Finite Group Databasebeta

← C2×#10594264 #11900961

Subgroups — C2×#10594264 #11900961

Order 1152.

4299 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#883C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63981C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63897C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594264C2116yesmaximal, direct product factor
17C2×#5653—31nomaximal
18C2×#5605—31nomaximal
19C24×C3⋊D3C2211yescharacteristic, complemented
20C23×D32C2211yescharacteristic
21C23×D32C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C22×C3×D12C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C22×C3×C4×D3C2211yescharacteristic, complemented
31C2×#3811—28no—
32C2×#3811C2218yescomplemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic, complemented
36C22×#626C2211yescharacteristic, complemented
37C22×#626C2211yescharacteristic, complemented
38C22×#624C2211yescharacteristic, complemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C2×D3×D12—28no—
41C2×D3×D12C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45#64091C2218yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#884C2218yescomplemented
53C3×#883C2218yescomplemented
54#63983C2218yescomplemented
55#63981C2218yescomplemented
56#63971C2218yescomplemented
57C2×#3724C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×#3722C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63923C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63909C2218yescomplemented
67#63897C2218yescomplemented
68#63886C2218yescomplemented
69#63854C2218yescomplemented
70#63850C2218yescomplemented
71C22×D3×D4—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C23×D12—31no—
75C2×C3×#123—31no—
76C2×C3×#121—31no—
77C2×#939—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#930—31no—
83C2×#929—31no—
84C22×(C2×D3)⋊C4—31no—
85#5653—316no—
86#5605—316no—
87C2×#895—31no—
88C2×#895—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#884—31no—
94C2×#884D311yescharacteristic, complemented
95C2×#883—31no—
96C2×#883D311yescharacteristic, complemented
97C2×#882—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#882—31no—
101C2×#882—31no—
102C2×#882—61no—
103C2×D3×C22⋊C4—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—42no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2311yescharacteristic
111C23×C3⋊D3C2314yescomplemented
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C23×C3×D3C2311yescharacteristic
115C22×D32—24no—
116C22×D32—42no—
117C22×D32—42no—
118C22×D32—42no—
119C22×D32—42no—
120C22×D32D418yescomplemented
121C22×D32C2314yes—
122C22×D32C2314yescomplemented
123C22×C32×C4C2311yescharacteristic
124C22×C32×C4C2311yescharacteristic
125C2×#638—42no—
126C2×#638C2314yescomplemented
127C22×C3⋊Dic3C2311yescharacteristic
128C2×C4⋊(C3⋊D3)—24no—
129C2×C4⋊(C3⋊D3)—42no—
130C2×C4⋊(C3⋊D3)C2314yes—
131C2×C4⋊(C3⋊D3)C2314yescomplemented
132C2×C3×#67—24no—
133C2×C3×#67—24no—
134C2×C3×#67—42no—
135C2×C3×#67C2314yes—
136C2×C3×#67C2314yescomplemented
137C2×C3×#67C2314yescomplemented
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2311yescharacteristic
143C2×C3×D12—24no—
144C2×C3×D12C2314yescomplemented
145C2×C3×C4×D3—24no—
146C2×C3×C4×D3—42no—
