Finite Group Databasebeta

← C2×#10594242 #11910192

Subgroups — C2×#10594242 #11910192

Order 1152.

3019 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64091C211yesmaximal, characteristic, complemented
2C2×C3×#884C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63971C211yesmaximal, characteristic, complemented
7C2×#63958C211yesmaximal, characteristic, complemented
8C2×#63911C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63909C211yesmaximal, characteristic, complemented
11C2×#63897C211yesmaximal, characteristic, complemented
12C2×#63890C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594242C2116yesmaximal, direct product factor
17C2×#5711—31nomaximal
18C2×#5620—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
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
37C2×#3752C2211yescharacteristic
38#64091C2218yescomplemented
39C2×C3×#217C2211yescharacteristic
40C2×C3×#217C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47C3×#884C2218yescomplemented
48C3×#879C2218yescomplemented
49#63981C2218yescomplemented
50#63981C2218yescomplemented
51#63971C2218yescomplemented
52C2×#3724C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60#63958C2218yescomplemented
61#63911C2218yescomplemented
62#63910C2218yescomplemented
63#63909C2218yescomplemented
64#63897C2218yescomplemented
65#63890C2218yescomplemented
66#63886C2218yescomplemented
67#63868C2218yescomplemented
68#63850C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#121—31no—
71C2×#940—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#930—31no—
78C2×#929—31no—
79#5711—316no—
80#5620—316no—
81C2×#898—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#895—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#886—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884D311yescharacteristic, complemented
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—61no—
99C2×#879D311yescharacteristic, complemented
100C2×#876—31no—
101C2×#874—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—42no—
104C23×C3⋊D3—42no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638—42no—
115C2×#638C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)—42no—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4⋊(C3⋊D3)C2314yes—
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
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—42no—
132C2×C3×D12C2314yescomplemented
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yescomplemented
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#3752C2314yes—
153#3752C2314yes—
154C3×#217C2314yes—
155C3×#217C2314yes—
156C3×(C2×D3)⋊C4C2314yescomplemented
157C3×C4⋊Dic3C2314yescomplemented
158C3×Dic3⋊C4C2314yescomplemented
159C3×Dic3⋊C4C2314yescomplemented
160C3×Dic3⋊C4C2314yescomplemented
161C3×C4×Dic3C2314yescomplemented
162#3724C2314yescomplemented
163Dic3⋊Dic3C2314yescomplemented
164#3722C2314yes—
165#3722C2314yes—
166#3722C2314yes—
167#3722C2314yes—
168#3722C2314yescomplemented
169(C2×D3)⋊Dic3C2314yescomplemented
170C2×#560—91noSylow
171C24×D3—31no—
172C24×D3—31no—
173C24×D3—61no—
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—61no—
187C22×#67C2×D311yescharacteristic
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—31no—
199C22×D12—31no—
200C22×D12—61no—
201C22×D12—61no—
202C22×D12C2×D311yescharacteristic, complemented
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3C2×D311yescharacteristic, complemented
207C3×#126—38no—
208C3×#121—38no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4—31no—
212C2×C3×C4⋊C4—31no—
213C2×C3×C22⋊C4—21no—
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—
220C2×#217—31no—
221C2×#217C2×D311yescharacteristic
222C2×#217C2×D311yescharacteristic
223#940—38no—
224#939—38no—
