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688#67—28no—
689#67—28no—
690#67—28no—
691#67—68no—
692#67—68no—
693#67—68no—
694#67—68no—
695#67—68no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—128no—
701C2×Dic3—22no—
702C2×Dic3—22no—
703C2×Dic3—28no—
704C2×Dic3—34no—
705C2×Dic3—34no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—316no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—64no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—68no—
722C2×Dic3—68no—
723C2×Dic3—122no—
724C2×Dic3—122no—
725C2×Dic3#23514yescomplemented
726C2×Dic3D3×D414yes—
727C2×Dic3#23714yescomplemented
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733D12—28no—
734D12—68no—
735D12—68no—
736D12—68no—
737C4×D3—28no—
738C4×D3—28no—
739C4×D3—316no—
740C4×D3—68no—
741C4×D3—68no—
742C4×D3—68no—
743C4×D3—68no—
744Dic6—68no—
745Dic6—68no—
746Dic6—68no—
747Dic6—68no—
748Dic6—128no—
749C2×C32—42no—
750C2×C32#53214yescomplemented
751C2×C32C23×D411yescharacteristic
752C2×C32C22×#4111yescharacteristic
753C2×C32C22×#4111yescharacteristic
754C3⋊D3—42no—
755C3×D3—24no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—91no—
762C24C2×D3211yescharacteristic
763#41—1832no—
764#41—1832no—
765C2×Q8—94no—
766C2×Q8—94no—
767C2×Q8—184no—
768C2×Q8—184no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—34no—
773C2×D4—64no—
774C2×D4—64no—
775C2×D4—64no—
776C2×D4—64no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—184no—
784C2×D4—184no—
785C2×D4—184no—
786C2×D4—184no—
787C2×D4—184no—
788C2×D4—184no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—34no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—34no—
796C22×C4—34no—
797C22×C4—64no—
798C22×C4—64no—
799C22×C4—64no—
800C22×C4—94no—
801C22×C4—94no—
802C22×C4—98no—
803C22×C4—94no—
804C22×C4—94no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—184no—
809C22×C4—184no—
810C22×C4—184no—
811C22×C4C2×D3211yescharacteristic
812C22×C4C2×D3211yescharacteristic
813C4⋊C4—34no—
814C4⋊C4—34no—
815C4⋊C4—94no—
816C4⋊C4—94no—
817C22⋊C4—34no—
818C22⋊C4—34no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4C2×D3214yes—
825C42—34no—
826C42—94no—
827C42—94no—
828C42—94no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—21no—
839C22×C3—34no—
840C22×C3—42no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—44no—
844C22×C3—44no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—68no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—84no—
855C22×C3—124no—
856C22×C3—124no—
857C22×C3C2×#23512yes—
858C22×C3C2×D3×D412yes—
859C22×C3C2×D3×D412yes—
860C22×C3C2×#23712yes—
861C22×C3D3×#4112yes—
862C22×C3D3×#4112yes—
863C22×C3C24×D311yescharacteristic
864C22×C3C24×D311yescharacteristic
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—28no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—44no—
875C2×D3—44no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—124no—
886C2×D3—124no—
887C2×D3—244no—
888C2×D3C2×D3×D414yes—
889C3×C4—22no—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—34no—
894C3×C4—34no—
895C3×C4—34no—
896C3×C4—42no—
897C3×C4—42no—
898C3×C4—62no—
899C3×C4—62no—
900Dic3—22no—
901Dic3—22no—
902Dic3—34no—
903Dic3—34no—
904Dic3—64no—
905Dic3—62no—
906Dic3—62no—
907Dic3—62no—
908Dic3—62no—
909Dic3—122no—
910Dic3—122no—
911Dic3C2×#23514yescomplemented
912Dic3C2×D3×D414yes—
913Dic3C2×#23714yescomplemented
914C32C2×#53211yescharacteristic, complemented, Sylow
915C23—22no—
916C23—22no—
917C23—22no—
918C23—34no—
919C23—32no—
920C23—32no—
921C23—32no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—92no—
