Finite Group Databasebeta

← #33245379

Subgroups — #33245379

Order 18688.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556551C211yesmaximal, characteristic
2C22×#14556547C211yesmaximal, characteristic, complemented
3C2×#117×D73C211yesmaximal, characteristic, complemented
4#22612877C212yesmaximal, complemented
5#22612859C212yesmaximal, complemented
6#22612854C212yesmaximal, complemented
7#22612829C212yesmaximal, complemented
8#22612801C211yesmaximal, characteristic, complemented
9#22612795C211yesmaximal, characteristic, complemented
10#22612783C211yesmaximal, characteristic, complemented
11#22612780C211yesmaximal, characteristic, complemented
12#22612777C211yesmaximal, characteristic, complemented
13C22⋊C4×C22⋊D73C211yesmaximal, characteristic
14#22612747C211yesmaximal, characteristic
15#22612391C212yesmaximal, complemented
16#22612373C212yesmaximal, complemented
17#22612367C212yesmaximal, complemented
18#22612333C211yesmaximal, characteristic, complemented
19#22612311C211yesmaximal, characteristic, complemented
20#22612309C211yesmaximal, characteristic, complemented
21C4×#14556551C212yesmaximal, complemented
22C4×#14556547C211yesmaximal, characteristic, complemented
23C73×#2342C211yesmaximal, characteristic, complemented
24C23×C22⋊D73C2211yescharacteristic
25C24×Dic73C2211yescharacteristic
26C23×C4×D73C2211yescharacteristic
27C2×C4×C22⋊D73C2212yes—
28C2×#14556551C4116yescomplemented
29C2×#14556551C2212yes—
30C2×#14556551C2211yescharacteristic
31C2×#14556551C2211yescharacteristic
32C2×#14556551C2211yescharacteristic
33C2×#14556551C2211yescharacteristic
34C2×#14556551C2211yescharacteristic
35C2×#14556551C2211yescharacteristic
36C2×#14556551C2211yescharacteristic
37C2×#14556551C2211yescharacteristic
38C2×#14556550C2211yescharacteristic
39C2×#14556549C2212yescomplemented
40C2×#14556548C2212yescomplemented
41C2×#14556547—28no—
42C2×#14556547C2211yescharacteristic
43C2×#14556547C2211yescharacteristic
44C2×#14556547C2211yescharacteristic
45C2×#14556547C2211yescharacteristic
46C2×#14556547C2211yescharacteristic
47C2×#14556547C2211yescharacteristic
48C2×#14556547C2212yescomplemented
49C2×#14556547C2212yescomplemented
50#117×D73—28no—
51C22×#11924007C2211yescharacteristic
52C22×#11924007C2212yescomplemented
53C2×C4⋊C4×D73C2212yescomplemented
54C22×C22⋊Dic73C2211yescharacteristic
55C22×#11924005C2211yescharacteristic
56C2×C22⋊C4×D73C2211yescharacteristic
57C2×C22⋊C4×D73C2211yescharacteristic
58C22×C4×Dic73C2211yescharacteristic
59C22×C4×Dic73C2212yescomplemented
60C2×C42×D73C2212yescomplemented
61#17988487C2212yes—
62#17988487C2212yes—
63#17988484C2212yescomplemented
64#17988482C2212yescomplemented
65#17988480C2212yescomplemented
66#17988480C2212yescomplemented
67#17988479C2212yescomplemented
68#17988478C2212yescomplemented
69#17988477C2212yescomplemented
70#17988476C2212yescomplemented
71#17988474C2212yescomplemented
72#17988471C2212yescomplemented
73#17988469C2212yescomplemented
