Finite Group Databasebeta

← C2×#10594959 #11903258

Subgroups — C2×#10594959 #11903258

Order 1152.

2609 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#924C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×#63982C211yesmaximal, characteristic, complemented
6C2×#67⋊Dic3C211yesmaximal, characteristic
7C2×#67⋊Dic3C211yesmaximal, characteristic
8#10594959C2116yesmaximal, direct product factor
9C2×#63899C211yesmaximal, characteristic, complemented
10C2×#63887C211yesmaximal, characteristic, complemented
11C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63851C211yesmaximal, characteristic, complemented
14C2×#63846C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5636—31nomaximal
18C2×#5539—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×C4×#67C2218yes—
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C3×#924C2218yescomplemented
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45#63982C2218yescomplemented
46#63982C2218yescomplemented
47#67⋊Dic3C2218yes—
48#67⋊Dic3C2218yes—
49C2×#3724C2211yescharacteristic
50C2×#3724C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63899C2218yescomplemented
62#63887C2218yescomplemented
63D3×Dic3⋊C4C2218yescomplemented
64#63867C2218yescomplemented
65#63851C2218yescomplemented
66#63846C2218yescomplemented
67#63839C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×C4×D4—31no—
71C2×#946—31no—
72C2×#944—31no—
73C2×D4×Dic3—31no—
74C2×D4×Dic3—31no—
75C2×C4×#67D311yescharacteristic
76C2×#924—31no—
77C2×#924D311yescharacteristic, complemented
78C22×Dic3⋊C4—31no—
79C22×Dic3⋊C4—31no—
80C22×Dic3⋊C4—31no—
81C22×Dic3⋊C4—61no—
82#5636—316no—
83#5539—316no—
84C2×#896—31no—
85C2×#896—31no—
86C2×D3×C4⋊C4—31no—
87C2×#890—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#888—31no—
91C2×#887—31no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#870—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4—42no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2314yes—
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3—42no—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2314yes—
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C3×#67Q818yescomplemented
117C2×C3×#67C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#627—24no—
130C2×#627—42no—
131C2×#627C2314yes—
132C2×#627C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3—42no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137#3750C2314yes—
138#3750C2314yes—
139#3750C2314yes—
140#3750C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161Dic32C2314yes—
162C2×#554—91noSylow
163C22×C3×Q8—31no—
164C22×C3×D4—31no—
165C23×C3×C4—21no—
166C23×C3×C4—31no—
167C23×C3×C4C2×D311yescharacteristic
168C23×C3×C4C2×D311yescharacteristic
169C22×#67C2×D311yescharacteristic
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C23×Dic3—31no—
176C23×Dic3—61no—
177C23×Dic3—61no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3C2×D311yescharacteristic
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6—31no—
184C22×Dic6—31no—
185C22×Dic6C2×D311yescharacteristic
186C3×C22⋊Q8—38no—
187C3×C4×D4—38no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C42—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217C2×D311yescharacteristic
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202#946—38no—
203#944—38no—
204D4×Dic3—38no—
205D4×Dic3—38no—
206C4×#67C2×D318yes—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3C2×D311yescharacteristic
217#924—38no—
218#924C2×D318yescomplemented
219C2×Dic3⋊C4—38no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—38no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—38no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4—61no—
242C2×Dic3⋊C4—61no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4—68no—
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3C2×D311yescharacteristic
253#896—38no—
254#896—38no—
255D3×C4⋊C4—38no—
256#890—38no—
257#889—38no—
258#889—38no—
259#888—38no—
260#887—38no—
261#67⋊C4—38no—
262#67⋊C4—38no—
263#878—38no—
264#878—38no—
265#878—38no—
266#878—38no—
267#878—38no—
268#878—38no—
269#870—38no—
270C4×Dic6—38no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2×Q814yes—
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3C2×Q814yes—
279C22×C3×D3C2412yes—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4—44no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3—28no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—44no—
290C2×C3⋊Dic3#4114yes—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C3×#67C2×Q8116yescomplemented
