Finite Group Databasebeta

← C2×#10594188 #11902538

Subgroups — C2×#10594188 #11902538

Order 1152.

3435 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C2×C3×#883C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63918C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63883C211yesmaximal, characteristic, complemented
12C2×#63880C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594188C2116yesmaximal, direct product factor
17C2×#5655—31nomaximal
18C2×#5551—31nomaximal
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#627C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C2×#3804—28no—
34C2×#3804C2218yescomplemented
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C2×#3798—28no—
38C2×#3798C2218yescomplemented
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×#3757C2211yescharacteristic
41C2×#3752C2211yescharacteristic
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C2×#3750C2211yescharacteristic
44#64092C2218yescomplemented
45C2×C3×#217C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×C4⋊Dic3C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52C3×#883C2218yescomplemented
53C3×#67⋊C4C2218yescomplemented
54#63970C2218yescomplemented
55C2×#3724C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58C2×Dic3⋊Dic3C2211yescharacteristic
59C2×Dic3⋊Dic3C2211yescharacteristic
60#63964C2218yescomplemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63#63958C2218yescomplemented
64#63918C2218yescomplemented
65#63891C2218yescomplemented
66#63883C2218yescomplemented
67#63880C2218yescomplemented
68D3×Dic3⋊C4C2218yescomplemented
69#63854C2218yescomplemented
70#63851C2218yescomplemented
71C22×#237—31no—
72C22×#235—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×C4×D4—31no—
77C2×#939—31no—
78C2×#938—31no—
79C2×#938—31no—
80C2×#924—31no—
81C2×#924—31no—
82C22×Dic3⋊C4—31no—
83#5655—316no—
84#5551—316no—
85C2×#896—31no—
86C2×#894—31no—
87C2×D3×C4⋊C4—31no—
88C2×D3×C4⋊C4—31no—
89C2×D3×C4⋊C4—31no—
90C2×#888—31no—
91C2×#886—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#883—61no—
98C2×#883D311yescharacteristic, complemented
99C2×#67⋊C4—31no—
100C2×#67⋊C4D311yescharacteristic, complemented
101C2×#878—31no—
102C2×C4×D12—31no—
103C2×#869—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×#638—24no—
111C2×#638C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2314yes—
117C2×C3×#67—24no—
118C2×C3×#67—24no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C22×C3×Dic3—24no—
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3—24no—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×#627—24no—
134C2×#627—24no—
135C2×#627C2314yes—
136C2×#627C2314yes—
137C2×#626—24no—
138C2×#626D418yescomplemented
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#625—24no—
142C2×#625C2314yes—
143C2×#624—24no—
144C2×#624—24no—
145C2×#624C2314yes—
146C2×#624C2314yes—
147#3804—232no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—24no—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152#3798—232no—
153C32×C22⋊C4C2314yes—
154#3757C2314yes—
155#3752C2314yes—
156C4⋊(C3⋊Dic3)C2314yes—
157#3750C2314yes—
158C3×#217C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×C4⋊Dic3C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×C4×Dic3C2314yes—
165#3724C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172C2×#547—91noSylow
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—61no—
185C22×#67C2×D311yescharacteristic
186C22×#67C2×D311yescharacteristic
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3C2×D311yescharacteristic
190C2×#237—38no—
191C2×#237—68no—
192C2×#235—38no—
193C2×#235—38no—
194C2×#235—38no—
195C2×#235—68no—
196C2×#235—68no—
197C2×#235—68no—
198C22×D12—31no—
199C22×D12—31no—
200C22×C4×D3—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—31no—
208C22×C4×D3—61no—
209C22×C4×D3C2×D311yescharacteristic
210C22×C4×D3C2×D311yescharacteristic
211C22×Dic6—31no—
212C22×Dic6—31no—
213C22×Dic6—31no—
214C22×Dic6—31no—
215C3×#123—38no—
216C3×C4×D4—38no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C4⋊C4—31no—
219C2×C3×C4⋊C4—31no—
220C2×C3×C22⋊C4—21no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4C2×D311yescharacteristic
225C2×C3×C22⋊C4C2×D311yescharacteristic
226C2×C3×C42—31no—
227C2×#217—31no—
228C2×#217—31no—
229C2×#217—31no—
230C2×#217—31no—
231C2×#217—61no—
232C2×#217C2×D311yescharacteristic