931C23—182no—
932C23—182no—
933C23—182no—
934C23C22×D3212yes—
935C23C22×D3211yescharacteristic
936Q8—188no—
937Q8—188no—
938D4—68no—
939D4—68no—
940D4—68no—
941D4—68no—
942D4—188no—
943D4—188no—
944D4—188no—
945D4—188no—
946D4—188no—
947D4—188no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—34no—
951C2×C4—34no—
952C2×C4—34no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—68no—
959C2×C4—68no—
960C2×C4—68no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—916no—
964C2×C4—94no—
965C2×C4—92no—
966C2×C4—92no—
967C2×C4—92no—
968C2×C4—188no—
969C2×C4—188no—
970C2×C4—188no—
971C2×C4—182no—
972C2×C4—182no—
973C2×C4C22×D3212yes—
974C2×C4C22×D3212yes—
975C2×C3—24no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—64no—
982C2×C3—82no—
983C2×C3—122no—
984C2×C3—122no—
985C2×C3#554814yescomplemented
986C2×C3#559614yescomplemented
987C2×C3C22×#23511yescharacteristic
988C2×C3C22×D3×D411yescharacteristic
989C2×C3C22×D3×D411yescharacteristic
990C2×C3C22×#23711yescharacteristic
991C2×C3C2×D3×#4111yescharacteristic
992C2×C3C2×D3×#4111yescharacteristic
993D3—24no—
994D3—42no—
995D3—42no—
996D3—122no—
997D3—122no—
998D3—242no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—34no—
1003C22—44no—
1004C22—68no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—124no—
1014C22—124no—
1015C22—182no—
1016C22—182no—
1017C22—182no—
1018C22—364no—
1019C22D3×#23512yes—
1020C22D32×D412yes—
1021C22D3×#23712yes—
1022C22C23×D3211yescharacteristic
1023C4—22no—
1024C4—22no—
1025C4—34no—
1026C4—34no—
1027C4—34no—
1028C4—62no—
1029C4—62no—
1030C4—94no—
1031C4—182no—
1032C4—182no—
1033C3—21no—
1034C3C2×#554811yescharacteristic, complemented
1035C3C2×#559611yescharacteristic, complemented
1036C2—42no—
1037C2—64no—
1038C2—122no—
1039C2—122no—
1040C2—362no—
1041C2#1059405814yesdirect product factor
1042C2C2×D3×#23511yescharacteristic
1043C2C2×D32×D411yescharacteristic
1044C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C22×#3795C2semidirect
3. C2×#64094C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63979C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×#63970C2semidirect
9. C2×#63915C2semidirect
10. C2×#63906C2semidirect
11. C2×#63904C2semidirect
12. C2×#63886C2semidirect
13. C2×#63880C2semidirect
14. C2×C4×D3×Dic3C2semidirect
15. C2×#63840C2semidirect
16. #10594058C2direct (N × H)
36. C2×#3804C22semidirect
41. C2×#3795C22semidirect
47. #64094C22semidirect
53. C3×#884C22semidirect
54. C3×#67⋊C4C22semidirect
55. #63979C22semidirect
56. Dic3×#67C22semidirect
57. #63970C22semidirect
64. #63915C22semidirect
65. #63906C22semidirect
66. #63904C22semidirect
67. #63886C22semidirect
68. #63880C22semidirect
69. C4×D3×Dic3C22semidirect
70. #63840C22semidirect
99. C2×#884D3semidirect
101. C2×#67⋊C4D3semidirect
154. C2×D3×Dic3D4semidirect
283. #884C2×D3semidirect
285. #67⋊C4C2×D3semidirect
328. C2×C3×Dic3#41semidirect
329. C2×C3×Dic3#41semidirect
347. D3×Dic3C2×D4semidirect
554. C3×Dic3C2×#41semidirect
555. C3×Dic3C2×#41semidirect
725. C2×Dic3#235semidirect
727. C2×Dic3#237semidirect
750. C2×C32#532semidirect
911. Dic3C2×#235semidirect
913. Dic3C2×#237semidirect
914. C32C2×#532semidirect
985. C2×C3#5548semidirect
986. C2×C3#5596semidirect
1034. C3C2×#5548semidirect
1035. C3C2×#5596semidirect
1041. C2#10594058direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C22×#37952
C2×#640942
C2×C3×#8842
C2×C3×#67⋊C42
C2×#639792
C2×Dic3×#672
C2×#639702
C2×#639152
C2×#639062
C2×#639042
C2×#638862
C2×#638802
C2×C4×D3×Dic32
C2×#638402
#105940582
C2×#55963
C2×#55483