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3C2×Q814yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C3×C4×D3—44no—
311C3×Dic6—44no—
312#627—28no—
313#627—44no—
314D3×Dic3—28no—
315D3×Dic3—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—91no—
319C2×#125—91no—
320C2×C22⋊Q8—31no—
321C2×C22⋊Q8—91no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C2×C22⋊Q8—91no—
325C2×C22⋊Q8—91no—
326C2×C4×Q8—91no—
327C2×C4×D4—31no—
328C2×C4×D4—91no—
329C2×C4×D4—91no—
330C22×C4⋊C4—91no—
331C22×C4⋊C4—91no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C2×C3×Q8—34no—
338C2×C3×Q8—122no—
339C2×C3×D4—38no—
340C2×C3×D4—34no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—24no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—42no—
353C22×C3×C4—42no—
354C22×C3×C4—44no—
355C22×C3×C4—122no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D314yes—
361C22×C3×C4C22×D314yes—
362C2×#67Dic618yescomplemented
363C2×#67C22×D314yes—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—34no—
367C22×Dic3—34no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—34no—
375C22×Dic3—34no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—61no—
379C22×Dic3—64no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—64no—
384C22×Dic3—64no—
385C22×Dic3—64no—
386C22×Dic3—64no—
387C22×Dic3—68no—
388C22×Dic3—122no—
389C22×Dic3—122no—
390C22×Dic3—122no—
391C22×Dic3—124no—
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—42no—
402C2×C4×D3—64no—
403C2×C4×D3—122no—
404C2×C4×D3C22×D314yes—
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6—34no—
409C2×Dic6—42no—
410C2×Dic6—64no—
411C2×Dic6—64no—
412C2×Dic6—122no—
413C2×Dic6—122no—
414C2×Dic6C22×D314yes—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C42—34no—
424#217—34no—
425#217—34no—
426#217C22×D314yes—
427#217C22×D314yes—
428#217C22×D314yes—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4C22×D314yes—
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3C22×D314yes—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—64no—
458Dic3⋊C4—64no—
459Dic3⋊C4—64no—
460Dic3⋊C4—64no—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3—34no—
468C4×Dic3C22×D314yes—
469C22×C32—28no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32C22×Q814yes—
473C22×C32C22×Q812yes—
474C22×C32C2×#4112yes—
475C22×C32H(5,𝔽2)12yes—
476C22×C32C2511yescharacteristic
477C2×C3×D3—28no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3C22×Q814yes—
481C32×C4—22no—
482C32×C4—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3C2×#4114yes—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C22×Q814yes—
494C22×Q8—31no—
495C22×Q8—91no—
496C22×Q8—91no—
497C22×D4—31no—
498C23×C4—31no—
499C23×C4—91no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4D3211yescharacteristic
504C4⋊Q8—98no—
505#125—98no—
506#125—98no—
507C22⋊Q8—38no—
508C22⋊Q8—98no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512C22⋊Q8—98no—
513C4×Q8—98no—
514C4×D4—38no—
515C4×D4—98no—
516C4×D4—98no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—98no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—91no—
534C2×C4⋊C4—98no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—31no—
538C2×C22⋊C4—31no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C42—31no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—24no—
545C23×C3—24no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—21no—
552C23×C3—24no—
553C23×C3—34no—
554C23×C3—32no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3C2×Dic614yes—
558C23×C3D3×Q814yes—
559C23×C3C23×D312yes—
560C23×C3C23×D312yes—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C22×D3—22no—
564C22×D3—22no—
565C22×D3C2×Dic614yes—
566C22×D3C23×D312yes—
567C3×Q8—124no—
568C3×D4—316no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—34no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—44no—
586C2×C3×C4—44no—
587C2×C3×C4—48no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599#67C2×Dic6116yescomplemented
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—34no—
607C2×Dic3—34no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—64no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—68no—
622C2×Dic3—68no—
623C2×Dic3—68no—
624C2×Dic3—616no—
625C2×Dic3—64no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—122no—
633C2×Dic3—122no—
634C2×Dic3—124no—
635C2×Dic3—124no—
636C2×Dic3—124no—
637C2×Dic3—128no—
638C2×Dic3C2×Dic614yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C4×D3—44no—
647C4×D3—68no—
648C4×D3—124no—
649Dic6—44no—
650Dic6—68no—
651Dic6—68no—
652Dic6—124no—
653Dic6—124no—
654C2×C32—24no—
655C2×C32#55414yescomplemented
