Finite Group Databasebeta

← #33102125

Subgroups — #33102125

Order 18688.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612780C212yesmaximal, complemented
2#22610917C212yesmaximal, complemented
3#22610390C212yesmaximal, complemented
4#22610385C212yesmaximal
5#22610008C211yesmaximal, characteristic, complemented
6#22610005C211yesmaximal, characteristic, complemented
7#22609919C211yesmaximal, characteristic, complemented
8C4×#14556506C211yesmaximal, characteristic, complemented
9#22609664C211yesmaximal, characteristic, complemented
10C2×#17988354C211yesmaximal, characteristic, complemented
11C2×#551×C73C211yesmaximal, characteristic
12C2×#14556550C2212yes—
13C22×C22⋊Dic73C2212yes—
14C2×#14556506C2212yes—
15C2×#14556506C2212yes—
16#17988480—22no—
17#17988480—22no—
18#17988462—22no—
19#17988450C2212yes—
20#17988447C2212yes—
21#17988443C2212yes—
22C22⋊C4×Dic73—22no—
23C4×C22⋊Dic73C2212yes—
24#17988354C2211yescharacteristic
25#17988354C2211yescharacteristic
26#17988354C2212yes—
27#17988354C2211yescharacteristic
28#17988354C2212yes—
29#17988354C2212yes—
30#17988354C2211yescharacteristic
31#17988354C2212yes—
32#551×C73—22no—
33#551×C73—22no—
34#551×C73—22no—
35#551×C73—22no—
36C2×#126×C73C411yescharacteristic, complemented
37C2×#126×C73C411yescharacteristic, complemented
38C2×#124×C73C411yescharacteristic, complemented
39C2×#123×C73C411yescharacteristic, complemented
40C2×#123×C73C411yescharacteristic, complemented
41C2×#123×C73C2211yescharacteristic
42C2×C22⋊Q8×C73C411yescharacteristic, complemented
43C2×C22⋊Q8×C73C2211yescharacteristic
44C2×#120×C73C2211yescharacteristic
45C2×C4×D4×C73C411yescharacteristic, complemented
46C2×C4×D4×C73C2211yescharacteristic
47C2×#117×C73C411yescharacteristic, complemented
48C2×#117×C73C2211yescharacteristic
49C22×C22⋊C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C23×Dic73—22no—
52#14556550—24no—
53#14556550—42no—
54C2×C4⋊Dic73—22no—
55C2×C4⋊Dic73—22no—
56C2×C22⋊Dic73—24no—
57C2×C22⋊Dic73—22no—
58C2×C22⋊Dic73—22no—
59C2×C22⋊Dic73—22no—
60C2×C22⋊Dic73—42no—
61C2×C22⋊Dic73C2312yes—
62C2×C22⋊Dic73C2312yes—
63C2×C22⋊Dic73C2312yes—
64C2×C22⋊Dic73C2312yes—
65C2×C4×Dic73—22no—
66C2×C4×Dic73—22no—
67#14556506—24no—
68#14556506—42no—
69#14556498—22no—
70#14556498—22no—
71#14556498—22no—
72#14556498—22no—
73C25×C73C2311yescharacteristic
74C22×Q8×C73C2×C411yescharacteristic, complemented
75C22×D4×C73C2×C411yescharacteristic
76C22×D4×C73C2×C411yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C23×C4×C73C2×C411yescharacteristic
79C23×C4×C73C2×C411yescharacteristic
80C23×C4×C73C2×C411yescharacteristic, complemented
81C23×C4×C73C2311yescharacteristic
82C23×C4×C73C2311yescharacteristic
83#126×C73—22no—
84#126×C73—22no—
85#126×C73—22no—
86#126×C73—22no—
87#124×C73—22no—
88#124×C73—22no—
89#123×C73—22no—
90#123×C73—22no—
91#123×C73—22no—
92#123×C73—22no—
93#123×C73—22no—
94#123×C73—22no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73—22no—
99#120×C73—22no—
100#120×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73—22no—