74#17988468C2212yescomplemented
75#17988466C2212yes—
76#17988464C2212yes—
77#17988463C2212yes—
78#17988463C2212yes—
79#17988462C2212yescomplemented
80#17988461C2212yescomplemented
81#17988458C2212yescomplemented
82#17988456C2212yescomplemented
83#17988451C2212yescomplemented
84#17988450C2211yescharacteristic
85#17988448C2211yescharacteristic
86#17988448C2211yescharacteristic
87#17988447C2211yescharacteristic
88#17988446C2212yescomplemented
89#17988446C2212yescomplemented
90#17988445C2211yescharacteristic
91#17988445C2211yescharacteristic
92#17988445C2212yescomplemented
93#17988445C2212yescomplemented
94#17988443C2211yescharacteristic
95#17988442C2211yescharacteristic
96#17988442C2211yescharacteristic
97C4⋊C4×Dic73C2212yescomplemented
98C4×#11924007C2212yescomplemented
99C4×#11924007C2212yescomplemented
100#17988438C2212yescomplemented
101#17988438C2212yescomplemented
102#17988438C2212yescomplemented
103C22⋊C4×Dic73C2211yescharacteristic
104C22⋊C4×Dic73C2211yescharacteristic
105C22⋊C4×Dic73C2212yescomplemented
106C22⋊C4×Dic73C2212yescomplemented
107C22⋊C4×Dic73C2212yescomplemented
108C4×#11924005C2212yescomplemented
109C4×C22⋊Dic73C2211yescharacteristic
110#17988434C2212yescomplemented
111#17988434C2212yescomplemented
112#17988434C2212yescomplemented
113#17988432C2212yescomplemented
114C42×Dic73C2212yescomplemented
115C2×#117×C73C2211yescharacteristic
116C22×C22⋊C4×C73C2211yescharacteristic
117C22×C22⋊C4×C73C2211yescharacteristic
118#388×C73C2212yescomplemented
119#388×C73C2212yescomplemented
120#385×C73C2212yescomplemented
121#381×C73C2211yescharacteristic
122#380×C73C2211yescharacteristic
123#379×C73C2211yescharacteristic
124C4×C22⋊C4×C73C2211yescharacteristic
125C4×C22⋊C4×C73C2212yescomplemented
126C24×D73C2311yescharacteristic
127C22×C22⋊D73—28no—
128C22×C22⋊D73C2×C418yes—
129C22×C22⋊D73C2311yescharacteristic
130C22×C22⋊D73C2311yescharacteristic
131C22×C22⋊D73C2311yescharacteristic
132C22×C22⋊D73C2311yescharacteristic
133C23×Dic73—24no—
134C23×Dic73—24no—
135C23×Dic73C2×C418yescomplemented
136C23×Dic73C2312yes—
137C23×Dic73C2311yescharacteristic
138C23×Dic73C2311yescharacteristic
139C23×Dic73C2311yescharacteristic
140C23×Dic73C2311yescharacteristic
141C23×Dic73C2311yescharacteristic
142C23×Dic73C2311yescharacteristic
143C23×Dic73C2311yescharacteristic
144C22×C4×D73—24no—
145C22×C4×D73—24no—
146C22×C4×D73C2×C418yescomplemented
147C22×C4×D73C2312yes—
148C22×C4×D73C2312yes—
149C22×C4×D73C2311yescharacteristic
150C22×C4×D73C2311yescharacteristic
151C22×C4×D73C2311yescharacteristic
152C22×C4×D73C2311yescharacteristic
153C4×C22⋊D73—28no—
154#14556551—28no—
155#14556551C2×C418yes—
156#14556551C2×C418yes—
157#14556551C2×C418yescomplemented
158#14556551C2×C418yescomplemented
159#14556551C2×C418yescomplemented
160#14556551C2×C418yescomplemented
161#14556551C2×C418yescomplemented
162#14556551C2×C418yescomplemented
163#14556550—24no—
164#14556549—28no—