656C2×C32C23×Q811yescharacteristic
657C2×C32C22×#4111yescharacteristic
658C2×C32C2×H(5,𝔽2)11yescharacteristic
659C3×D3—24no—
660C24—31no—
661C24C2×D3211yescharacteristic
662C2×Q8—34no—
663C2×Q8—94no—
664C2×Q8—94no—
665C2×Q8—122no—
666C2×Q8—184no—
667C2×Q8—362no—
668C2×D4—34no—
669C2×D4—38no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—34no—
678C22×C4—42no—
679C22×C4—94no—
680C22×C4—94no—
681C22×C4—91no—
682C22×C4—94no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—94no—
687C22×C4—122no—
688C22×C4—184no—
689C22×C4—184no—
690C22×C4—362no—
691C22×C4—362no—
692C22×C4C2×D3211yescharacteristic
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3214yes—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C42—34no—
718C42—94no—
719C42—94no—
720C22×C3—24no—
721C22×C3—24no—
722C22×C3—216no—
723C22×C3—28no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—28no—
729C22×C3—24no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—34no—
735C22×C3—68no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3C22×Dic614yes—
739C22×C3C22×Dic612yes—
740C22×C3#100412yes—
741C22×C3#100412yes—
742C22×C3C2×D3×Q814yes—
743C22×C3C2×D3×Q812yes—
744C22×C3D3×#4112yes—
745C22×C3D3×#4112yes—
746C22×C3C24×D311yescharacteristic
747C22×C3C24×D311yescharacteristic
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—28no—
751C2×D3C22×Dic614yes—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—34no—
757C3×C4—42no—
758C3×C4—42no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—34no—
772Dic3—34no—
773Dic3—64no—
774Dic3—64no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782Dic3—122no—
783Dic3C22×Dic614yes—
784C32C2×#55411yescharacteristic, complemented, Sylow
785C23—22no—
786C23—22no—
787C23—34no—
788C23—32no—
789C23—62no—
790C23—62no—
791C23D3×Dic614yes—
792C23C22×D3212yes—
793C23C22×D3211yescharacteristic
794Q8—124no—
795Q8—188no—
796Q8—364no—
797D4—316no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—34no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—44no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—62no—
815C2×C4—94no—
816C2×C4—92no—
817C2×C4—92no—
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—124no—
821C2×C4—188no—
822C2×C4—188no—
823C2×C4—182no—
824C2×C4—182no—
825C2×C4—182no—
826C2×C4—364no—
827C2×C4—364no—
828C2×C4C22×D3212yes—
829C2×C4C22×D3212yes—
830C2×C3—28no—
831C2×C3—24no—
832C2×C3—24no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—24no—
837C2×C3—64no—
838C2×C3#553914yescomplemented
839C2×C3#563614yescomplemented
840C2×C3C23×Dic611yescharacteristic
841C2×C3C2×#100411yescharacteristic
842C2×C3C2×#100411yescharacteristic
843C2×C3C22×D3×Q811yescharacteristic
844C2×C3C2×D3×#4111yescharacteristic
845C2×C3C2×D3×#4111yescharacteristic
846D3—24no—
847C22—22no—
848C22—22no—
849C22—28no—
850C22—34no—
851C22—62no—
852C22—62no—
853C22—68no—
854C22C2×D3×Dic614yes—
855C22C2×D3×Dic612yes—
856C22#6430612yes—
857C22#6433012yes—
858C22C23×D3211yescharacteristic
859C4—22no—
860C4—22no—
861C4—34no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—62no—
868C4—94no—
869C4—182no—
870C4—182no—
871C4—182no—
872C3—21no—
873C3C2×#553911yescharacteristic, complemented
874C3C2×#563611yescharacteristic, complemented
875C2—24no—
876C2—64no—
877C2#1059495914yesdirect product factor
878C2C22×D3×Dic611yescharacteristic
879C2C2×#6430611yescharacteristic
880C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3750C2semidirect
3. C2×C3×#924C2semidirect
4. C2×#63982C2semidirect
5. C2×#63982C2semidirect
8. #10594959C2direct (N × H)
9. C2×#63899C2semidirect
10. C2×#63887C2semidirect
11. C2×D3×Dic3⋊C4C2semidirect
12. C2×#63867C2semidirect
13. C2×#63851C2semidirect
14. C2×#63846C2semidirect
15. C2×#63839C2semidirect
16. C2×#63837C2semidirect
33. C2×#3750C22semidirect
40. C3×#924C22semidirect
45. #63982C22semidirect
46. #63982C22semidirect
61. #63899C22semidirect
62. #63887C22semidirect
63. D3×Dic3⋊C4C22semidirect
64. #63867C22semidirect
65. #63851C22semidirect
66. #63846C22semidirect
67. #63839C22semidirect
68. #63837C22semidirect
77. C2×#924D3semidirect
116. C2×C3×#67Q8semidirect
218. #924C2×D3semidirect
295. C3×#67C2×Q8semidirect
362. C2×#67Dic6semidirect
599. #67C2×Dic6semidirect
655. C2×C32#554semidirect
784. C32C2×#554semidirect
838. C2×C3#5539semidirect
839. C2×C3#5636semidirect
873. C3C2×#5539semidirect
874. C3C2×#5636semidirect
877. C2#10594959direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×C4×#672
C2×C3×#9242
C2×#639822
C2×#67⋊Dic32
#105949592
C2×#638992
C2×#638872
C2×D3×Dic3⋊C42
C2×#638672
C2×#638512
C2×#638462
C2×#638392
C2×#638372
C2×#56363
C2×#55393