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73—21no—
106C4×D4×C73—21no—
107#117×C73—22no—
108#117×C73—22no—
109#117×C73—21no—
110#117×C73—21no—
111#117×C73—21no—
112#117×C73—21no—
113C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
115C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
116C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
117C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
118C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
119C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
120C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C22⋊C4×C73C2×C411yescharacteristic
125C2×C22⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130C2×C22⋊C4×C73C2×C411yescharacteristic
131C2×C22⋊C4×C73C2×C411yescharacteristic, complemented
132C2×C22⋊C4×C73C2×C411yescharacteristic, complemented
133C2×C22⋊C4×C73C2×C411yescharacteristic, complemented
134C2×C22⋊C4×C73D412yes—
135C2×C22⋊C4×C73D412yes—
136C2×C22⋊C4×C73D412yes—
137C2×C22⋊C4×C73D412yes—
138C2×C22⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73C2311yescharacteristic
141C2×C42×C73C2×C411yescharacteristic, complemented
142C2×C42×C73C2×C411yescharacteristic, complemented
143C2×C42×C73C2×C411yescharacteristic, complemented
144C22×Dic73—22no—
145C22×Dic73—22no—
146C22×Dic73—22no—
147C22×Dic73—22no—
148C22×Dic73—44no—
149C22×Dic73—44no—
150C22×Dic73—82no—
151C4⋊Dic73—44no—
152C4⋊Dic73—82no—
153C22⋊Dic73—22no—
154C22⋊Dic73—22no—
155C22⋊Dic73—22no—
156C22⋊Dic73—22no—
157C22⋊Dic73—22no—
158C22⋊Dic73—22no—
159C22⋊Dic73—22no—
160C22⋊Dic73—44no—
161C22⋊Dic73—44no—
162C22⋊Dic73—82no—
163C22⋊Dic73#4114yes—
164C4×Dic73—44no—
165C4×Dic73—82no—
166C24×C73—22no—
167C24×C73—21no—
168C24×C73—21no—
169C24×C73—42no—
170C24×C73—81no—
171C24×C73C22×C411yescharacteristic
172C24×C73C22×C411yescharacteristic
173C24×C73C22×C411yescharacteristic
174C24×C73C2×D412yes—
175C24×C73C2×D412yes—
176C24×C73C2411yescharacteristic
177C2×Q8×C73—22no—
178C2×Q8×C73—81no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—22no—
182C2×D4×C73—22no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—22no—
186C2×D4×C73—42no—
187C2×D4×C73—81no—
188C22×C4×C73—22no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—42no—
198C22×C4×C73—81no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73C22×C411yescharacteristic
202C22×C4×C73C22×C411yescharacteristic
203C22×C4×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C22×C411yescharacteristic
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C2×D412yes—
213C22×C4×C73C2×D412yes—
214C22×C4×C73C2×D412yes—
215C22×C4×C73C2×D412yes—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—22no—
227C22⋊C4×C73—22no—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—21no—
230C22⋊C4×C73—21no—
231C22⋊C4×C73—22no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—22no—
235C22⋊C4×C73—22no—
236C22⋊C4×C73—21no—
237C22⋊C4×C73—21no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73C22⋊C411yescharacteristic
240C22⋊C4×C73C22⋊C411yescharacteristic