225#939—38no—
226#938—38no—
227#937—38no—
228#937—38no—
229#930—38no—
230#929—38no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
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—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—61no—
247C2×(C2×D3)⋊C4—61no—
248C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
249C2×C4⋊Dic3—31no—
250C2×C4⋊Dic3C2×D311yescharacteristic, complemented
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255C2×Dic3⋊C4C2×D311yescharacteristic, complemented
256C2×Dic3⋊C4C2×D311yescharacteristic, complemented
257C2×C4×Dic3C2×D311yescharacteristic, complemented
258#898—38no—
259#895—38no—
260#895—38no—
261#895—38no—
262#894—38no—
263#894—38no—
264#894—38no—
265#894—38no—
266#886—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#884C2×D318yescomplemented
271#882—38no—
272#882—38no—
273#882—38no—
274#882—38no—
275#882—68no—
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⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—44no—
294C22×C3⋊D3—44no—
295C22×C3⋊D3—44no—
296C22×C3⋊D3—416no—
297C22×C3⋊D3C2412yes—
298C22×C3⋊D3C2412yes—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
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⋊Dic3C2412yes—
315C4⋊(C3⋊D3)—44no—
316C4⋊(C3⋊D3)—44no—
317C3×#67—44no—
318C3×#67—44no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C3×D12—44no—
332C3×C4×D3—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—31no—
349C2×#121—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×#121—91no—
353C2×#121—91no—
354C2×#120—91no—
355C2×#120—91no—
356C2×#120—91no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3—31no—
360C24×C3C22×D311yescharacteristic
361C24×C3C22×D311yescharacteristic
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—31no—
366C23×D3—31no—
367C23×D3—31no—
368C23×D3—34no—
369C23×D3—34no—
370C23×D3—61no—
371C23×D3—61no—
372C23×D3—64no—
373C23×D3—61no—
374C23×D3—122no—
375C23×D3—122no—
376C23×D3—122no—
377C23×D3—122no—
378C23×D3—122no—
379C23×D3—122no—
380C23×D3—124no—
381C23×D3—124no—
382C23×D3—124no—
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—34no—
388C2×C3×D4—122no—
389C2×C3×D4—122no—
390C2×C3×D4—122no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—34no—
400C22×C3×C4—122no—
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
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—42no—
414C2×#67—42no—
415C2×#67—64no—
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—124no—
425C2×#67C22×D314yes—
426C2×#67C22×D314yes—
427C22×Dic3—31no—
428C22×Dic3—31no—
429C22×Dic3—34no—
430C22×Dic3—61no—
431C22×Dic3—122no—
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D311yescharacteristic
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C2×D12—34no—
439C2×D12—34no—
440C2×D12—34no—
441C2×D12—34no—
442C2×D12—34no—
443C2×D12—34no—
444C2×D12—34no—
445C2×D12—34no—
446C2×D12—34no—
447C2×D12—34no—
448C2×D12—42no—
449C2×D12—64no—
450C2×D12—64no—
451C2×D12—122no—
452C2×D12—122no—
453C2×D12—122no—
454C2×D12—122no—
455C2×D12—124no—
456C2×D12—124no—
457C2×D12—122no—
458C2×D12—122no—
459C2×D12—122no—
460C2×D12—122no—
461C2×D12—122no—
462C2×D12—122no—
463C2×D12C22×D314yescomplemented
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—42no—
468C2×C4×D3—122no—
469C2×C4×D3—122no—
470C2×C4×D3—122no—
471C2×C4×D3C22×D314yescomplemented
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C4⋊C4—34no—
475C3×C4⋊C4—34no—
476C3×C22⋊C4—24no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4C22×D314yes—
481C3×C22⋊C4C22×D314yes—
482C3×C42—34no—
483#217—34no—
484#217C22×D314yes—
485#217C22×D314yes—
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—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—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—64no—
