Finite Group Databasebeta

← C2×#10594236 #11910191

Subgroups — C2×#10594236 #11910191

Order 1152.

2901 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63977C211yesmaximal, characteristic, complemented
5C2×#63977C211yesmaximal, characteristic, complemented
6C2×#63971C211yesmaximal, characteristic, complemented
7C2×#63958C211yesmaximal, characteristic, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×#63911C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63886C211yesmaximal, characteristic, complemented
12C2×#63884C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594236C2116yesmaximal, direct product factor
17C2×#5711—31nomaximal
18C2×#5595—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic, complemented
33C22×#624C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C2×C32×C22⋊C4C2211yescharacteristic
36C2×#3752C2211yescharacteristic, complemented
37C2×#3750C2211yescharacteristic, complemented
38#64093C2218yescomplemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#882C2218yescomplemented
48C3×#879C2218yescomplemented
49#63977C2218yescomplemented
50#63977C2218yescomplemented
51#63971C2218yescomplemented
52C2×#3724C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60#63958C2218yescomplemented
61#63916C2218yescomplemented
62#63911C2218yescomplemented
63#63910C2218yescomplemented
64#63886C2218yescomplemented
65#63884C2218yescomplemented
66#63859C2218yescomplemented
67#63854C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#120—31no—
71C2×#953—31no—
72C2×#953—31no—
73C2×#940—31no—
74C2×#939—31no—
75C2×#939—31no—
76C2×#938—31no—
77C2×#938—31no—
78C2×#935—31no—
79#5711—316no—
80#5595—316no—
81C2×#895—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#894—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#884—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—61no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882D311yescharacteristic, complemented
98C2×#879—31no—
99C2×#879D311yescharacteristic, complemented
100C2×#876—31no—
101C2×#874—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3—42no—
106C23×C3×D3—42no—
107C23×C3×D3—42no—
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638—42no—
115C2×#638—42no—
116C2×#638C2314yes—
117C2×#638C2314yes—
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C2×C4⋊(C3⋊D3)—42no—
121C2×C4⋊(C3⋊D3)C2314yescomplemented
122C2×C4×C3⋊D3—42no—
123C2×C4×C3⋊D3C2314yescomplemented
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—42no—
132C2×C3×D12—42no—
133C2×C3×D12C2314yes—
134C2×C3×D12C2314yes—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626—42no—
140C2×#626—42no—
141C2×#626C2314yes—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yescomplemented
146C2×#626C2314yescomplemented
147C2×#624—42no—
148C2×#624C2314yescomplemented
149C2×D3×Dic3—42no—
150C2×D3×Dic3C2314yescomplemented
151C32×C22⋊C4C2314yes—
152#3752C2314yescomplemented
153#3750C2314yescomplemented
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×C4⋊Dic3C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160C3×Dic3⋊C4C2314yescomplemented
161C3×C4×Dic3C2314yescomplemented
162#3724C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164#3722C2314yescomplemented
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yescomplemented
170C2×#560—91noSylow
171C25×C3—31no—
172C24×D3C2×D311yescharacteristic
173C22×C3×D4—31no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×#67—31no—
177C22×#67—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—61no—
187C22×#67—61no—
188C22×#67C2×D311yescharacteristic
189C23×Dic3—31no—
190C22×D12—31no—
191C22×D12—31no—
192C22×D12—31no—