147C2×C3×C4×D3C2314yescomplemented
148C2×C3×C4×D3C2314yescomplemented
149#3811—232no—
150C2×#626—24no—
151C2×#626—24no—
152C2×#626—24no—
153C2×#626—24no—
154C2×#626—42no—
155C2×#626C2314yes—
156C2×#626C2314yes—
157C2×#626C2314yescomplemented
158C2×#626C2314yescomplemented
159C2×#626C2314yescomplemented
160C2×#624—24no—
161C2×#624C2314yescomplemented
162C2×D3×Dic3—42no—
163C2×D3×Dic3C2314yescomplemented
164D3×D12—232no—
165C32×C22⋊C4C2314yescomplemented
166#3752C2314yescomplemented
167#3752C2314yescomplemented
168C3×#217C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×C4⋊Dic3C2314yescomplemented
172C3×Dic3⋊C4C2314yescomplemented
173C3×Dic3⋊C4C2314yescomplemented
174#3724C2314yescomplemented
175#3722C2314yescomplemented
176#3722C2314yescomplemented
177#3722C2314yescomplemented
178#3722C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C24×D3—31no—
183C24×D3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3—31no—
187C24×D3—31no—
188C24×D3—61no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C22×C3×D4—31no—
193C23×C3×C4—31no—
194C23×C3×C4—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—61no—
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic, complemented
205C22×#67C2×D311yescharacteristic, complemented
206C23×Dic3—31no—
207C2×D3×D4—38no—
208C2×D3×D4—38no—
209C2×D3×D4—38no—
210C2×D3×D4—68no—
211C2×D3×D4—68no—
212C2×D3×D4—68no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12—31no—
219C22×D12—31no—
220C22×D12—31no—
221C22×D12—31no—
222C22×D12—38no—
223C22×D12—61no—
224C22×D12—61no—
225C22×D12—68no—
226C22×D12C2×D311yescharacteristic, complemented
227C22×C4×D3—31no—
228C22×C4×D3—31no—
229C22×C4×D3—31no—
230C22×C4×D3C2×D311yescharacteristic, complemented
231C22×C4×D3C2×D311yescharacteristic, complemented
232C3×#123—38no—
233C3×#121—38no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C4⋊C4—31no—
236C2×C3×C4⋊C4—31no—
237C2×C3×C22⋊C4—21no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—31no—
241C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
242C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
243C2×#217—31no—
244C2×#217—31no—
245C2×#217C2×D311yescharacteristic, complemented
246#939—38no—
247#939—38no—
248#937—38no—
249#937—38no—
250#937—38no—
251#930—38no—
252#929—38no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—31no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—38no—
268C2×(C2×D3)⋊C4—61no—
269C2×(C2×D3)⋊C4—61no—
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
272C2×C4⋊Dic3C2×D311yescharacteristic, complemented
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4C2×D311yescharacteristic, complemented
276C2×Dic3⋊C4C2×D311yescharacteristic, complemented
277#895—38no—
278#895—38no—
279#894—38no—
280#894—38no—
281#894—38no—
282#894—38no—
283#884—38no—
284#884C2×D318yescomplemented
285#883—38no—
286#883C2×D318yescomplemented
287#882—38no—
288#882—38no—
289#882—38no—
290#882—38no—
291#882—38no—
292#882—68no—
293D3×C22⋊C4—38no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2412yes—
298C23×C32C2411yescharacteristic
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—22no—
306C22×C3⋊D3—22no—
307C22×C3⋊D3—28no—
308C22×C3⋊D3—44no—