165#14556548—28no—
166#14556547—24no—
167#14556547—24no—
168#14556547—24no—
169#14556547—28no—
170#14556547—24no—
171#14556547—28no—
172#14556547—24no—
173#14556547D418yescomplemented
174C2×C4⋊Dic73C2312yes—
175C2×C4⋊Dic73C2312yes—
176C2×#11924007—28no—
177C2×#11924007C2×C418yescomplemented
178C2×#11924007C2312yes—
179C2×#11924007C2312yes—
180C2×#11924007C2312yes—
181C2×#11924007C2312yes—
182C2×#11924007C2312yes—
183C2×#11924007C2312yes—
184C2×#11924007C2312yes—
185C2×#11924007C2311yescharacteristic
186C2×#11924007C2311yescharacteristic
187C2×#11924007C2311yescharacteristic
188C2×#11924007C2311yescharacteristic
189C2×#11924007C2312yes—
190C4⋊C4×D73—28no—
191C2×C22⋊Dic73—24no—
192C2×C22⋊Dic73C2311yescharacteristic
193C2×C22⋊Dic73C2312yes—
194C2×C22⋊Dic73C2311yescharacteristic
195C2×C22⋊Dic73C2311yescharacteristic
196C2×C22⋊Dic73C2312yes—
197C2×C22⋊Dic73C2312yes—
198C2×C22⋊Dic73C2311yescharacteristic
199C2×#11924005C2×C418yescomplemented
200C2×#11924005C2312yes—
201C2×#11924005C2312yes—
202C2×#11924005C2312yes—
203C2×#11924005C2312yes—
204C2×#11924005C2312yes—
205C2×#11924005C2312yes—
206C2×#11924005C2311yescharacteristic
207C2×#11924005C2311yescharacteristic
208C2×#11924005C2311yescharacteristic
209C2×#11924005C2311yescharacteristic
210C22⋊C4×D73—24no—
211C22⋊C4×D73—24no—
212C2×C4×Dic73—28no—
213C2×C4×Dic73C2×C418yescomplemented
214C2×C4×Dic73C2312yes—
215C2×C4×Dic73C2312yes—
216C2×C4×Dic73C2312yes—
217C2×C4×Dic73C2312yes—
218C2×C4×Dic73C2312yes—
219C2×C4×Dic73C2312yes—
220C2×C4×Dic73C2312yes—
221C2×C4×Dic73C2312yes—
222C2×C4×Dic73C2312yes—
223C2×C4×Dic73C2311yescharacteristic
224C2×C4×Dic73C2311yescharacteristic
225C2×C4×Dic73C2311yescharacteristic
226C2×C4×Dic73C2311yescharacteristic
227C2×C4×Dic73C2312yes—
228C42×D73—28no—
229#14556498C2312yes—
230#14556498C2312yes—
231#14556498C2312yes—
232#14556498C2312yes—
233#14556498C2312yes—
234#14556498C2312yes—
235#14556498C2312yes—
236#14556498C2312yes—
237#14556498C2312yes—
238#14556498C2312yes—
239#14556498C2312yes—
240#14556498C2312yes—
241C25×C73C2311yescharacteristic
242C23×C4×C73C2312yes—
243C23×C4×C73C2311yescharacteristic
244C23×C4×C73C2311yescharacteristic
245#117×C73—24no—
246C2×C4⋊C4×C73C2312yes—
247C2×C4⋊C4×C73C2312yes—
248C2×C22⋊C4×C73—24no—
249C2×C22⋊C4×C73C2×C418yescomplemented
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2312yes—
252C2×C22⋊C4×C73C2311yescharacteristic
253C2×C22⋊C4×C73C2311yescharacteristic
254C2×C22⋊C4×C73C2312yes—
255C2×C22⋊C4×C73C2312yes—
256C2×C22⋊C4×C73C2311yescharacteristic
257C2×C22⋊C4×C73C2311yescharacteristic
258C2×C22⋊C4×C73C2311yescharacteristic
259C2×C22⋊C4×C73C2311yescharacteristic
260C2×C22⋊C4×C73C2311yescharacteristic
261C2×C42×C73C2312yes—
262C2×C42×C73C2312yes—
263#95×C73C2312yes—
264#95×C73C2312yes—
265#95×C73C2312yes—
266#95×C73C2312yes—
267C23×D73—22no—
268C23×D73—22no—
269C23×D73—24no—
270C23×D73—42no—
271C23×D73C22×C414yes—
272C23×D73C2411yescharacteristic