193C22×D12—31no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12—61no—
199C22×D12C2×D311yescharacteristic
200C22×D12C2×D311yescharacteristic
201C22×C4×D3—31no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—61no—
207C3×#126—38no—
208C3×#120—38no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C22⋊C4—21no—
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—31no—
217C2×C3×C22⋊C4C2×D311yescharacteristic
218C2×C3×C22⋊C4C2×D311yescharacteristic
219C2×C3×C42—31no—
220#953—38no—
221#953—38no—
222C2×#217—31no—
223C2×#217—31no—
224C2×#217—31no—
225C2×#217—31no—
226C2×#217—31no—
227C2×#217C2×D311yescharacteristic
228C2×#217C2×D311yescharacteristic
229#940—38no—
230#939—38no—
231#939—38no—
232#938—38no—
233#938—38no—
234#935—38no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
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×C4⋊Dic3—31no—
248C2×C4⋊Dic3C2×D311yescharacteristic, complemented
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—61no—
255C2×Dic3⋊C4C2×D311yescharacteristic, complemented
256C2×Dic3⋊C4C2×D311yescharacteristic, complemented
257C2×C4×Dic3C2×D311yescharacteristic, complemented
258#895—38no—
259#895—38no—
260#895—38no—
261#894—38no—
262#894—38no—
263#894—38no—
264#884—38no—
265#884—38no—
266#884—38no—
267#884—38no—
268#884—38no—
269#884—68no—
270#883—38no—
271#883—38no—
272#882—38no—
273#882—38no—
274#882C2×D318yescomplemented
275#879—38no—
276#879C2×D318yescomplemented
277#876—38no—
278#874—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⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3C2412yes—
291C22×C3⋊D3C2412yes—
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—22no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3—44no—
304C22×C3×D3—416no—
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—
313#638—44no—
314C2×C3⋊Dic3—22no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C4⋊(C3⋊D3)—44no—
319C4×C3⋊D3—44no—
320C3×#67—44no—
321C2×C3×Dic3—22no—
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—
330C2×C3×Dic3C2412yes—
331C3×D12—44no—
332C3×D12—44no—
333#626—44no—
334#626—44no—
335#626—44no—
336#626—44no—
337#626—44no—
338#626—44no—
339#624—44no—
340D3×Dic3—44no—
341#560—916no—
342C2×#127—91no—
343C2×#126—31no—
344C2×#126—91no—
345C2×#123—91no—
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—34no—
362C24×C3—122no—
363C24×C3—122no—
364C24×C3—122no—
365C24×C3C22×D311yescharacteristic
366C24×C3C22×D311yescharacteristic
367C23×D3—31no—
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—42no—
372C23×D3—42no—
373C23×D3—42no—
374C23×D3—61no—
375C23×D3—61no—
376C23×D3C22×D311yescharacteristic
377C23×D3C22×D311yescharacteristic
378C23×D3C22×D311yescharacteristic
379C23×D3C22×D314yes—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—122no—
384C2×C3×D4—122no—
385C2×C3×D4—122no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C2×#67—34no—
398C2×#67—34no—
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—42no—
408C2×#67—64no—
409C2×#67—64no—
410C2×#67—122no—
411C2×#67—122no—
412C2×#67—122no—
413C2×#67—122no—
414C2×#67—122no—
415C2×#67—122no—
416C2×#67—122no—
417C2×#67—122no—
418C2×#67—122no—
419C2×#67—122no—
420C2×#67—124no—
421C2×#67—124no—
422C2×#67C22×D314yes—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—31no—
426C22×Dic3—31no—
427C22×Dic3—34no—
428C22×Dic3—61no—
429C22×Dic3—61no—
430C22×Dic3—122no—
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D311yescharacteristic
435C22×Dic3C22×D311yescharacteristic
436C2×D12—34no—
437C2×D12—34no—
438C2×D12—34no—
439C2×D12—34no—
440C2×D12—34no—
441C2×D12—34no—
442C2×D12—34no—
443C2×D12—34no—
444C2×D12—42no—
445C2×D12—42no—
446C2×D12—64no—
447C2×D12—122no—
448C2×D12—122no—