241C22⋊C4×C73C22⋊C411yescharacteristic
242C22⋊C4×C73C22⋊C411yescharacteristic
243C22⋊C4×C73C22⋊C412yes—
244C22⋊C4×C73C22⋊C412yes—
245C22⋊C4×C73C22⋊C412yes—
246C22⋊C4×C73C22⋊C412yes—
247C22⋊C4×C73C22⋊C412yes—
248C22⋊C4×C73C22⋊C412yes—
249C42×C73—21no—
250C42×C73—21no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—21no—
254C42×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—24no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—22no—
264C23×C73—22no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—42no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—42no—
275C23×C73—42no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—84no—
279C23×C73—82no—
280C23×C73—82no—
281C23×C73C2×C22⋊C412yes—
282C23×C73C2×C22⋊C411yescharacteristic
283C23×C73C2×C22⋊C411yescharacteristic
284C23×C73C23×C411yescharacteristic
285C23×C73C22×D412yes—
286C23×C73C2×#4112yes—
287C23×C73H(5,𝔽2)11yescharacteristic
288C23×C732−1+411yescharacteristic
289Q8×C73—82no—
290D4×C73—42no—
291D4×C73—42no—
292D4×C73—42no—
293D4×C73—42no—
294D4×C73—82no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—81no—
325C2×C4×C73—81no—
326C2×C4×C73—81no—
327C2×C4×C73—81no—
328C2×C4×C73C2×C22⋊C411yescharacteristic
329C2×C4×C73C2×C22⋊C411yescharacteristic
330C2×C4×C73C2×C22⋊C411yescharacteristic
331C2×C4×C73C2×C22⋊C411yescharacteristic
332C2×C4×C73C2×C22⋊C412yes—
333C2×C4×C73C2×C22⋊C412yes—
334C2×Dic73—24no—
335C2×Dic73—42no—
336C2×Dic73—42no—
337C2×Dic73—42no—
338C2×Dic73—42no—
339C2×Dic73—42no—
340C2×Dic73—42no—
341C2×Dic73—42no—
342C2×Dic73—42no—
343C2×Dic73—42no—
344C2×Dic73—42no—
345C2×Dic73—42no—
346C2×Dic73—88no—
347C22×C73—21no—
348C22×C73—22no—
349C22×C73—21no—
350C22×C73—22no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—21no—
354C22×C73—22no—
355C22×C73—21no—
356C22×C73—22no—
357C22×C73—21no—
358C22×C73—22no—
359C22×C73—42no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—44no—
363C22×C73—44no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—82no—
370C22×C73—82no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73#41012yes—
376C22×C73C22×C22⋊C411yescharacteristic
377C22×C73C4×#4111yescharacteristic
378C22×C73#52011yescharacteristic
379C22×C73#54612yes—
380C22×C73#54712yes—
381C4×C73—21no—
382C4×C73—22no—
383C4×C73—21no—
384C4×C73—21no—
385C4×C73—21no—
386C4×C73—22no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73—41no—
390C4×C73—41no—
391C4×C73—41no—
392C4×C73—41no—
393C4×C73—41no—
394Dic73—44no—
395Dic73—82no—
396Dic73—82no—
397Dic73—82no—
398#22477—731nomaximal, Sylow
399C2×C73—22no—
400C2×C73—22no—
401C2×C73—22no—
402C2×C73—21no—
403C2×C73—21no—
404C2×C73—41no—
405C2×C73—42no—
406C2×C73—81no—
407C2×C73#233911yescharacteristic
408C2×C73C2×#41011yescharacteristic
409C2×C73#288311yescharacteristic
410C2×#551D7311yescharacteristic
411#2342—732no—
412#1996—732no—
413#1899—732no—
414#1898—732no—
415#1820—731no—
416#1819—731no—
417#1799—731no—
418C4×#99—731no—
419#1740—731no—
420C2×#342—731no—
421C73#2247711yescharacteristic, complemented, Sylow
422#551—22no—
