Finite Group Databasebeta

← C2×#10594233 #11910185

Subgroups — C2×#10594233 #11910185

Order 1152.

2859 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64092C211yesmaximal, characteristic, complemented
2C2×C3×#883C211yesmaximal, characteristic, complemented
3C2×C3×#882C211yesmaximal, characteristic, complemented
4C2×#63979C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63969C211yesmaximal, characteristic, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×#63912C211yesmaximal, characteristic, complemented
10C2×#63908C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16#10594233C2116yesmaximal, direct product factor
17C2×#5666—31nomaximal
18C2×#5595—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic, complemented
30C22×#626C2211yescharacteristic, complemented
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37C2×#3752C2211yescharacteristic, complemented
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C2×#3750C2211yescharacteristic, complemented
40#64092C2218yescomplemented
41C2×C3×#217C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#883C2218yescomplemented
48C3×#882C2218yescomplemented
49#63979C2218yescomplemented
50#63977C2218yescomplemented
51#63976C2218yescomplemented
52#63969C2218yescomplemented
53C2×#3724C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63916C2218yescomplemented
62#63912C2218yescomplemented
63#63908C2218yescomplemented
64#63906C2218yescomplemented
65#63886C2218yescomplemented
66#63885C2218yescomplemented
67#63861C2218yescomplemented
68#63858C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#940—31no—
74C2×#940—31no—
75C2×#939—31no—
76C2×#939—31no—
77C2×#938—31no—
78C2×#938—31no—
79C2×#937—31no—
80C2×#935—31no—
81C2×#930—31no—
82C2×#930—31no—
83#5666—316no—
84#5595—316no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#895—31no—
88C2×#895—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—61no—
97C2×#883D311yescharacteristic, complemented
98C2×#882—31no—
99C2×#882D311yescharacteristic, complemented
100C2×#879—31no—
101C2×#879—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3—42no—
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638—42no—
115C2×#638C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×C4×C3⋊D3—42no—
120C2×C4×C3⋊D3C2314yescomplemented
121C2×C3×#67—42no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—42no—
130C2×C3×D12—42no—
131C2×C3×D12C2314yes—
132C2×C3×D12C2314yes—
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yescomplemented
135C2×#626—42no—
136C2×#626—42no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yescomplemented
142C2×#626C2314yescomplemented
143C2×#625—42no—
144C2×#625—42no—
145C2×#625—42no—
146C2×#625C2314yes—
147C2×#625C2314yes—
148C2×#625C2314yescomplemented
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151C32×C22⋊C4C2314yes—
152#3757C2314yes—
153#3752C2314yescomplemented
154C4⋊(C3⋊Dic3)C2314yescomplemented
155#3750C2314yescomplemented
156C3×#217C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yescomplemented
160C3×C4⋊Dic3C2314yescomplemented
161C3×Dic3⋊C4C2314yescomplemented
162#3724C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yescomplemented
169Dic32C2314yescomplemented
170C2×#560—91noSylow
171C25×C3—31no—
172C24×D3C2×D311yescharacteristic
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—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—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—61no—
191C22×#67C2×D311yescharacteristic
192C22×#67C2×D311yescharacteristic
193C23×Dic3—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12C2×D311yescharacteristic
199C22×D12C2×D311yescharacteristic
200C22×C4×D3—31no—