502(C2×D3)⋊C4—64no—
503(C2×D3)⋊C4C22×D314yescomplemented
504C4⋊Dic3—34no—
505C4⋊Dic3C22×D314yescomplemented
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4C22×D314yescomplemented
510Dic3⋊C4C22×D314yescomplemented
511Dic3⋊C4C22×D314yescomplemented
512C4×Dic3C22×D314yescomplemented
513C22×C32—22no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—44no—
517C22×C32H(5,𝔽2)12yes—
518C22×C32H(5,𝔽2)12yes—
519C22×C32H(5,𝔽2)12yes—
520C22×C32C2511yescharacteristic
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—416no—
531C2×C3⋊D3—44no—
532C2×C3⋊D3—44no—
533C2×C3⋊D3—44no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—44no—
541C2×C3×D3—44no—
542C32×C4—22no—
543C32×C4—22no—
544C3⋊Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C25—91no—
552C22×D4—31no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—91no—
556C22×D4—91no—
557C22×D4—91no—
558C22×D4—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—91no—
563C22×D4—91no—
564C23×C4—31no—
565C23×C4—91no—
566C23×C4—91no—
567#127—98no—
568#126—38no—
569#126—98no—
570#123—98no—
571#123—98no—
572#123—98no—
573#121—38no—
574#121—98no—
575#121—98no—
576#121—98no—
577#121—98no—
578#121—98no—
579#120—98no—
580#120—98no—
581#120—98no—
582C2×C4⋊C4—31no—
583C2×C4⋊C4—31no—
584C2×C4⋊C4—31no—
585C2×C4⋊C4—31no—
586C2×C4⋊C4—91no—
587C2×C4⋊C4—91no—
588C2×C22⋊C4—31no—
589C2×C22⋊C4—31no—
590C2×C22⋊C4—31no—
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⋊C4—91no—
598C2×C22⋊C4—91no—
599C2×C22⋊C4D3211yescharacteristic
600C2×C42—31no—
601C23×C3—24no—
602C23×C3—22no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—22no—
606C23×C3—22no—
607C23×C3—22no—
608C23×C3—22no—
609C23×C3—21no—
610C23×C3—32no—
611C23×C3—32no—
612C23×C3—42no—
613C23×C3—42no—
614C23×C3—62no—
615C23×C3—62no—
616C23×C3—62no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3—62no—
620C23×C3C23×D312yes—
621C23×C3C23×D312yes—
622C23×C3C23×D311yescharacteristic
623C23×C3C23×D311yescharacteristic
624C22×D3—22no—
625C22×D3—22no—
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—32no—
631C22×D3—32no—
632C22×D3—32no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—32no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—64no—
640C22×D3—64no—
641C22×D3—62no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
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—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3—122no—
666C22×D3—124no—
667C22×D3—124no—
668C22×D3—124no—
669C22×D3—124no—
670C22×D3—124no—
671C22×D3—124no—
672C22×D3—128no—
673C22×D3—128no—
674C22×D3—128no—
675C22×D3—1232no—
676C22×D3—1216no—
677C22×D3—1216no—
678C22×D3C23×D312yes—
679C22×D3C23×D312yes—
680C3×D4—124no—
681C3×D4—124no—
682C3×D4—124no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—32no—
690C2×C3×C4—32no—
691C2×C3×C4—32no—
692C2×C3×C4—32no—
693C2×C3×C4—32no—
694C2×C3×C4—32no—
695C2×C3×C4—42no—
696C2×C3×C4—42no—
697C2×C3×C4—62no—
698C2×C3×C4—62no—
699C2×C3×C4—62no—
700C2×C3×C4—62no—
701C2×C3×C4—62no—
702C2×C3×C4—62no—
703C2×C3×C4—124no—
704C2×C3×C4C23×D312yes—
705C2×C3×C4C23×D312yes—
706C2×C3×C4C23×D312yes—
707C2×C3×C4C23×D312yes—
708#67—44no—
709#67—44no—
710#67—124no—
711#67—124no—
712#67—124no—
713#67—124no—
714#67—124no—
715#67—124no—
716#67—124no—
717#67—124no—
718#67—128no—
719C2×Dic3—22no—
720C2×Dic3—22no—
721C2×Dic3—22no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—22no—
725C2×Dic3—32no—
726C2×Dic3—32no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—122no—
731C2×Dic3—124no—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735C2×Dic3C23×D312yes—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D312yes—
738D12—44no—
739D12—124no—
740D12—124no—
741D12—124no—
742D12—124no—
743D12—128no—