273C23×D73C2411yescharacteristic
274C2×C22⋊D73—24no—
275C2×C22⋊D73—24no—
276C2×C22⋊D73—232no—
277C2×C22⋊D73—24no—
278C2×C22⋊D73C22×C414yes—
279C2×C22⋊D73C22×C414yes—
280C2×C22⋊D73C22×C414yes—
281C2×C22⋊D73C22×C414yes—
282C2×C22⋊D73#4118yes—
283C22×Dic73—22no—
284C22×Dic73—22no—
285C22×Dic73—232no—
286C22×Dic73—22no—
287C22×Dic73—22no—
288C22×Dic73—22no—
289C22×Dic73—22no—
290C22×Dic73—22no—
291C22×Dic73—22no—
292C22×Dic73—22no—
293C22×Dic73—22no—
294C22×Dic73—24no—
295C22×Dic73—24no—
296C22×Dic73—24no—
297C22×Dic73—42no—
298C22×Dic73C22×C414yes—
299C22×Dic73C22×C414yes—
300C22×Dic73C22×C414yes—
301C22×Dic73C22×C414yes—
302C22×Dic73C22×C414yes—
303C22×Dic73C22×C414yes—
304C22×Dic73C22×C414yes—
305C22×Dic73C2×D414yes—
306C22×Dic73#4114yes—
307C22×Dic73C2412yes—
308C22×Dic73C2412yes—
309C22×Dic73C2412yes—
310C22×Dic73C2411yescharacteristic
311C22×Dic73C2411yescharacteristic
312C22×Dic73C2411yescharacteristic
313C22×Dic73C2412yes—
314C22×Dic73C2411yescharacteristic
315C22×Dic73C2411yescharacteristic
316C22×Dic73C2411yescharacteristic
317C2×C4×D73—232no—
318C2×C4×D73—22no—
319C2×C4×D73—22no—
320C2×C4×D73—22no—
321C2×C4×D73—22no—
322C2×C4×D73—22no—
323C2×C4×D73—22no—
324C2×C4×D73—22no—
325C2×C4×D73—22no—
326C2×C4×D73—24no—
327C2×C4×D73—24no—
328C2×C4×D73—24no—
329C2×C4×D73—24no—
330C2×C4×D73—42no—
331C2×C4×D73—42no—
332C2×C4×D73C22×C414yes—
333C2×C4×D73C22×C414yes—
334C2×C4×D73C22×C414yes—
335C2×C4×D73C22×C414yes—
336C4⋊Dic73—24no—
337C4⋊Dic73—42no—
338#11924007—24no—
339#11924007—24no—
340#11924007—24no—
341#11924007—24no—
342#11924007—24no—
343#11924007—24no—
344#11924007—24no—
345#11924007C22×C414yes—
346#11924007C22×C414yes—
347#11924007C22×C414yes—
348#11924007C22×C414yes—
349#11924007C2×D418yescomplemented
350C22⋊Dic73—22no—
351C22⋊Dic73—22no—
352C22⋊Dic73—22no—
353C22⋊Dic73—24no—
354C22⋊Dic73—24no—
355C22⋊Dic73—42no—
356C22⋊Dic73C2×D414yes—
357#11924005—24no—
358#11924005—24no—
359#11924005—24no—
360#11924005—24no—
361#11924005—42no—
362#11924005—42no—
363#11924005C22×C414yes—
364#11924005C22×C414yes—
365#11924005C22×C414yes—
366#11924005C22×C414yes—
367C4×Dic73—24no—
368C4×Dic73—24no—
369C4×Dic73—24no—
370C4×Dic73—24no—
371C4×Dic73—24no—
372C4×Dic73—24no—
373C4×Dic73—24no—
374C4×Dic73—24no—
375C4×Dic73—42no—
376C4×Dic73C22×C414yes—
377C4×Dic73C22×C414yes—
378C4×Dic73C22×C414yes—
379C4×Dic73C22×C414yes—
380C4×Dic73C2×D418yescomplemented
381C24×C73—22no—
382C24×C73—22no—
383C24×C73—24no—
384C24×C73—42no—
385C24×C73C22×C414yes—
386C24×C73C2411yescharacteristic
387C24×C73C2411yescharacteristic
388C24×C73C2411yescharacteristic
389C22×C4×C73—22no—
390C22×C4×C73—22no—
391C22×C4×C73—24no—
392C22×C4×C73—24no—
393C22×C4×C73—42no—
394C22×C4×C73—42no—
395C22×C4×C73C22×C414yes—
396C22×C4×C73C22×C414yes—
397C22×C4×C73C2412yes—
398C22×C4×C73C2412yes—
399C22×C4×C73C2412yes—
400C22×C4×C73C2411yescharacteristic
401C22×C4×C73C2411yescharacteristic
402C22×C4×C73C2411yescharacteristic