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—61no—
204C22×C4×D3C2×D311yescharacteristic, complemented
205C3×#123—38no—
206C3×#120—38no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C22⋊C4—21no—
210C2×C3×C22⋊C4—31no—
211C2×C3×C22⋊C4—31no—
212C2×C3×C22⋊C4—31no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4C2×D311yescharacteristic
215C2×C3×C22⋊C4C2×D311yescharacteristic
216#953—38no—
217#953—38no—
218C2×#217—31no—
219C2×#217—31no—
220C2×#217—31no—
221C2×#217—31no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—61no—
226C2×#217C2×D311yescharacteristic
227#940—38no—
228#940—38no—
229#939—38no—
230#939—38no—
231#938—38no—
232#938—38no—
233#937—38no—
234#935—38no—
235#930—38no—
236#930—38no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—61no—
245C2×(C2×D3)⋊C4C2×D311yescharacteristic
246C2×(C2×D3)⋊C4C2×D311yescharacteristic
247C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3—31no—
251C2×C4⋊Dic3—61no—
252C2×C4⋊Dic3C2×D311yescharacteristic, complemented
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—61no—
259C2×Dic3⋊C4C2×D311yescharacteristic, complemented
260C2×C4×Dic3—31no—
261C2×C4×Dic3—31no—
262#898—38no—
263#898—38no—
264#895—38no—
265#895—38no—
266#884—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#883—38no—
271#883—38no—
272#883—38no—
273#883—68no—
274#883C2×D318yescomplemented
275#882—38no—
276#882C2×D318yescomplemented
277#879—38no—
278#879—38no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2411yescharacteristic
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3C2412yes—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—416no—
304C22×C3×D3C2412yes—
305C22×C3×D3C2412yes—
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C2×C32×C4—22no—
309C2×C32×C4—22no—
310C2×C32×C4C2412yes—
311C2×C32×C4C2412yes—
312#638—44no—
313C2×C3⋊Dic3—22no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C4×C3⋊D3—44no—
320C3×#67—44no—
321C3×#67—44no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C3×D12—44no—
331C3×D12—44no—
332C3×C4×D3—44no—
333#626—44no—
334#626—44no—
335#626—44no—
336#626—44no—
337#625—44no—
338#625—44no—
339#625—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—91no—
344C2×#126—91no—
345C2×#123—31no—
346C2×#123—91no—
347C2×#123—91no—
348C2×#121—91no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—31no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3—31no—
361C24×C3—31no—
362C24×C3—34no—
363C24×C3—122no—
364C24×C3—122no—
365C24×C3—122no—
366C24×C3C22×D311yescharacteristic
367C24×C3C22×D311yescharacteristic
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—42no—
371C23×D3—42no—
372C23×D3—42no—
373C23×D3—61no—
374C23×D3C22×D311yescharacteristic
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D314yes—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—122no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C2×C3×D4—122no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—34no—
394C22×C3×C4—122no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—42no—
412C2×#67—42no—
413C2×#67—64no—
414C2×#67—122no—
415C2×#67—122no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
419C2×#67—122no—
420C2×#67—122no—
421C2×#67—122no—
422C2×#67—122no—
423C2×#67—122no—
424C2×#67—122no—
425C2×#67—122no—
426C2×#67—124no—
427C2×#67C22×D314yes—
428C2×#67C22×D314yes—
429C22×Dic3—31no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—31no—
434C22×Dic3—31no—
435C22×Dic3—34no—
436C22×Dic3—61no—
437C22×Dic3—61no—
438C22×Dic3—61no—
439C22×Dic3—122no—
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443C22×Dic3C22×D311yescharacteristic
444C2×D12—34no—
445C2×D12—34no—
446C2×D12—34no—
447C2×D12—34no—
448C2×D12—42no—