744D12—128no—
745D12—124no—
746D12—124no—
747D12—124no—
748D12—124no—
749D12—124no—
750D12—124no—
751C4×D3—44no—
752C4×D3—124no—
753C4×D3—124no—
754C4×D3—124no—
755C2×C32—42no—
756C2×C32#56014yescomplemented
757C2×C32C2×H(5,𝔽2)11yescharacteristic
758C2×C32C2×H(5,𝔽2)11yescharacteristic
759C2×C32C2×H(5,𝔽2)11yescharacteristic
760C3⋊D3—42no—
761C3⋊D3—42no—
762C3⋊D3—42no—
763C3×D3—42no—
764C3×D3—42no—
765C24—31no—
766C24—31no—
767C24—91no—
768C24—91no—
769C24—91no—
770C24—94no—
771C24—362no—
772C24—362no—
773C24—362no—
774C24C2×D3211yescharacteristic
775C2×D4—34no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—122no—
788C2×D4—122no—
789C2×D4—122no—
790C2×D4—362no—
791C2×D4—362no—
792C2×D4—362no—
793C2×D4—362no—
794C2×D4—362no—
795C2×D4—362no—
796C2×D4—362no—
797C2×D4—362no—
798C2×D4—362no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—31no—
805C22×C4—34no—
806C22×C4—94no—
807C22×C4—94no—
808C22×C4—91no—
809C22×C4—122no—
810C22×C4—362no—
811C22×C4—362no—
812C22×C4C2×D3211yescharacteristic
813C22×C4C2×D3211yescharacteristic
814C4⋊C4—34no—
815C4⋊C4—34no—
816C4⋊C4—34no—
817C4⋊C4—34no—
818C4⋊C4—94no—
819C4⋊C4—94no—
820C22⋊C4—34no—
821C22⋊C4—34no—
822C22⋊C4—34no—
823C22⋊C4—94no—
824C22⋊C4—94no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4C2×D3214yes—
832C42—34no—
833C22×C3—24no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—21no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—48no—
847C22×C3—44no—
848C22×C3—44no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—124no—
856C22×C3—124no—
857C22×C3#100412yes—
858C22×C3#100412yes—
859C22×C3#100912yes—
860C22×C3#100912yes—
861C22×C3#100912yes—
862C22×C3#100912yes—
863C22×C3C24×D311yescharacteristic
864C22×C3C24×D311yescharacteristic
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—44no—
872C2×D3—44no—
873C2×D3—64no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
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—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—122no—
898C2×D3—122no—
899C2×D3—122no—
900C2×D3—128no—
901C2×D3—128no—
902C2×D3—1232no—
903C2×D3—1216no—
904C2×D3—1216no—
905C2×D3—124no—
906C2×D3—124no—
907C2×D3—124no—
908C2×D3—124no—
909C2×D3—124no—
910C2×D3—124no—
911C2×D3—244no—
912C3×C4—22no—
913C3×C4—22no—
914C3×C4—22no—
915C3×C4—22no—
916C3×C4—42no—
917C3×C4—42no—
918C3×C4—62no—
919C3×C4—62no—
920C3×C4—62no—
921C3×C4—62no—
922C3×C4—62no—
923C3×C4—62no—
924Dic3—22no—
925Dic3—22no—
926Dic3—22no—
927Dic3—22no—
928Dic3—22no—
929Dic3—22no—
930Dic3—62no—
931Dic3—62no—
932Dic3—122no—
933C32C2×#56011yescharacteristic, complemented, Sylow
934C23—22no—
935C23—22no—
936C23—22no—
937C23—32no—
938C23—32no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—62no—
943C23—62no—
944C23—62no—
945C23—92no—
946C23—92no—
947C23—92no—
948C23—182no—
949C23—182no—
950C23—182no—
951C23—182no—
952C23—182no—
953C23—182no—
954C23—182no—
955C23—182no—
956C23—182no—
957C23—364no—
958C23—364no—
959C23—364no—
960C23—3616no—
961C23C22×D3212yes—
962C23C22×D3211yescharacteristic
963D4—124no—
964D4—124no—
965D4—124no—
966D4—364no—
967D4—364no—
968D4—364no—
969D4—364no—
970D4—364no—
971D4—364no—
972D4—364no—
973D4—364no—
974D4—364no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—32no—
978C2×C4—32no—
979C2×C4—32no—
980C2×C4—32no—
981C2×C4—32no—
982C2×C4—32no—
983C2×C4—62no—
984C2×C4—62no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—62no—
988C2×C4—62no—
989C2×C4—92no—
990C2×C4—124no—
991C2×C4—182no—
992C2×C4—364no—
993C2×C4—364no—
994C2×C4C22×D3212yes—
995C2×C4C22×D3212yes—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—24no—
1000C2×C3—44no—
1001C2×C3—42no—
1002C2×C3—42no—
1003C2×C3—122no—
1004C2×C3—122no—
1005C2×C3#562014yescomplemented
1006C2×C3#571114yescomplemented