233#939—38no—
234#938—38no—
235#938—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—61no—
241C2×(C2×D3)⋊C4C2×D311yescharacteristic
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—61no—
250C2×C4⋊Dic3C2×D311yescharacteristic
251#924—38no—
252#924—38no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—38no—
262C2×Dic3⋊C4—61no—
263C2×Dic3⋊C4C2×D311yescharacteristic
264C2×Dic3⋊C4C2×D311yescharacteristic
265C2×C4×Dic3C2×D311yescharacteristic
266#896—38no—
267#894—38no—
268D3×C4⋊C4—38no—
269D3×C4⋊C4—38no—
270D3×C4⋊C4—38no—
271#888—38no—
272#886—38no—
273#884—38no—
274#883—38no—
275#883—38no—
276#883—38no—
277#883—38no—
278#883—68no—
279#883C2×D318yescomplemented
280#67⋊C4—38no—
281#67⋊C4C2×D318yescomplemented
282#878—38no—
283C4×D12—38no—
284#869—38no—
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2412yes—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3C2×D414yes—
293C22×C3⋊D3C2412yes—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2×D414yes—
300C22×C3×D3C2412yes—
301C22×C3×D3C2412yes—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306#638—28no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C4×C3⋊D3—28no—
314C3×#67—28no—
315C3×#67—28no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—28no—
321C2×C3×Dic3C2×D414yes—
322C2×C3×Dic3#4114yescomplemented
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C3×C4×D3—28no—
330C3×C4×D3—28no—
331#627—28no—
332#627—28no—
333#626—28no—
334#626C2×D4116yescomplemented
335#625—28no—
336#624—28no—
337#624—28no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340C22×#41—91no—
341C22×#41—91no—
342#547—916no—
343C2×C4⋊Q8—91no—
344C2×#123—31no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×C22⋊Q8—91no—
349C2×C22⋊Q8—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×C4×D4—31no—
353C2×C4×D4—91no—
354C22×C4⋊C4—91no—
355C22×C4⋊C4—91no—
356C24×C3—21no—
357C24×C3—31no—
358C24×C3—31no—
359C24×C3C22×D311yescharacteristic
360C24×C3C22×D311yescharacteristic
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—61no—
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—64no—
369C2×C3×D4—64no—
370C22×C3×C4—21no—
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—34no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—64no—
382C22×C3×C4—64no—
383C22×C3×C4—64no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—24no—
389C2×#67—24no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—38no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—64no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—64no—
403C2×#67—124no—
404C2×#67C22×D314yes—
405C2×#67C22×D314yes—
406C22×Dic3—24no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—34no—
414C22×Dic3—34no—
415C22×Dic3—61no—
416C22×Dic3—61no—
417C22×Dic3—61no—
418C22×Dic3—64no—
419C22×Dic3—64no—
420C22×Dic3C22×D314yes—
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427#237—632no—
428#235—632no—
429#235—632no—
430#235—632no—
431C2×D12—38no—
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—64no—
435C2×C4×D3—24no—
436C2×C4×D3—24no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—64no—
446C2×C4×D3—64no—
447C2×C4×D3—64no—
448C2×C4×D3—64no—
449C2×C4×D3—64no—
450C2×C4×D3—64no—
451C2×C4×D3—64no—
452C2×C4×D3—64no—
453C2×C4×D3—64no—
454C2×C4×D3—124no—
455C2×C4×D3C22×D314yes—
456C2×C4×D3C22×D314yes—
457C2×Dic6—34no—
458C2×Dic6—34no—
459C2×Dic6—34no—
460C2×Dic6—34no—
461C2×Dic6—64no—
462C2×Dic6—64no—
463C2×Dic6—64no—
464C2×Dic6—64no—
465C3×C4⋊C4—34no—
466C3×C4⋊C4—34no—
467C3×C4⋊C4—34no—
468C3×C22⋊C4—24no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4C22×D314yes—
473C3×C22⋊C4C22×D314yes—
474C3×C42—34no—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—64no—
480#217C22×D314yes—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4C22×D314yes—
487(C2×D3)⋊C4C22×D314yes—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—34no—
493C4⋊Dic3—34no—
494C4⋊Dic3—64no—
495C4⋊Dic3C22×D314yes—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—64no—
505Dic3⋊C4C22×D314yes—
506Dic3⋊C4C22×D314yes—
507C4×Dic3C22×D314yes—
508C22×C32—22no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32—44no—
512C22×C32C22×D412yes—
513C22×C32C2×#4112yes—
514C22×C322−1+412yes—
515C22×C32C2511yescharacteristic
516C2×C3⋊D3—28no—
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3C22×D414yes—