449C2×D12—42no—
450C2×D12—122no—
451C2×D12—122no—
452C2×D12—122no—
453C2×D12—122no—
454C2×D12C22×D314yes—
455C2×D12C22×D314yes—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—42no—
460C2×C4×D3—64no—
461C2×C4×D3—122no—
462C2×C4×D3—122no—
463C2×C4×D3—122no—
464C2×C4×D3—124no—
465C2×C4×D3C22×D314yescomplemented
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⋊C4—34no—
473C3×C22⋊C4C22×D314yes—
474C3×C22⋊C4C22×D314yes—
475#217—34no—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—34no—
481#217—34no—
482#217—64no—
483#217C22×D314yes—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—64no—
492(C2×D3)⋊C4C22×D314yes—
493(C2×D3)⋊C4C22×D314yes—
494(C2×D3)⋊C4C22×D314yescomplemented
495C4⋊Dic3—34no—
496C4⋊Dic3—34no—
497C4⋊Dic3—34no—
498C4⋊Dic3—64no—
499C4⋊Dic3C22×D314yescomplemented
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—64no—
506Dic3⋊C4C22×D314yescomplemented
507C4×Dic3—34no—
508C4×Dic3—34no—
509C22×C32—22no—
510C22×C32—22no—
511C22×C32—22no—
512C22×C32—44no—
513C22×C32H(5,𝔽2)12yes—
514C22×C32H(5,𝔽2)12yes—
515C22×C32H(5,𝔽2)12yes—
516C22×C32C2511yescharacteristic
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—44no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—416no—
534C2×C3×D3—44no—
535C2×C3×D3—44no—
536C2×C3×D3—44no—
537C2×C3×D3—44no—
538C32×C4—22no—
539C32×C4—22no—
540C3⋊Dic3—22no—
541C3⋊Dic3—22no—
542C3⋊Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C25—31no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—91no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C23×C4—31no—
561C23×C4—91no—
562C23×C4—91no—
563#127—98no—
564#126—98no—
565#126—98no—
566#123—38no—
567#123—98no—
568#123—98no—
569#121—98no—
570#121—98no—
571#121—98no—
572#121—98no—
573#121—98no—
574#121—98no—
575#120—38no—
576#120—98no—
577#120—98no—
578C2×C4⋊C4—31no—
579C2×C4⋊C4—31no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C4⋊C4—91no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4D3211yescharacteristic
596C2×C42—91no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—21no—
605C23×C3—32no—
606C23×C3—32no—
607C23×C3—32no—
608C23×C3—32no—
609C23×C3—42no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—62no—
613C23×C3—62no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3—62no—
620C23×C3—62no—
621C23×C3—62no—
622C23×C3—62no—
623C23×C3—62no—
624C23×C3—124no—
625C23×C3—124no—
626C23×C3—124no—
627C23×C3—1216no—
628C23×C3C23×D312yes—
629C23×C3C23×D312yes—
630C23×C3C23×D311yescharacteristic
631C23×C3C23×D311yescharacteristic
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
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—22no—
644C22×D3—32no—
645C22×D3—32no—
646C22×D3—44no—
647C22×D3—44no—
648C22×D3—44no—
649C22×D3—416no—
650C22×D3—62no—
651C22×D3—64no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3C23×D312yes—
661C22×D3C23×D312yes—
662C22×D3C23×D312yes—
663C22×D3C23×D312yes—
664C3×D4—124no—
665C3×D4—124no—
666C3×D4—124no—
667C3×D4—124no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—32no—
675C2×C3×C4—32no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—42no—
679C2×C3×C4—42no—
680C2×C3×C4—62no—
681C2×C3×C4—62no—
682C2×C3×C4—62no—
683C2×C3×C4—62no—
684C2×C3×C4—124no—
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D312yes—
689#67—44no—
690#67—44no—
691#67—124no—
692#67—124no—
693#67—124no—
694#67—124no—
695#67—124no—
696#67—124no—
697#67—124no—
698#67—124no—
699#67—124no—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—128no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—22no—
707C2×Dic3—22no—
708C2×Dic3—32no—
709C2×Dic3—32no—
710C2×Dic3—32no—
711C2×Dic3—32no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—62no—