309C22×C3⋊D3—44no—
310C22×C3⋊D3—416no—
311C22×C3⋊D3C2×D414yes—
312C22×C3⋊D3C2412yes—
313C22×C3⋊D3C2412yes—
314C22×C3⋊D3C2412yes—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—22no—
318C22×C3×D3—22no—
319C22×C3×D3—22no—
320C22×C3×D3—22no—
321C22×C3×D3—22no—
322C22×C3×D3C2×D414yes—
323C22×C3×D3C2×D414yes—
324C22×C3×D3C2412yes—
325C22×C3×D3C2412yes—
326C22×C3×D3C2412yes—
327C2×D32—28no—
328C2×D32—416no—
329C2×D32—44no—
330C2×D32—44no—
331C2×D32—44no—
332C2×D32—44no—
333C2×D32—416no—
334C2×D32C2×D4116yescomplemented
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2412yes—
338C2×C32×C4C2412yes—
339#638—44no—
340C2×C3⋊Dic3—22no—
341C2×C3⋊Dic3C2412yes—
342C4⋊(C3⋊D3)—28no—
343C4⋊(C3⋊D3)—44no—
344C3×#67—28no—
345C3×#67—28no—
346C3×#67—44no—
347C2×C3×Dic3—22no—
348C2×C3×Dic3—22no—
349C2×C3×Dic3—22no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C3×D12—28no—
358C3×C4×D3—28no—
359C3×C4×D3—44no—
360#626—28no—
361#626—28no—
362#626—28no—
363#626—28no—
364#626—44no—
365#624—28no—
366D3×Dic3—44no—
367C23×D4—91no—
368C23×D4—91no—
369#534—916no—
370C2×#123—31no—
371C2×#123—91no—
372C2×#123—91no—
373C2×#123—91no—
374C2×#121—31no—
375C2×#121—91no—
376C2×#121—91no—
377C2×#121—91no—
378C2×#120—91no—
379C2×#120—91no—
380C2×#120—91no—
381C2×#120—91no—
382C22×C22⋊C4—91no—
383C24×C3—21no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3C22×D311yescharacteristic
388C24×C3C22×D311yescharacteristic
389C23×D3—31no—
390C23×D3—31no—
391C23×D3—38no—
392C23×D3—38no—
393C23×D3—34no—
394C23×D3—34no—
395C23×D3—31no—
396C23×D3—31no—
397C23×D3—31no—
398C23×D3—31no—
399C23×D3—34no—
400C23×D3—34no—
401C23×D3—34no—
402C23×D3—34no—
403C23×D3—61no—
404C23×D3—61no—
405C23×D3—61no—
406C23×D3—64no—
407C23×D3—64no—
408C23×D3—64no—
409C23×D3—64no—
410C23×D3—64no—
411C23×D3—124no—
412C23×D3—122no—
413C23×D3—122no—
414C23×D3—122no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3—122no—
418C23×D3—122no—
419C23×D3—122no—
420C23×D3—122no—
421C23×D3—122no—
422C23×D3—122no—
423C23×D3—122no—
424C23×D3—124no—
425C23×D3—124no—
426C23×D3C22×D311yescharacteristic
427C23×D3C22×D311yescharacteristic
428C23×D3C22×D311yescharacteristic
429C2×C3×D4—34no—
430C2×C3×D4—34no—
431C2×C3×D4—34no—
432C2×C3×D4—34no—
433C2×C3×D4—64no—
434C2×C3×D4—64no—
435C2×C3×D4—64no—
436C2×C3×D4—122no—
437C22×C3×C4—21no—
438C22×C3×C4—21no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—31no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—34no—
445C22×C3×C4—34no—
446C22×C3×C4—64no—
447C22×C3×C4—122no—
448C22×C3×C4C22×D311yescharacteristic
449C22×C3×C4C22×D311yescharacteristic
450C22×C3×C4C22×D311yescharacteristic
451C22×C3×C4C22×D311yescharacteristic
452C2×#67—24no—
453C2×#67—24no—
454C2×#67—34no—
455C2×#67—34no—
456C2×#67—34no—
457C2×#67—34no—
458C2×#67—34no—
459C2×#67—34no—
460C2×#67—34no—
461C2×#67—42no—
462C2×#67—64no—
463C2×#67—64no—
464C2×#67—64no—
465C2×#67—64no—
466C2×#67—64no—
467C2×#67—122no—
468C2×#67—122no—
469C2×#67—122no—
470C2×#67—124no—
471C2×#67C22×D314yes—
472C2×#67C22×D314yescomplemented
473C2×#67C22×D314yescomplemented
474C22×Dic3—31no—
475C22×Dic3—31no—
476C22×Dic3—34no—
477C22×Dic3—61no—
478C22×Dic3—122no—
479C22×Dic3C22×D311yescharacteristic