520C2×C3×D3—28no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—44no—
527C2×C3×D3C22×D414yes—
528C32×C4—22no—
529C32×C4—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3×Dic3—22no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3C22×D414yes—
538C3×Dic3C2×#4114yescomplemented
539C2×#41—98no—
540C2×#41—98no—
541C2×#41—188no—
542C2×#41—188no—
543C22×Q8—91no—
544C22×Q8—91no—
545C22×D4—31no—
546C22×D4—31no—
547C22×D4—91no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C23×C4—31no—
552C23×C4—31no—
553C23×C4—31no—
554C23×C4—91no—
555C23×C4—91no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4—91no—
559C4⋊Q8—98no—
560#123—38no—
561#123—98no—
562#123—98no—
563#123—98no—
564C22⋊Q8—98no—
565C22⋊Q8—98no—
566#121—98no—
567#121—98no—
568C4×D4—38no—
569C4×D4—98no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—98no—
574C2×C4⋊C4—98no—
575C2×C4⋊C4—91no—
576C2×C4⋊C4—91no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—91no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4D3211yescharacteristic
590C2×C42—31no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—21no—
599C23×C3—34no—
600C23×C3—32no—
601C23×C3—32no—
602C23×C3—42no—
603C23×C3—42no—
604C23×C3—42no—
605C23×C3—62no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3—62no—
610C23×C3C23×D312yes—
611C23×C3C23×D312yes—
612C23×C3C23×D311yescharacteristic
613C23×C3C23×D311yescharacteristic
614C22×D3—22no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—22no—
619C22×D3—34no—
620C22×D3—34no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—64no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3D3×D414yes—
632C22×D3C23×D312yes—
633C22×D3C23×D312yes—
634C3×D4—68no—
635C3×D4—68no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—34no—
643C2×C3×C4—34no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—42no—
651C2×C3×C4—42no—
652C2×C3×C4—68no—
653C2×C3×C4—68no—
654C2×C3×C4—68no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663#67—28no—
664#67—28no—
665#67—316no—
666#67—68no—
667#67—68no—
668#67—68no—
669#67—68no—
670#67—68no—
671#67—128no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—28no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—68no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—68no—
694C2×Dic3—122no—
695C2×Dic3—122no—
696C2×Dic3—122no—
697C2×Dic3#23514yescomplemented
698C2×Dic3D3×D414yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705D12—316no—
706D12—68no—
707C4×D3—28no—
708C4×D3—28no—
709C4×D3—68no—
710C4×D3—68no—
711C4×D3—68no—
712C4×D3—68no—
713C4×D3—68no—
714C4×D3—68no—
715C4×D3—68no—
716C4×D3—68no—
717C4×D3—128no—
718Dic6—68no—
719Dic6—68no—
720Dic6—68no—
721Dic6—68no—
722C2×C32—42no—
723C2×C32#54714yescomplemented
724C2×C32C23×D411yescharacteristic
725C2×C32C22×#4111yescharacteristic
726C2×C32C2×2−1+411yescharacteristic
727C3⋊D3—24no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—91no—
733C24C2×D3211yescharacteristic
734#41—1832no—
735#41—1832no—
736C2×Q8—94no—
737C2×Q8—94no—
738C2×Q8—184no—
739C2×Q8—184no—
740C2×D4—34no—
741C2×D4—34no—
742C2×D4—64no—
743C2×D4—64no—
744C2×D4—94no—
745C2×D4—98no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—184no—
750C2×D4—184no—
751C2×D4—184no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—34no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—34no—
760C22×C4—34no—
761C22×C4—64no—
762C22×C4—64no—
763C22×C4—64no—
764C22×C4—94no—
765C22×C4—94no—
766C22×C4—94no—
767C22×C4—94no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—94no—
772C22×C4—184no—
773C22×C4—184no—
774C22×C4—184no—
775C22×C4—184no—
776C22×C4—184no—
777C22×C4C2×D3211yescharacteristic
778C22×C4C2×D3211yescharacteristic
779C4⋊C4—34no—
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—94no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—34no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4C2×D3214yes—
797C42—34no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—21no—
808C22×C3—34no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—44no—
813C22×C3—44no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—68no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—84no—
821C22×C3—124no—
822C22×C3C2×#23512yes—
823C22×C3C2×D3×D412yes—
824C22×C3C2×D3×D412yes—
825C22×C3D3×#4112yes—
826C22×C3#101012yes—
827C22×C3#101012yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—28no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—34no—