423#551—22no—
424#551—22no—
425#551—22no—
426C2×#126Dic7311yescharacteristic, complemented
427C2×#126Dic7311yescharacteristic, complemented
428C2×#124Dic7311yescharacteristic, complemented
429C2×#123Dic7311yescharacteristic, complemented
430C2×#123Dic7311yescharacteristic, complemented
431C2×#123C2×D7311yescharacteristic
432C2×C22⋊Q8Dic7311yescharacteristic, complemented
433C2×C22⋊Q8C2×D7311yescharacteristic
434C2×#120C2×D7311yescharacteristic
435C2×C4×D4Dic7311yescharacteristic, complemented
436C2×C4×D4C2×D7311yescharacteristic
437C2×#117—732no—
438C2×#117Dic7311yescharacteristic, complemented
439C2×#117C2×D7311yescharacteristic
440C22×C22⋊C4—732no—
441C22×C22⋊C4C2×D7311yescharacteristic
442C22×C22⋊C4C2×D7311yescharacteristic
443C2×#99—732no—
444C2×#99—732no—
445#388—1462no—
446#388—1462no—
447#385—1462no—
448#381—732no—
449#380—732no—
450#379—732no—
451C4×C22⋊C4—732no—
452C4×C22⋊C4—1462no—
453#342—731no—
454#342—731no—
455#342—731no—
456#342—732no—
457#342—732no—
458#342—732no—
459#342—732no—
460#342—731no—
461C25C22×D7311yescharacteristic
462C22×Q8C2×Dic7311yescharacteristic, complemented
463C22×D4C2×Dic7311yescharacteristic
464C22×D4C2×Dic7311yescharacteristic
465C22×D4C22×D7311yescharacteristic
466C23×C4—1462no—
467C23×C4C2×Dic7311yescharacteristic
468C23×C4C2×Dic7311yescharacteristic
469C23×C4C2×Dic7311yescharacteristic, complemented
470C23×C4C22×D7311yescharacteristic
471C23×C4C22×D7311yescharacteristic
472#126—22no—
473#126—22no—
474#126—22no—
475#126—22no—
476#124—22no—
477#124—22no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#120—22no—
489#120—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117—2922no—
503#117—1464no—
504C2×C4⋊C4—1462no—
505C2×C4⋊C4—1462no—
506C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
507C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
508C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
509C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
510C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
511C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
512C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
513C2×C4⋊C4C2×Dic7311yescharacteristic, complemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—2922no—
517C2×C22⋊C4—732no—
518C2×C22⋊C4—732no—
519C2×C22⋊C4—732no—
520C2×C22⋊C4—732no—
521C2×C22⋊C4—1462no—
522C2×C22⋊C4—1462no—
523C2×C22⋊C4—1464no—
524C2×C22⋊C4—1462no—
525C2×C22⋊C4C2×Dic7311yescharacteristic
526C2×C22⋊C4C2×Dic7311yescharacteristic
527C2×C22⋊C4C2×Dic7311yescharacteristic
528C2×C22⋊C4C2×Dic7311yescharacteristic
529C2×C22⋊C4C2×Dic7311yescharacteristic
530C2×C22⋊C4C2×Dic7311yescharacteristic
531C2×C22⋊C4C2×Dic7311yescharacteristic
532C2×C22⋊C4C2×Dic7311yescharacteristic
533C2×C22⋊C4C2×Dic7311yescharacteristic, complemented
534C2×C22⋊C4C2×Dic7311yescharacteristic, complemented
535C2×C22⋊C4C2×Dic7311yescharacteristic, complemented
536C2×C22⋊C4C22⋊D7312yes—
537C2×C22⋊C4C22⋊D7312yes—
538C2×C22⋊C4C22⋊D7312yes—
539C2×C22⋊C4C22⋊D7312yes—
540C2×C22⋊C4C22×D7311yescharacteristic