715C2×Dic3—62no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—122no—
724C2×Dic3—122no—
725C2×Dic3—122no—
726C2×Dic3—124no—
727C2×Dic3C23×D312yes—
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731D12—44no—
732D12—44no—
733D12—124no—
734D12—124no—
735D12—124no—
736D12—124no—
737C4×D3—44no—
738C4×D3—124no—
739C4×D3—124no—
740C4×D3—124no—
741C4×D3—128no—
742C2×C32—42no—
743C2×C32#56014yescomplemented
744C2×C32C2×H(5,𝔽2)11yescharacteristic
745C2×C32C2×H(5,𝔽2)11yescharacteristic
746C2×C32C2×H(5,𝔽2)11yescharacteristic
747C3⋊D3—42no—
748C3×D3—42no—
749C3×D3—42no—
750C3×D3—42no—
751C3×D3—42no—
752C24—31no—
753C24—31no—
754C24—31no—
755C24—31no—
756C24—34no—
757C24—91no—
758C24—122no—
759C24—122no—
760C24—122no—
761C24C2×D3211yescharacteristic
762C2×D4—34no—
763C2×D4—34no—
764C2×D4—34no—
765C2×D4—34no—
766C2×D4—94no—
767C2×D4—94no—
768C2×D4—94no—
769C2×D4—94no—
770C2×D4—94no—
771C2×D4—94no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—122no—
775C2×D4—122no—
776C2×D4—122no—
777C2×D4—122no—
778C2×D4—362no—
779C2×D4—362no—
780C2×D4—362no—
781C2×D4—362no—
782C2×D4—362no—
783C2×D4—362no—
784C2×D4—362no—
785C2×D4—362no—
786C22×C4—31no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—34no—
791C22×C4—94no—
792C22×C4—91no—
793C22×C4—91no—
794C22×C4—91no—
795C22×C4—94no—
796C22×C4—122no—
797C22×C4—362no—
798C22×C4—362no—
799C22×C4C2×D3211yescharacteristic
800C22×C4C2×D3211yescharacteristic
801C4⋊C4—34no—
802C4⋊C4—34no—
803C4⋊C4—94no—
804C4⋊C4—94no—
805C4⋊C4—94no—
806C4⋊C4—94no—
807C22⋊C4—34no—
808C22⋊C4—34no—
809C22⋊C4—34no—
810C22⋊C4—34no—
811C22⋊C4—94no—
812C22⋊C4—94no—
813C22⋊C4—94no—
814C22⋊C4—94no—
815C22⋊C4—94no—
816C22⋊C4—94no—
817C22⋊C4—94no—
818C22⋊C4C2×D3214yes—
819C42—94no—
820C22×C3—22no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—21no—
830C22×C3—42no—
831C22×C3—42no—
832C22×C3—42no—
833C22×C3—44no—
834C22×C3—44no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—84no—
848C22×C3—1216no—
849C22×C3—124no—
850C22×C3—124no—
851C22×C3—124no—
852C22×C3—124no—
853C22×C3#100412yes—
854C22×C3#100412yes—
855C22×C3#100412yes—
856C22×C3#100412yes—
857C22×C3#100912yes—
858C22×C3#100912yes—
859C22×C3C24×D311yescharacteristic
860C22×C3C24×D311yescharacteristic
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—416no—
874C2×D3—44no—
875C2×D3—44no—
876C2×D3—44no—
877C2×D3—44no—
878C2×D3—64no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3—128no—
888C2×D3—124no—
889C2×D3—124no—
890C3×C4—22no—
891C3×C4—22no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—42no—
895C3×C4—42no—
896C3×C4—62no—
897C3×C4—62no—
898C3×C4—62no—
899C3×C4—62no—
900Dic3—22no—
901Dic3—22no—
902Dic3—22no—
903Dic3—22no—
904Dic3—62no—
905Dic3—62no—
906Dic3—62no—
907Dic3—62no—
908Dic3—62no—
909Dic3—62no—
910Dic3—122no—
911Dic3—122no—
912Dic3—122no—
913C32C2×#56011yescharacteristic, complemented, Sylow
914C23—22no—
915C23—22no—
916C23—22no—
917C23—32no—
918C23—32no—
919C23—32no—
920C23—32no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—92no—
934C23—124no—
935C23—124no—
936C23—124no—
937C23—1216no—
938C23—182no—
939C23—182no—
940C23—182no—
941C23C22×D3212yes—
942C23C22×D3211yescharacteristic
943D4—124no—
944D4—124no—
945D4—124no—
946D4—124no—
947D4—364no—
948D4—364no—
949D4—364no—
950D4—364no—
951D4—364no—
952D4—364no—
953D4—364no—
954D4—364no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—92no—
966C2×C4—92no—
967C2×C4—92no—
968C2×C4—124no—
969C2×C4—182no—
970C2×C4—182no—
971C2×C4—182no—
972C2×C4—364no—
973C2×C4—364no—
974C2×C4C22×D3212yes—
975C2×C4C22×D3212yes—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—24no—
980C2×C3—42no—
981C2×C3—42no—
982C2×C3—82no—