480C22×Dic3C22×D311yescharacteristic
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484D3×D4—632no—
485D3×D4—632no—
486D3×D4—632no—
487C2×D12—24no—
488C2×D12—34no—
489C2×D12—34no—
490C2×D12—34no—
491C2×D12—34no—
492C2×D12—34no—
493C2×D12—34no—
494C2×D12—34no—
495C2×D12—34no—
496C2×D12—34no—
497C2×D12—64no—
498C2×D12—64no—
499C2×D12—632no—
500C2×D12—64no—
501C2×D12—64no—
502C2×D12—64no—
503C2×D12—64no—
504C2×D12—64no—
505C2×D12—64no—
506C2×D12—124no—
507C2×D12—122no—
508C2×D12—122no—
509C2×D12—124no—
510C2×D12—122no—
511C2×D12C22×D314yescomplemented
512C2×C4×D3—24no—
513C2×C4×D3—34no—
514C2×C4×D3—34no—
515C2×C4×D3—34no—
516C2×C4×D3—42no—
517C2×C4×D3—64no—
518C2×C4×D3—64no—
519C2×C4×D3—122no—
520C2×C4×D3C22×D314yescomplemented
521C2×C4×D3C22×D314yescomplemented
522C3×C4⋊C4—34no—
523C3×C4⋊C4—34no—
524C3×C4⋊C4—34no—
525C3×C22⋊C4—24no—
526C3×C22⋊C4—34no—
527C3×C22⋊C4—34no—
528C3×C22⋊C4—34no—
529C3×C22⋊C4C22×D314yescomplemented
530C3×C22⋊C4C22×D314yescomplemented
531#217—34no—
532#217—34no—
533#217C22×D314yescomplemented
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—34no—
540(C2×D3)⋊C4—34no—
541(C2×D3)⋊C4—34no—
542(C2×D3)⋊C4—34no—
543(C2×D3)⋊C4—34no—
544(C2×D3)⋊C4—34no—
545(C2×D3)⋊C4—34no—
546(C2×D3)⋊C4—34no—
547(C2×D3)⋊C4—34no—
548(C2×D3)⋊C4—64no—
549(C2×D3)⋊C4—64no—
550(C2×D3)⋊C4C22×D314yescomplemented
551(C2×D3)⋊C4C22×D314yescomplemented
552C4⋊Dic3C22×D314yescomplemented
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4C22×D314yescomplemented
556Dic3⋊C4C22×D314yescomplemented
557C22×C32—22no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—44no—
561C22×C32C22×D412yes—
562C22×C32H(5,𝔽2)12yes—
563C22×C32H(5,𝔽2)12yes—
564C22×C32C2511yescharacteristic
565C2×C3⋊D3—22no—
566C2×C3⋊D3—28no—
567C2×C3⋊D3—22no—
568C2×C3⋊D3—22no—
569C2×C3⋊D3—22no—
570C2×C3⋊D3—22no—
571C2×C3⋊D3—22no—
572C2×C3⋊D3—22no—
573C2×C3⋊D3—22no—
574C2×C3⋊D3—416no—
575C2×C3⋊D3—44no—
576C2×C3⋊D3—44no—
577C2×C3⋊D3C22×D414yes—
578C2×C3×D3—28no—
579C2×C3×D3—28no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—22no—
586C2×C3×D3—22no—
587C2×C3×D3—44no—
588C2×C3×D3C22×D414yes—
589C2×C3×D3C22×D414yes—
590D32—416no—
591D32—416no—
592C32×C4—22no—
593C32×C4—22no—
594C3⋊Dic3—22no—
595C3×Dic3—22no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C3×Dic3—22no—
599C3×Dic3—22no—
600C25—91no—
601C25—91no—
602C25—91no—
603C22×D4—31no—
604C22×D4—31no—
605C22×D4—31no—
606C22×D4—31no—
607C22×D4—98no—
608C22×D4—91no—
609C22×D4—91no—
610C22×D4—91no—
611C22×D4—91no—
612C22×D4—91no—
613C22×D4—98no—
614C22×D4—91no—
615C22×D4—91no—
616C22×D4—91no—
617C22×D4—188no—
618C22×D4—188no—
619C23×C4—31no—
620C23×C4—31no—
621C23×C4—91no—
622C23×C4—91no—
623#123—38no—
624#123—98no—
625#123—98no—
626#123—98no—
627#121—38no—
628#121—98no—
629#121—98no—
630#121—98no—
631#120—98no—
632#120—98no—
633#120—98no—
634#120—98no—
635C2×C4⋊C4—31no—
636C2×C4⋊C4—31no—
637C2×C4⋊C4—31no—
638C2×C4⋊C4—91no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—98no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—91no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C2×C22⋊C4—91no—
649C2×C22⋊C4—91no—
650C2×C22⋊C4—91no—
651C2×C22⋊C4D3211yescharacteristic, complemented