449C2×D12—124no—
450C2×D12—122no—
451C2×D12—122no—
452C2×D12—122no—
453C2×D12—122no—
454C2×D12—122no—
455C2×D12—122no—
456C2×D12C22×D314yes—
457C2×D12C22×D314yes—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—34no—
462C2×C4×D3—34no—
463C2×C4×D3—64no—
464C2×C4×D3—122no—
465C2×C4×D3—122no—
466C2×C4×D3—122no—
467C2×C4×D3—122no—
468C2×C4×D3—124no—
469C2×C4×D3—122no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C22⋊C4—24no—
474C3×C22⋊C4—34no—
475C3×C22⋊C4—34no—
476C3×C22⋊C4—34no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4C22×D314yes—
479C3×C22⋊C4C22×D314yes—
480C3×C42—34no—
481#217—34no—
482#217—34no—
483#217—34no—
484#217—34no—
485#217—34no—
486#217C22×D314yes—
487#217C22×D314yes—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—34no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—64no—
498(C2×D3)⋊C4C22×D314yes—
499(C2×D3)⋊C4C22×D314yes—
500C4⋊Dic3—34no—
501C4⋊Dic3C22×D314yescomplemented
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—64no—
508Dic3⋊C4C22×D314yescomplemented
509Dic3⋊C4C22×D314yescomplemented
510C4×Dic3C22×D314yescomplemented
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—44no—
515C22×C32H(5,𝔽2)12yes—
516C22×C32H(5,𝔽2)12yes—
517C22×C32H(5,𝔽2)12yes—
518C22×C32C2511yescharacteristic
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—22no—
525C2×C3⋊D3—44no—
526C2×C3⋊D3—44no—
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—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—416no—
537C2×C3×D3—44no—
538C2×C3×D3—44no—
539C2×C3×D3—44no—
540C32×C4—22no—
541C32×C4—22no—
542C3⋊Dic3—22no—
543C3⋊Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C25—31no—
550C22×D4—31no—
551C22×D4—31no—
552C22×D4—31no—
553C22×D4—91no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C23×C4—91no—
563C23×C4—91no—
564C23×C4—91no—
565#127—98no—
566#126—38no—
567#126—98no—
568#123—98no—
569#123—98no—
570#123—98no—
571#121—98no—
572#121—98no—
573#121—98no—
574#121—98no—
575#121—98no—
576#121—98no—
577#120—38no—
578#120—98no—
579#120—98no—
580C2×C4⋊C4—31no—
581C2×C4⋊C4—31no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—91no—
584C2×C4⋊C4—91no—
585C2×C4⋊C4—91no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—31no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4—91no—
592C2×C22⋊C4—91no—
593C2×C22⋊C4—91no—
594C2×C22⋊C4—91no—
595C2×C22⋊C4—91no—
596C2×C22⋊C4—91no—
597C2×C22⋊C4D3211yescharacteristic
598C2×C42—31no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—21no—
607C23×C3—32no—
608C23×C3—32no—
609C23×C3—32no—
610C23×C3—42no—
611C23×C3—42no—
612C23×C3—42no—
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—124no—
623C23×C3—124no—
624C23×C3—124no—
625C23×C3—1216no—
626C23×C3C23×D312yes—
627C23×C3C23×D312yes—
628C23×C3C23×D311yescharacteristic
629C23×C3C23×D311yescharacteristic
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—22no—
639C22×D3—32no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—44no—
644C22×D3—44no—
645C22×D3—44no—
646C22×D3—416no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—64no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—62no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3—122no—
666C22×D3—122no—
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—124no—
671C3×D4—124no—
672C3×D4—124no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—32no—
684C2×C3×C4—42no—
685C2×C3×C4—42no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694C2×C3×C4C23×D312yes—
695#67—44no—
696#67—124no—
697#67—124no—
698#67—124no—
699#67—124no—
700#67—124no—
701#67—124no—
702#67—124no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—128no—