541C2×C22⋊C4C22×D7311yescharacteristic
542C2×C22⋊C4C22×D7311yescharacteristic
543C2×C42—1462no—
544C2×C42—1462no—
545C2×C42C2×Dic7311yescharacteristic, complemented
546C2×C42C2×Dic7311yescharacteristic, complemented
547C2×C42C2×Dic7311yescharacteristic, complemented
548#99—2922no—
549#99—1464no—
550#95—1462no—
551#95—1462no—
552#95—1462no—
553#95—1462no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—42no—
558C24—81no—
559C24C22×Dic7311yescharacteristic
560C24C22×Dic7311yescharacteristic
561C24C22×Dic7311yescharacteristic
562C24C2×C22⋊D7312yes—
563C24C2×C22⋊D7312yes—
564C24C23×D7311yescharacteristic
565C2×Q8—22no—
566C2×Q8—81no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—42no—
575C2×D4—81no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—2924no—
590C22×C4—2924no—
591C22×C4—5842no—
592C22×C4—1462no—
593C22×C4—1462no—
594C22×C4—1462no—
595C22×C4—1462no—
596C22×C4C22×Dic7311yescharacteristic
597C22×C4C22×Dic7311yescharacteristic
598C22×C4C22×Dic7311yescharacteristic
599C22×C4C22×Dic7311yescharacteristic
600C22×C4C22×Dic7311yescharacteristic
601C22×C4C22×Dic7311yescharacteristic
602C22×C4C22×Dic7311yescharacteristic
603C22×C4C22×Dic7311yescharacteristic
604C22×C4C22×Dic7311yescharacteristic
605C22×C4C22×Dic7311yescharacteristic
606C22×C4C22×Dic7311yescharacteristic
607C22×C4C2×C22⋊D7312yes—
608C22×C4C2×C22⋊D7312yes—
609C22×C4C2×C22⋊D7312yes—
610C22×C4C2×C22⋊D7312yes—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—2924no—
623C4⋊C4—5842no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—22no—
636C22⋊C4—2924no—
637C22⋊C4—2924no—
638C22⋊C4—5842no—
639C22⋊C4—734no—
640C22⋊C4—1462no—
641C22⋊C4—1462no—
642C22⋊C4—1462no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C22⋊C4C22⋊Dic7311yescharacteristic
648C22⋊C4C22⋊Dic7311yescharacteristic
649C22⋊C4C22⋊Dic7311yescharacteristic
650C22⋊C4C22⋊Dic7311yescharacteristic
651C22⋊C4C22⋊Dic7312yes—
652C22⋊C4C22⋊Dic7312yes—
653C22⋊C4C22⋊Dic7312yes—
654C22⋊C4C22⋊Dic7312yes—
655C22⋊C4C22⋊Dic7312yes—
656C22⋊C4C22⋊Dic7312yes—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—2924no—
664C42—5842no—
665C23—22no—
666C23—22no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—82no—
690C23—82no—
691C23C2×C22⋊Dic7312yes—
692C23C2×C22⋊Dic7311yescharacteristic
693C23C2×C22⋊Dic7311yescharacteristic
694C23C23×Dic7311yescharacteristic
695C23C22×C22⋊D7312yes—
696C23#41×D7312yes—
697C23#1455663711yescharacteristic
698C23#1455663811yescharacteristic
699Q8—82no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—82no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—2922no—
739C2×C4—2922no—
740C2×C4—2922no—
741C2×C4—2922no—
742C2×C4—2922no—
743C2×C4—2922no—
744C2×C4—2922no—
745C2×C4—2922no—
746C2×C4—2922no—
747C2×C4—2922no—
748C2×C4—2922no—
749C2×C4—5848no—
750C2×C4—1464no—
751C2×C4C2×C22⋊Dic7311yescharacteristic
752C2×C4C2×C22⋊Dic7311yescharacteristic
753C2×C4C2×C22⋊Dic7311yescharacteristic
754C2×C4C2×C22⋊Dic7311yescharacteristic
755C2×C4C2×C22⋊Dic7312yes—
756C2×C4C2×C22⋊Dic7312yes—
757C22—21no—
758C22—22no—