837C2×D3—34no—
838C2×D3—44no—
839C2×D3—64no—
840C2×D3—68no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—68no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—128no—
849C2×D3C2×D3×D414yes—
850C3×C4—22no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—22no—
854C3×C4—34no—
855C3×C4—34no—
856C3×C4—42no—
857C3×C4—42no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—62no—
862Dic3—22no—
863Dic3—22no—
864Dic3—22no—
865Dic3—22no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—62no—
872Dic3—122no—
873Dic3—122no—
874Dic3—122no—
875Dic3C2×#23514yescomplemented
876Dic3C2×D3×D414yes—
877C32C2×#54711yescharacteristic, complemented, Sylow
878C23—22no—
879C23—22no—
880C23—22no—
881C23—34no—
882C23—32no—
883C23—32no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—62no—
889C23—94no—
890C23—92no—
891C23—182no—
892C23—182no—
893C23C22×D3212yes—
894C23C22×D3211yescharacteristic
895Q8—188no—
896Q8—188no—
897D4—68no—
898D4—68no—
899D4—916no—
900D4—188no—
901D4—188no—
902D4—188no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—34no—
906C2×C4—34no—
907C2×C4—32no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—32no—
913C2×C4—68no—
914C2×C4—68no—
915C2×C4—68no—
916C2×C4—62no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—92no—
921C2×C4—92no—
922C2×C4—92no—
923C2×C4—188no—
924C2×C4—188no—
925C2×C4—188no—
926C2×C4—188no—
927C2×C4—188no—
928C2×C4—182no—
929C2×C4—182no—
930C2×C4—182no—
931C2×C4C22×D3212yes—
932C2×C4C22×D3212yes—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—24no—
937C2×C3—42no—
938C2×C3—42no—
939C2×C3—64no—
940C2×C3—82no—
941C2×C3—122no—
942C2×C3#555114yescomplemented
943C2×C3#565514yescomplemented
944C2×C3C22×#23511yescharacteristic
945C2×C3C22×D3×D411yescharacteristic
946C2×C3C22×D3×D411yescharacteristic
947C2×C3C2×D3×#4111yescharacteristic
948C2×C3C2×#101011yescharacteristic
949C2×C3C2×#101011yescharacteristic
950D3—24no—
951D3—42no—
952D3—64no—
953D3—64no—
954D3—124no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—34no—
959C22—44no—
960C22—62no—
961C22—62no—
962C22—68no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—94no—
967C22—124no—
968C22—182no—
969C22—182no—
970C22—188no—
971C22D3×#23512yes—
972C22#6430912yes—
973C22D32×D412yes—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—22no—
977C4—34no—
978C4—34no—
979C4—62no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—182no—
984C4—182no—
985C4—182no—
986C3—21no—
987C3C2×#555111yescharacteristic, complemented
988C3C2×#565511yescharacteristic, complemented
989C2—42no—
990C2—64no—
991C2—122no—
992C2—184no—
993C2#1059418814yesdirect product factor
994C2C2×D3×#23511yescharacteristic
995C2C2×#6430911yescharacteristic
996C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#547
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×#3798C2semidirect
3. C2×#64092C2semidirect
4. C2×C3×#883C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63970C2semidirect
7. C2×#63964C2semidirect
8. C2×#63958C2semidirect
9. C2×#63918C2semidirect
10. C2×#63891C2semidirect
11. C2×#63883C2semidirect
12. C2×#63880C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63854C2semidirect
15. C2×#63851C2semidirect
16. #10594188C2direct (N × H)
34. C2×#3804C22semidirect
38. C2×#3798C22semidirect
44. #64092C22semidirect
52. C3×#883C22semidirect
53. C3×#67⋊C4C22semidirect
54. #63970C22semidirect
60. #63964C22semidirect
63. #63958C22semidirect
64. #63918C22semidirect
65. #63891C22semidirect
66. #63883C22semidirect
67. #63880C22semidirect
68. D3×Dic3⋊C4C22semidirect
69. #63854C22semidirect
70. #63851C22semidirect
98. C2×#883D3semidirect
100. C2×#67⋊C4D3semidirect
138. C2×#626D4semidirect
279. #883C2×D3semidirect
281. #67⋊C4C2×D3semidirect
322. C2×C3×Dic3#41semidirect
334. #626C2×D4semidirect
538. C3×Dic3C2×#41semidirect
697. C2×Dic3#235semidirect
723. C2×C32#547semidirect
875. Dic3C2×#235semidirect
877. C32C2×#547semidirect
942. C2×C3#5551semidirect
943. C2×C3#5655semidirect
987. C3C2×#5551semidirect
988. C3C2×#5655semidirect
993. C2#10594188direct (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×#37982
C2×#640922
C2×C3×#8832
C2×C3×#67⋊C42
C2×#639702
C2×#639642
C2×#639582
C2×#639182
C2×#638912
C2×#638832
C2×#638802
C2×D3×Dic3⋊C42
C2×#638542
C2×#638512
#105941882
C2×#56553
C2×#55513