1007C2×C3C2×#100411yescharacteristic
1008C2×C3C2×#100411yescharacteristic
1009C2×C3C2×#100911yescharacteristic
1010C2×C3C2×#100911yescharacteristic
1011C2×C3C2×#100911yescharacteristic
1012C2×C3C2×#100911yescharacteristic
1013D3—42no—
1014D3—42no—
1015D3—124no—
1016D3—124no—
1017D3—122no—
1018D3—122no—
1019D3—122no—
1020D3—122no—
1021D3—122no—
1022D3—122no—
1023D3—242no—
1024C22—22no—
1025C22—22no—
1026C22—22no—
1027C22—44no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—124no—
1035C22—124no—
1036C22—182no—
1037C22—182no—
1038C22—182no—
1039C22—182no—
1040C22—182no—
1041C22—182no—
1042C22—182no—
1043C22—182no—
1044C22—182no—
1045C22—3616no—
1046C22—364no—
1047C22—364no—
1048C22—364no—
1049C22#6430812yes—
1050C22#6431412yes—
1051C22#6431412yes—
1052C22C23×D3211yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—62no—
1056C4—62no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—62no—
1061C4—182no—
1062C3—21no—
1063C3C2×#562011yescharacteristic, complemented
1064C3C2×#571111yescharacteristic, complemented
1065C2—42no—
1066C2—122no—
1067C2—122no—
1068C2—362no—
1069C2—362no—
1070C2—362no—
1071C2#1059424214yesdirect product factor
1072C2C2×#6430811yescharacteristic
1073C2C2×#6431411yescharacteristic
1074C2C2×#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×#64091C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63981C2semidirect
5. C2×#63981C2semidirect
6. C2×#63971C2semidirect
7. C2×#63958C2semidirect
8. C2×#63911C2semidirect
9. C2×#63910C2semidirect
10. C2×#63909C2semidirect
11. C2×#63897C2semidirect
12. C2×#63890C2semidirect
13. C2×#63886C2semidirect
14. C2×#63868C2semidirect
15. C2×#63850C2semidirect
16. #10594242C2direct (N × H)
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
33. C22×#624C22semidirect
34. C22×D3×Dic3C22semidirect
38. #64091C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. C3×#884C22semidirect
48. C3×#879C22semidirect
49. #63981C22semidirect
50. #63981C22semidirect
51. #63971C22semidirect
52. C2×#3724C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. #63958C22semidirect
61. #63911C22semidirect
62. #63910C22semidirect
63. #63909C22semidirect
64. #63897C22semidirect
65. #63890C22semidirect
66. #63886C22semidirect
67. #63868C22semidirect
68. #63850C22semidirect
93. C2×#884D3semidirect
99. C2×#879D3semidirect
132. C2×C3×D12C23semidirect
134. C2×C3×C4×D3C23semidirect
145. C2×#626C23semidirect
146. C2×#626C23semidirect
148. C2×#624C23semidirect
150. C2×D3×Dic3C23semidirect
156. C3×(C2×D3)⋊C4C23semidirect
157. C3×C4⋊Dic3C23semidirect
158. C3×Dic3⋊C4C23semidirect
159. C3×Dic3⋊C4C23semidirect
160. C3×Dic3⋊C4C23semidirect
161. C3×C4×Dic3C23semidirect
162. #3724C23semidirect
163. Dic3⋊Dic3C23semidirect
168. #3722C23semidirect
169. (C2×D3)⋊Dic3C23semidirect
202. C22×D12C2×D3semidirect
206. C22×C4×D3C2×D3semidirect
248. C2×(C2×D3)⋊C4C2×D3semidirect
250. C2×C4⋊Dic3C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
255. C2×Dic3⋊C4C2×D3semidirect
256. C2×Dic3⋊C4C2×D3semidirect
257. C2×C4×Dic3C2×D3semidirect
270. #884C2×D3semidirect
276. #879C2×D3semidirect
463. C2×D12C22×D3semidirect
471. C2×C4×D3C22×D3semidirect
503. (C2×D3)⋊C4C22×D3semidirect
505. C4⋊Dic3C22×D3semidirect
509. Dic3⋊C4C22×D3semidirect
510. Dic3⋊C4C22×D3semidirect
511. Dic3⋊C4C22×D3semidirect
512. C4×Dic3C22×D3semidirect
756. C2×C32#560semidirect
933. C32C2×#560semidirect
1005. C2×C3#5620semidirect
1006. C2×C3#5711semidirect
1063. C3C2×#5620semidirect
1064. C3C2×#5711semidirect
1071. C2#10594242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640912
C2×C3×#8842
C2×C3×#8792
C2×#639812
C2×#639712
C2×#639582
C2×#639112
C2×#639102
C2×#639092
C2×#638972
C2×#638902
C2×#638862
C2×#638682
C2×#638502
#105942422
C2×#57113
C2×#56203