759C22—21no—
760C22—22no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—22no—
767C22—22no—
768C22—21no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—44no—
773C22—44no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—82no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#1798856112yes—
786C22C22×C22⋊Dic7311yescharacteristic
787C22#41×Dic7311yescharacteristic
788C22#1798907011yescharacteristic
789C22#1798922512yes—
790C22#1798923612yes—
791C4—21no—
792C4—21no—
793C4—22no—
794C4—21no—
795C4—22no—
796C4—21no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—2924no—
805C4—5842no—
806C4—5842no—
807C4—5842no—
808C2—22no—
809C2—22no—
810C2—22no—
811C2—21no—
812C2—21no—
813C2—41no—
814C2—42no—
815C2—81no—
816C2#2261276111yescharacteristic
817C2C2×#1798856111yescharacteristic
818C2#2261839211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic73
commutatorC23×C73C23×C4
FrattiniC24C23×D73
FittingC2×#551×C73C2
socleC22×C73C22×C22⋊C4
prime radicalC2×#120×C73C22
cosocleC24×C73C24
hypercenterC2×#551D73
hypocenterC73#22477
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #22612780C2semidirect
2. #22610917C2semidirect
3. #22610390C2semidirect
5. #22610008C2semidirect
6. #22610005C2semidirect
7. #22609919C2semidirect
8. C4×#14556506C2semidirect
9. #22609664C2semidirect
10. C2×#17988354C2semidirect
36. C2×#126×C73C4semidirect
37. C2×#126×C73C4semidirect
38. C2×#124×C73C4semidirect
39. C2×#123×C73C4semidirect
40. C2×#123×C73C4semidirect
42. C2×C22⋊Q8×C73C4semidirect
45. C2×C4×D4×C73C4semidirect
47. C2×#117×C73C4semidirect
74. C22×Q8×C73C2×C4semidirect
80. C23×C4×C73C2×C4semidirect
113. C2×C4⋊C4×C73C2×C4semidirect
114. C2×C4⋊C4×C73C2×C4semidirect
115. C2×C4⋊C4×C73C2×C4semidirect
116. C2×C4⋊C4×C73C2×C4semidirect
117. C2×C4⋊C4×C73C2×C4semidirect
118. C2×C4⋊C4×C73C2×C4semidirect
119. C2×C4⋊C4×C73C2×C4semidirect
120. C2×C4⋊C4×C73C2×C4semidirect
131. C2×C22⋊C4×C73C2×C4semidirect
132. C2×C22⋊C4×C73C2×C4semidirect
133. C2×C22⋊C4×C73C2×C4semidirect
141. C2×C42×C73C2×C4semidirect
142. C2×C42×C73C2×C4semidirect
143. C2×C42×C73C2×C4semidirect
421. C73#22477semidirect
426. C2×#126Dic73semidirect
427. C2×#126Dic73semidirect
428. C2×#124Dic73semidirect
429. C2×#123Dic73semidirect
430. C2×#123Dic73semidirect
432. C2×C22⋊Q8Dic73semidirect
435. C2×C4×D4Dic73semidirect
438. C2×#117Dic73semidirect
462. C22×Q8C2×Dic73semidirect
469. C23×C4C2×Dic73semidirect
506. C2×C4⋊C4C2×Dic73semidirect
507. C2×C4⋊C4C2×Dic73semidirect
508. C2×C4⋊C4C2×Dic73semidirect
509. C2×C4⋊C4C2×Dic73semidirect
510. C2×C4⋊C4C2×Dic73semidirect
511. C2×C4⋊C4C2×Dic73semidirect
512. C2×C4⋊C4C2×Dic73semidirect
513. C2×C4⋊C4C2×Dic73semidirect
533. C2×C22⋊C4C2×Dic73semidirect
534. C2×C22⋊C4C2×Dic73semidirect
535. C2×C22⋊C4C2×Dic73semidirect
545. C2×C42C2×Dic73semidirect
546. C2×C42C2×Dic73semidirect
547. C2×C42C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
#226127802
#226109172
#226103902
#226103852
#226100082
#226100052
#226099192
C4×#145565062
#226096642
C2×#179883542
C2×#551×C732
#2247773