652C23×C3—24no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—22no—
656C23×C3—22no—
657C23×C3—22no—
658C23×C3—22no—
659C23×C3—22no—
660C23×C3—21no—
661C23×C3—34no—
662C23×C3—34no—
663C23×C3—32no—
664C23×C3—32no—
665C23×C3—32no—
666C23×C3—42no—
667C23×C3—42no—
668C23×C3—62no—
669C23×C3—62no—
670C23×C3—62no—
671C23×C3—62no—
672C23×C3—62no—
673C23×C3—62no—
674C23×C3—62no—
675C23×C3C23×D312yes—
676C23×C3C23×D312yes—
677C23×C3C23×D311yescharacteristic
678C23×C3C23×D311yescharacteristic
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—22no—
683C22×D3—22no—
684C22×D3—22no—
685C22×D3—22no—
686C22×D3—34no—
687C22×D3—34no—
688C22×D3—32no—
689C22×D3—32no—
690C22×D3—316no—
691C22×D3—316no—
692C22×D3—32no—
693C22×D3—32no—
694C22×D3—32no—
695C22×D3—32no—
696C22×D3—64no—
697C22×D3—62no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—68no—
701C22×D3—68no—
702C22×D3—68no—
703C22×D3—62no—
704C22×D3—62no—
705C22×D3—62no—
706C22×D3—62no—
707C22×D3—64no—
708C22×D3—62no—
709C22×D3—62no—
710C22×D3—62no—
711C22×D3—62no—
712C22×D3—62no—
713C22×D3—62no—
714C22×D3—62no—
715C22×D3—62no—
716C22×D3—62no—
717C22×D3—62no—
718C22×D3—62no—
719C22×D3—62no—
720C22×D3—68no—
721C22×D3—128no—
722C22×D3—122no—
723C22×D3—122no—
724C22×D3—122no—
725C22×D3—122no—
726C22×D3—122no—
727C22×D3—122no—
728C22×D3—122no—
729C22×D3—1216no—
730C22×D3—124no—
731C22×D3—124no—
732C22×D3—124no—
733C22×D3—124no—
734C22×D3—124no—
735C22×D3—124no—
736C22×D3—1216no—
737C22×D3—124no—
738C22×D3—124no—
739C22×D3—1216no—
740C22×D3—1216no—
741C22×D3—124no—
742C22×D3—124no—
743C22×D3—124no—
744C22×D3—124no—
745C22×D3—128no—
746C22×D3—1216no—
747C22×D3—1216no—
748C22×D3—128no—
749C22×D3—1232no—
750C22×D3D3×D414yes—
751C22×D3D3×D414yes—
752C22×D3C23×D312yes—
753C22×D3C23×D312yes—
754C22×D3C23×D312yes—
755C3×D4—68no—
756C3×D4—68no—
757C3×D4—68no—
758C3×D4—124no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—32no—
766C2×C3×C4—32no—
767C2×C3×C4—32no—
768C2×C3×C4—32no—
769C2×C3×C4—32no—
770C2×C3×C4—42no—
771C2×C3×C4—42no—
772C2×C3×C4—68no—
773C2×C3×C4—62no—
774C2×C3×C4—62no—
775C2×C3×C4—62no—
776C2×C3×C4—62no—
777C2×C3×C4—62no—
778C2×C3×C4—124no—
779C2×C3×C4C23×D312yes—
780C2×C3×C4C23×D312yes—
781C2×C3×C4C23×D312yes—
782C2×C3×C4C23×D312yes—
783#67—28no—
784#67—28no—
785#67—44no—
786#67—68no—
787#67—68no—
788#67—68no—
789#67—68no—
790#67—124no—
791#67—124no—
792#67—124no—
793#67—128no—
794C2×Dic3—22no—
795C2×Dic3—22no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—22no—
799C2×Dic3—32no—
800C2×Dic3—32no—
801C2×Dic3—62no—
802C2×Dic3—62no—
803C2×Dic3—62no—
804C2×Dic3—122no—
805C2×Dic3—124no—
806C2×Dic3C23×D312yes—
807C2×Dic3C23×D312yes—
808C2×Dic3C23×D312yes—
809C2×Dic3C23×D312yes—
810C2×Dic3C23×D312yes—
811D12—28no—
812D12—68no—
813D12—68no—
814D12—68no—
815D12—68no—
816D12—68no—
817D12—68no—
818D12—128no—
819D12—124no—
820D12—124no—
821D12—128no—
822D12—124no—
823C4×D3—28no—
824C4×D3—44no—
825C4×D3—68no—
826C4×D3—68no—
827C4×D3—124no—
828C2×C32—42no—
829C2×C32#53414yescomplemented
830C2×C32C23×D411yescharacteristic
831C2×C32C2×H(5,𝔽2)11yescharacteristic
832C2×C32C2×H(5,𝔽2)11yescharacteristic
833C3⋊D3—24no—
834C3⋊D3—42no—
835C3⋊D3—42no—
836C3×D3—24no—