983C2×C3—122no—
984C2×C3—122no—
985C2×C3—122no—
986C2×C3—122no—
987C2×C3#559514yescomplemented
988C2×C3#566614yescomplemented
989C2×C3C2×#100411yescharacteristic
990C2×C3C2×#100411yescharacteristic
991C2×C3C2×#100411yescharacteristic
992C2×C3C2×#100411yescharacteristic
993C2×C3C2×#100911yescharacteristic
994C2×C3C2×#100911yescharacteristic
995D3—42no—
996D3—42no—
997D3—42no—
998D3—42no—
999D3—124no—
1000D3—122no—
1001D3—122no—
1002C22—22no—
1003C22—22no—
1004C22—22no—
1005C22—44no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—1216no—
1019C22—124no—
1020C22—124no—
1021C22—124no—
1022C22—124no—
1023C22—182no—
1024C22—182no—
1025C22—182no—
1026C22—364no—
1027C22#6430712yes—
1028C22#6431312yes—
1029C22#6431412yes—
1030C22C23×D3211yescharacteristic
1031C4—22no—
1032C4—22no—
1033C4—62no—
1034C4—62no—
1035C4—62no—
1036C4—62no—
1037C4—182no—
1038C4—182no—
1039C4—182no—
1040C3—21no—
1041C3C2×#559511yescharacteristic, complemented
1042C3C2×#566611yescharacteristic, complemented
1043C2—42no—
1044C2—122no—
1045C2—122no—
1046C2—122no—
1047C2—122no—
1048C2—362no—
1049C2#1059423314yesdirect product factor
1050C2C2×#6430711yescharacteristic
1051C2C2×#6431311yescharacteristic
1052C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64092C2semidirect
2. C2×C3×#883C2semidirect
3. C2×C3×#882C2semidirect
4. C2×#63979C2semidirect
5. C2×#63977C2semidirect
6. C2×#63976C2semidirect
7. C2×#63969C2semidirect
8. C2×#63916C2semidirect
9. C2×#63912C2semidirect
10. C2×#63908C2semidirect
11. C2×#63906C2semidirect
12. C2×#63886C2semidirect
13. C2×#63885C2semidirect
14. C2×#63861C2semidirect
15. C2×#63858C2semidirect
16. #10594233C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
26. C22×C3×C4×D3C22semidirect
29. C22×#626C22semidirect
30. C22×#626C22semidirect
33. C22×#625C22semidirect
34. C22×D3×Dic3C22semidirect
37. C2×#3752C22semidirect
38. C2×C4⋊(C3⋊Dic3)C22semidirect
39. C2×#3750C22semidirect
40. #64092C22semidirect
44. C2×C3×(C2×D3)⋊C4C22semidirect
45. C2×C3×C4⋊Dic3C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#883C22semidirect
48. C3×#882C22semidirect
49. #63979C22semidirect
50. #63977C22semidirect
51. #63976C22semidirect
52. #63969C22semidirect
53. C2×#3724C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63916C22semidirect
62. #63912C22semidirect
63. #63908C22semidirect
64. #63906C22semidirect
65. #63886C22semidirect
66. #63885C22semidirect
67. #63861C22semidirect
68. #63858C22semidirect
97. C2×#883D3semidirect
99. C2×#882D3semidirect
120. C2×C4×C3⋊D3C23semidirect
134. C2×C3×C4×D3C23semidirect
141. C2×#626C23semidirect
142. C2×#626C23semidirect
148. C2×#625C23semidirect
150. C2×D3×Dic3C23semidirect
153. #3752C23semidirect
154. C4⋊(C3⋊Dic3)C23semidirect
155. #3750C23semidirect
159. C3×(C2×D3)⋊C4C23semidirect
160. C3×C4⋊Dic3C23semidirect
161. C3×Dic3⋊C4C23semidirect
162. #3724C23semidirect
163. Dic3⋊Dic3C23semidirect
168. (C2×D3)⋊Dic3C23semidirect
169. Dic32C23semidirect
204. C22×C4×D3C2×D3semidirect
247. C2×(C2×D3)⋊C4C2×D3semidirect
252. C2×C4⋊Dic3C2×D3semidirect
259. C2×Dic3⋊C4C2×D3semidirect
274. #883C2×D3semidirect
276. #882C2×D3semidirect
465. C2×C4×D3C22×D3semidirect
494. (C2×D3)⋊C4C22×D3semidirect
499. C4⋊Dic3C22×D3semidirect
506. Dic3⋊C4C22×D3semidirect
743. C2×C32#560semidirect
913. C32C2×#560semidirect
987. C2×C3#5595semidirect
988. C2×C3#5666semidirect
1041. C3C2×#5595semidirect
1042. C3C2×#5666semidirect
1049. C2#10594233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640922
C2×C3×#8832
C2×C3×#8822
C2×#639792
C2×#639772
C2×#639762
C2×#639692
C2×#639162
C2×#639122
C2×#639082
C2×#639062
C2×#638862
C2×#638852
C2×#638612
C2×#638582
#105942332
C2×#56663
C2×#55953