707#67—128no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—22no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3—64no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—122no—
725C2×Dic3—124no—
726C2×Dic3C23×D312yes—
727C2×Dic3C23×D312yes—
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731D12—44no—
732D12—44no—
733D12—124no—
734D12—124no—
735D12—128no—
736D12—124no—
737D12—124no—
738D12—124no—
739D12—124no—
740D12—124no—
741D12—124no—
742C4×D3—124no—
743C4×D3—124no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—128no—
747C4×D3—124no—
748C2×C32—42no—
749C2×C32#56014yescomplemented
750C2×C32C2×H(5,𝔽2)11yescharacteristic
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C3⋊D3—42no—
754C3⋊D3—42no—
755C3×D3—42no—
756C3×D3—42no—
757C3×D3—42no—
758C24—31no—
759C24—31no—
760C24—31no—
761C24—34no—
762C24—91no—
763C24—91no—
764C24—122no—
765C24—122no—
766C24—122no—
767C24C2×D3211yescharacteristic
768C2×D4—34no—
769C2×D4—34no—
770C2×D4—34no—
771C2×D4—94no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—122no—
781C2×D4—122no—
782C2×D4—122no—
783C2×D4—362no—
784C2×D4—362no—
785C2×D4—362no—
786C2×D4—362no—
787C2×D4—362no—
788C2×D4—362no—
789C2×D4—362no—
790C2×D4—362no—
791C2×D4—362no—
792C22×C4—31no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—94no—
798C22×C4—94no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—94no—
802C22×C4—362no—
803C22×C4—362no—
804C22×C4—362no—
805C22×C4C2×D3211yescharacteristic
806C22×C4C2×D3211yescharacteristic
807C4⋊C4—34no—
808C4⋊C4—34no—
809C4⋊C4—34no—
810C4⋊C4—94no—
811C4⋊C4—94no—
812C4⋊C4—94no—
813C22⋊C4—34no—
814C22⋊C4—34no—
815C22⋊C4—34no—
816C22⋊C4—34no—
817C22⋊C4—94no—
818C22⋊C4—94no—
819C22⋊C4—94no—
820C22⋊C4—94no—
821C22⋊C4—94no—
822C22⋊C4—94no—
823C22⋊C4—94no—
824C22⋊C4C2×D3214yes—
825C42—34no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—42no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—44no—
840C22×C3—44no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—84no—
851C22×C3—1216no—
852C22×C3—124no—
853C22×C3—124no—
854C22×C3—124no—
855C22×C3#100412yes—
856C22×C3#100412yes—
857C22×C3#100412yes—
858C22×C3#100912yes—
859C22×C3#100912yes—
860C22×C3#100912yes—
861C22×C3C24×D311yescharacteristic
862C22×C3C24×D311yescharacteristic
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—416no—
873C2×D3—44no—
874C2×D3—44no—
875C2×D3—44no—
876C2×D3—64no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—128no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3—124no—
899C2×D3—244no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—22no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—62no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—22no—
915Dic3—22no—
916Dic3—64no—
917Dic3—62no—
918Dic3—62no—
919Dic3—62no—
920Dic3—62no—
921Dic3—122no—
922C32C2×#56011yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—32no—
927C23—32no—
928C23—32no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—92no—
939C23—92no—
940C23—124no—
941C23—124no—
942C23—124no—
943C23—1216no—
944C23—182no—
945C23—182no—
946C23—182no—
947C23—182no—
948C23—182no—
949C23—182no—
950C23C22×D3212yes—
951C23C22×D3211yescharacteristic
952D4—124no—
953D4—124no—
954D4—124no—
955D4—364no—
956D4—364no—
957D4—364no—
958D4—364no—
959D4—364no—
960D4—364no—
961D4—364no—
962D4—364no—
963D4—364no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—32no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—62no—
975C2×C4—62no—
976C2×C4—92no—
977C2×C4—92no—
978C2×C4—182no—
979C2×C4—182no—
980C2×C4—364no—
981C2×C4—364no—
982C2×C4—364no—
983C2×C4C22×D3212yes—
984C2×C4C22×D3212yes—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—24no—
989C2×C3—42no—