837C3×D3—24no—
838C3×D3—42no—
839C24—31no—
840C24—31no—
841C24—31no—
842C24—94no—
843C24—98no—
844C24—94no—
845C24—91no—
846C24—91no—
847C24—91no—
848C24—94no—
849C24—184no—
850C24—184no—
851C24—362no—
852C24—362no—
853C24—362no—
854C24—362no—
855C24—362no—
856C24—362no—
857C24C2×D3211yescharacteristic
858C2×D4—34no—
859C2×D4—34no—
860C2×D4—34no—
861C2×D4—34no—
862C2×D4—64no—
863C2×D4—64no—
864C2×D4—64no—
865C2×D4—94no—
866C2×D4—94no—
867C2×D4—94no—
868C2×D4—94no—
869C2×D4—94no—
870C2×D4—94no—
871C2×D4—94no—
872C2×D4—94no—
873C2×D4—122no—
874C2×D4—184no—
875C2×D4—1832no—
876C2×D4—184no—
877C2×D4—184no—
878C2×D4—184no—
879C2×D4—184no—
880C2×D4—1832no—
881C2×D4—362no—
882C2×D4—362no—
883C2×D4—362no—
884C22×C4—31no—
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—31no—
889C22×C4—34no—
890C22×C4—34no—
891C22×C4—64no—
892C22×C4—94no—
893C22×C4—94no—
894C22×C4—91no—
895C22×C4—122no—
896C22×C4—184no—
897C22×C4—362no—
898C22×C4C2×D3211yescharacteristic
899C22×C4C2×D3211yescharacteristic
900C4⋊C4—34no—
901C4⋊C4—34no—
902C4⋊C4—34no—
903C4⋊C4—94no—
904C22⋊C4—34no—
905C22⋊C4—34no—
906C22⋊C4—34no—
907C22⋊C4—94no—
908C22⋊C4—94no—
909C22⋊C4—94no—
910C22⋊C4—94no—
911C22⋊C4—94no—
912C22⋊C4—94no—
913C22⋊C4—94no—
914C22⋊C4—94no—
915C22⋊C4C2×D3214yescomplemented
916C22×C3—24no—
917C22×C3—22no—
918C22×C3—22no—
919C22×C3—22no—
920C22×C3—22no—
921C22×C3—22no—
922C22×C3—22no—
923C22×C3—22no—
924C22×C3—22no—
925C22×C3—22no—
926C22×C3—21no—
927C22×C3—34no—
928C22×C3—34no—
929C22×C3—42no—
930C22×C3—42no—
931C22×C3—48no—
932C22×C3—44no—
933C22×C3—44no—
934C22×C3—68no—
935C22×C3—62no—
936C22×C3—62no—
937C22×C3—62no—
938C22×C3—62no—
939C22×C3—68no—
940C22×C3—62no—
941C22×C3—62no—
942C22×C3—62no—
943C22×C3—124no—
944C22×C3C2×D3×D412yes—
945C22×C3C2×D3×D412yes—
946C22×C3#100412yes—
947C22×C3#100912yes—
948C22×C3#100912yes—
949C22×C3#100912yes—
950C22×C3C24×D311yescharacteristic
951C22×C3C24×D311yescharacteristic
952C2×D3—28no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—22no—
956C2×D3—22no—
957C2×D3—28no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—34no—
962C2×D3—34no—
963C2×D3—44no—
964C2×D3—64no—
965C2×D3—68no—
966C2×D3—62no—
967C2×D3—62no—
968C2×D3—62no—
969C2×D3—62no—
970C2×D3—68no—
971C2×D3—64no—
972C2×D3—62no—
973C2×D3—62no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—62no—
979C2×D3—62no—
980C2×D3—62no—
981C2×D3—62no—
982C2×D3—62no—
983C2×D3—62no—
984C2×D3—122no—
985C2×D3—122no—
986C2×D3—128no—
987C2×D3—122no—
988C2×D3—122no—
989C2×D3—122no—
990C2×D3—122no—
991C2×D3—122no—
992C2×D3—1216no—
993C2×D3—1216no—
994C2×D3—1216no—
995C2×D3—1216no—
996C2×D3—1216no—
997C2×D3—1216no—
998C2×D3—128no—
999C2×D3—1232no—
1000C2×D3—124no—
1001C2×D3—124no—
1002C2×D3—124no—
1003C2×D3—124no—
1004C2×D3—244no—
1005C2×D3C2×D3×D414yes—
1006C2×D3C2×D3×D414yes—
1007C3×C4—22no—
1008C3×C4—22no—
1009C3×C4—22no—
1010C3×C4—22no—
1011C3×C4—42no—
1012C3×C4—42no—
1013C3×C4—62no—
1014C3×C4—62no—
1015C3×C4—62no—
1016C3×C4—62no—
1017C3×C4—62no—
1018Dic3—22no—
1019Dic3—22no—
1020Dic3—22no—
1021Dic3—22no—
1022Dic3—22no—
1023Dic3—62no—
1024Dic3—62no—
1025Dic3—122no—
1026C32C2×#53411yescharacteristic, complemented, Sylow