990C2×C3—42no—
991C2×C3—82no—
992C2×C3—122no—
993C2×C3—122no—
994C2×C3—122no—
995C2×C3#559514yescomplemented
996C2×C3#571114yescomplemented
997C2×C3C2×#100411yescharacteristic
998C2×C3C2×#100411yescharacteristic
999C2×C3C2×#100411yescharacteristic
1000C2×C3C2×#100911yescharacteristic
1001C2×C3C2×#100911yescharacteristic
1002C2×C3C2×#100911yescharacteristic
1003D3—42no—
1004D3—42no—
1005D3—42no—
1006D3—124no—
1007D3—122no—
1008D3—122no—
1009D3—122no—
1010D3—122no—
1011D3—242no—
1012C22—22no—
1013C22—22no—
1014C22—22no—
1015C22—44no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—1216no—
1026C22—124no—
1027C22—124no—
1028C22—124no—
1029C22—182no—
1030C22—182no—
1031C22—182no—
1032C22—182no—
1033C22—182no—
1034C22—182no—
1035C22—364no—
1036C22—364no—
1037C22#6430712yes—
1038C22#6431412yes—
1039C22#6431412yes—
1040C22C23×D3211yescharacteristic
1041C4—22no—
1042C4—22no—
1043C4—62no—
1044C4—62no—
1045C4—62no—
1046C4—62no—
1047C4—62no—
1048C4—182no—
1049C4—182no—
1050C3—21no—
1051C3C2×#559511yescharacteristic, complemented
1052C3C2×#571111yescharacteristic, complemented
1053C2—42no—
1054C2—122no—
1055C2—122no—
1056C2—122no—
1057C2—362no—
1058C2—362no—
1059C2#1059423614yesdirect product factor
1060C2C2×#6430711yescharacteristic
1061C2C2×#6431411yescharacteristic
1062C2C2×#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×#64093C2semidirect
2. C2×C3×#882C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63977C2semidirect
5. C2×#63977C2semidirect
6. C2×#63971C2semidirect
7. C2×#63958C2semidirect
8. C2×#63916C2semidirect
9. C2×#63911C2semidirect
10. C2×#63910C2semidirect
11. C2×#63886C2semidirect
12. C2×#63884C2semidirect
13. C2×#63859C2semidirect
14. C2×#63854C2semidirect
15. C2×#63853C2semidirect
16. #10594236C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4×C3⋊D3C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
33. C22×#624C22semidirect
34. C22×D3×Dic3C22semidirect
36. C2×#3752C22semidirect
37. C2×#3750C22semidirect
38. #64093C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#882C22semidirect
48. C3×#879C22semidirect
49. #63977C22semidirect
50. #63977C22semidirect
51. #63971C22semidirect
52. C2×#3724C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. #63958C22semidirect
61. #63916C22semidirect
62. #63911C22semidirect
63. #63910C22semidirect
64. #63886C22semidirect
65. #63884C22semidirect
66. #63859C22semidirect
67. #63854C22semidirect
68. #63853C22semidirect
97. C2×#882D3semidirect
99. C2×#879D3semidirect
121. C2×C4⋊(C3⋊D3)C23semidirect
123. C2×C4×C3⋊D3C23semidirect
145. C2×#626C23semidirect
146. C2×#626C23semidirect
148. C2×#624C23semidirect
150. C2×D3×Dic3C23semidirect
152. #3752C23semidirect
153. #3750C23semidirect
158. C3×C4⋊Dic3C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. C3×Dic3⋊C4C23semidirect
161. C3×C4×Dic3C23semidirect
162. #3724C23semidirect
163. Dic3⋊Dic3C23semidirect
164. #3722C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
248. C2×C4⋊Dic3C2×D3semidirect
255. C2×Dic3⋊C4C2×D3semidirect
256. C2×Dic3⋊C4C2×D3semidirect
257. C2×C4×Dic3C2×D3semidirect
274. #882C2×D3semidirect
276. #879C2×D3semidirect
501. C4⋊Dic3C22×D3semidirect
508. Dic3⋊C4C22×D3semidirect
509. Dic3⋊C4C22×D3semidirect
510. C4×Dic3C22×D3semidirect
749. C2×C32#560semidirect
922. C32C2×#560semidirect
995. C2×C3#5595semidirect
996. C2×C3#5711semidirect
1051. C3C2×#5595semidirect
1052. C3C2×#5711semidirect
1059. C2#10594236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640932
C2×C3×#8822
C2×C3×#8792
C2×#639772
C2×#639712
C2×#639582
C2×#639162
C2×#639112
C2×#639102
C2×#638862
C2×#638842
C2×#638592
C2×#638542
C2×#638532
#105942362
C2×#57113
C2×#55953