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—34no—
1031C23—34no—
1032C23—32no—
1033C23—32no—
1034C23—32no—
1035C23—62no—
1036C23—62no—
1037C23—62no—
1038C23—62no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—916no—
1043C23—94no—
1044C23—92no—
1045C23—92no—
1046C23—92no—
1047C23—188no—
1048C23—188no—
1049C23—182no—
1050C23—182no—
1051C23—182no—
1052C23—182no—
1053C23—182no—
1054C23—182no—
1055C23—182no—
1056C23—182no—
1057C23—364no—
1058C23—364no—
1059C23—3616no—
1060C23—364no—
1061C23—364no—
1062C23—364no—
1063C23—364no—
1064C23—3616no—
1065C23—3616no—
1066C23C22×D3212yes—
1067C23C22×D3211yescharacteristic
1068D4—68no—
1069D4—68no—
1070D4—68no—
1071D4—124no—
1072D4—188no—
1073D4—188no—
1074D4—188no—
1075D4—188no—
1076D4—188no—
1077D4—364no—
1078D4—364no—
1079D4—364no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—32no—
1083C2×C4—32no—
1084C2×C4—32no—
1085C2×C4—32no—
1086C2×C4—32no—
1087C2×C4—68no—
1088C2×C4—62no—
1089C2×C4—62no—
1090C2×C4—62no—
1091C2×C4—62no—
1092C2×C4—62no—
1093C2×C4—92no—
1094C2×C4—124no—
1095C2×C4—188no—
1096C2×C4—182no—
1097C2×C4—364no—
1098C2×C4C22×D3212yes—
1099C2×C4C22×D3212yes—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—24no—
1104C2×C3—44no—
1105C2×C3—42no—
1106C2×C3—42no—
1107C2×C3—64no—
1108C2×C3—64no—
1109C2×C3—122no—
1110C2×C3#560514yescomplemented
1111C2×C3#565314yescomplemented
1112C2×C3C22×D3×D411yescharacteristic
1113C2×C3C22×D3×D411yescharacteristic
1114C2×C3C2×#100411yescharacteristic
1115C2×C3C2×#100911yescharacteristic
1116C2×C3C2×#100911yescharacteristic
1117C2×C3C2×#100911yescharacteristic
1118D3—24no—
1119D3—24no—
1120D3—42no—
1121D3—64no—
1122D3—64no—
1123D3—124no—
1124D3—124no—
1125D3—122no—
1126D3—122no—
1127D3—122no—
1128D3—122no—
1129D3—242no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—34no—
1134C22—34no—
1135C22—44no—
1136C22—62no—
1137C22—62no—
1138C22—62no—
1139C22—62no—
1140C22—68no—
1141C22—68no—
1142C22—62no—
1143C22—62no—
1144C22—62no—
1145C22—94no—
1146C22—124no—
1147C22—182no—
1148C22—182no—
1149C22—188no—
1150C22—182no—
1151C22—182no—
1152C22—182no—
1153C22—182no—
1154C22—182no—
1155C22—182no—
1156C22—3616no—
1157C22—3616no—
1158C22—3616no—
1159C22—364no—
1160C22—364no—
1161C22#6430812yes—
1162C22D32×D412yes—
1163C22#6431412yes—
1164C22C23×D3211yescharacteristic
1165C4—22no—
1166C4—22no—
1167C4—62no—
1168C4—62no—
1169C4—62no—
1170C4—62no—
1171C4—62no—
1172C4—182no—
1173C3—21no—
1174C3C2×#560511yescharacteristic, complemented
1175C3C2×#565311yescharacteristic, complemented
1176C2—42no—
1177C2—64no—
1178C2—64no—
1179C2—122no—
1180C2—184no—
1181C2—362no—
1182C2—362no—
1183C2#1059426414yesdirect product factor
1184C2C2×#6430811yescharacteristic
1185C2C2×D32×D411yescharacteristic
1186C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#534
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×#3811C2semidirect
2. C22×D3×D12C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#883C2semidirect
6. C2×#63983C2semidirect
7. C2×#63981C2semidirect
8. C2×#63971C2semidirect
9. C2×#63923C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63909C2semidirect
12. C2×#63897C2semidirect
13. C2×#63886C2semidirect
14. C2×#63854C2semidirect
15. C2×#63850C2semidirect
16. #10594264C2direct (N × H)
19. C24×C3⋊D3C22semidirect
21. C23×D32C22semidirect
22. C22×#638C22semidirect
24. C22×C4⋊(C3⋊D3)C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C22×C3×D12C22semidirect
29. C22×C3×C4×D3C22semidirect
30. C22×C3×C4×D3C22semidirect
32. C2×#3811C22semidirect
35. C22×#626C22semidirect
36. C22×#626C22semidirect
37. C22×#626C22semidirect
38. C22×#624C22semidirect
39. C22×D3×Dic3C22semidirect
41. C2×D3×D12C22semidirect
42. C2×C32×C22⋊C4C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. #64091C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#884C22semidirect
53. C3×#883C22semidirect
54. #63983C22semidirect
55. #63981C22semidirect
56. #63971C22semidirect
57. C2×#3724C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63923C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63909C22semidirect
67. #63897C22semidirect
68. #63886C22semidirect
69. #63854C22semidirect
70. #63850C22semidirect
94. C2×#884D3semidirect
96. C2×#883D3semidirect
111. C23×C3⋊D3C23semidirect
120. C22×D32D4semidirect
122. C22×D32C23semidirect
126. C2×#638C23semidirect
131. C2×C4⋊(C3⋊D3)C23semidirect
136. C2×C3×#67C23semidirect
137. C2×C3×#67C23semidirect
144. C2×C3×D12C23semidirect
147. C2×C3×C4×D3C23semidirect
148. C2×C3×C4×D3C23semidirect
157. C2×#626C23semidirect
158. C2×#626C23semidirect
159. C2×#626C23semidirect
161. C2×#624C23semidirect
163. C2×D3×Dic3C23semidirect
165. C32×C22⋊C4C23semidirect
166. #3752C23semidirect
167. #3752C23semidirect
168. C3×#217C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×C4⋊Dic3C23semidirect
172. C3×Dic3⋊C4C23semidirect
173. C3×Dic3⋊C4C23semidirect
174. #3724C23semidirect
175. #3722C23semidirect
176. #3722C23semidirect
177. #3722C23semidirect
178. #3722C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
204. C22×#67C2×D3semidirect
205. C22×#67C2×D3semidirect
226. C22×D12C2×D3semidirect
230. C22×C4×D3C2×D3semidirect
231. C22×C4×D3C2×D3semidirect
241. C2×C3×C22⋊C4C2×D3semidirect
242. C2×C3×C22⋊C4C2×D3semidirect
245. C2×#217C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
271. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×C4⋊Dic3C2×D3semidirect
275. C2×Dic3⋊C4C2×D3semidirect
276. C2×Dic3⋊C4C2×D3semidirect
284. #884C2×D3semidirect
286. #883C2×D3semidirect
334. C2×D32C2×D4semidirect
472. C2×#67C22×D3semidirect
473. C2×#67C22×D3semidirect
511. C2×D12C22×D3semidirect
520. C2×C4×D3C22×D3semidirect
521. C2×C4×D3C22×D3semidirect
529. C3×C22⋊C4C22×D3semidirect
530. C3×C22⋊C4C22×D3semidirect
533. #217C22×D3semidirect
550. (C2×D3)⋊C4C22×D3semidirect
551. (C2×D3)⋊C4C22×D3semidirect
552. C4⋊Dic3C22×D3semidirect
555. Dic3⋊C4C22×D3semidirect
556. Dic3⋊C4C22×D3semidirect
651. C2×C22⋊C4D32semidirect
829. C2×C32#534semidirect
915. C22⋊C4C2×D32semidirect
1026. C32C2×#534semidirect
1110. C2×C3#5605semidirect
1111. C2×C3#5653semidirect
1174. C3C2×#5605semidirect
1175. C3C2×#5653semidirect
1183. C2#10594264direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×D3×D122
C2×#640912
C2×C3×#8842
C2×C3×#8832
C2×#639832
C2×#639812
C2×#639712
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×#638972
C2×#638862
C2×#638542
C2×#638502
#105942642
C2×#56533
C2×#56053