403C22×C4×C73C2411yescharacteristic
404C22×C4×C73C2412yes—
405C4⋊C4×C73—24no—
406C4⋊C4×C73—42no—
407C22⋊C4×C73—22no—
408C22⋊C4×C73—22no—
409C22⋊C4×C73—22no—
410C22⋊C4×C73—24no—
411C22⋊C4×C73—24no—
412C22⋊C4×C73—42no—
413C22⋊C4×C73C22×C414yes—
414C22⋊C4×C73C22×C414yes—
415C22⋊C4×C73C22×C414yes—
416C22⋊C4×C73C22×C414yes—
417C22⋊C4×C73C2×D414yes—
418C42×C73—24no—
419C42×C73—42no—
420C23×C73—21no—
421C23×C73—21no—
422C23×C73—22no—
423C23×C73—22no—
424C23×C73—22no—
425C23×C73—28no—
426C23×C73—28no—
427C23×C73—21no—
428C23×C73—21no—
429C23×C73—22no—
430C23×C73—22no—
431C23×C73—44no—
432C23×C73—48no—
433C23×C73—48no—
434C23×C73C23×C412yes—
435C23×C73C23×C412yes—
436C23×C73C23×C412yes—
437C23×C73C22×D412yes—
438C23×C73C2×#4114yes—
439C23×C73C2×#4112yes—
440C23×C73C2511yescharacteristic
441C22×D73—21no—
442C22×D73—21no—
443C22×D73—22no—
444C22×D73—28no—
445C22×D73—21no—
446C22×D73—21no—
447C22×D73—22no—
448C22×D73—22no—
449C22×D73—28no—
450C22×D73—44no—
451C22×D73—48no—
452C22×D73—48no—
453C22×D73C23×C412yes—
454C22×D73C23×C412yes—
455C22×D73C2×#4114yes—
456C2×C4×C73—28no—
457C2×C4×C73—21no—
458C2×C4×C73—21no—
459C2×C4×C73—22no—
460C2×C4×C73—21no—
461C2×C4×C73—21no—
462C2×C4×C73—22no—
463C2×C4×C73—22no—
464C2×C4×C73—22no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—44no—
475C2×C4×C73—48no—
476C2×C4×C73C23×C412yes—
477C2×C4×C73C23×C412yes—
478C2×C4×C73C23×C412yes—
479C2×C4×C73C23×C412yes—
480C2×C4×C73C22×D414yes—
481C22⋊D73—28no—
482C22⋊D73—28no—
483C22⋊D73—28no—
484C22⋊D73#117116yescomplemented
485C2×Dic73—28no—
486C2×Dic73—21no—
487C2×Dic73—21no—
488C2×Dic73—22no—
489C2×Dic73—21no—
490C2×Dic73—21no—
491C2×Dic73—22no—
492C2×Dic73—22no—
493C2×Dic73—28no—
494C2×Dic73—28no—
495C2×Dic73—28no—
496C2×Dic73—28no—
497C2×Dic73—28no—
498C2×Dic73—22no—
499C2×Dic73—22no—
500C2×Dic73—22no—
501C2×Dic73—22no—
502C2×Dic73—22no—
503C2×Dic73—22no—
504C2×Dic73—22no—
505C2×Dic73—22no—
506C2×Dic73—22no—
507C2×Dic73—48no—
508C2×Dic73C4×D4116yescomplemented
509C2×Dic73C23×C412yes—
510C2×Dic73C23×C412yes—
511C2×Dic73C23×C412yes—
512C2×Dic73C23×C412yes—
513C2×Dic73C23×C412yes—
514C2×Dic73C23×C412yes—
515C2×Dic73C22×D414yes—
516C2×Dic73C22×D412yes—
517C2×Dic73C22×D412yes—
518C2×Dic73C2×#4114yes—
519C2×Dic73C2×#4112yes—
520C2×Dic73C2×#4112yes—
521C4×D73—28no—
522C4×D73—28no—
523C4×D73—28no—
524C4×D73—28no—
525C4×D73—48no—
526C4×D73—48no—
527C22×C73—22no—
528C22×C73—22no—
529C22×C73—22no—
530C22×C73—22no—
531C22×C73—24no—
532C22×C73—24no—
533C22×C73—24no—
534C22×C73—24no—
535C22×C73—22no—
536C22×C73—22no—
537C22×C73—22no—
538C22×C73—416no—
539C22×C73—42no—
540C22×C73—42no—
541C22×C73C2×#11714yescomplemented
542C22×C73C2×C4×D414yes—
543C22×C73C24×C411yescharacteristic
544C22×C73C23×D411yescharacteristic
545C22×C73C22×#4112yes—
546C22×C73C22×#4111yescharacteristic
547C22×C73#58512yes—
548C2×D73—22no—
549C2×D73—22no—
550C2×D73—24no—
551C2×D73—24no—
552C2×D73—22no—
553C2×D73—22no—
554C2×D73—22no—
555C2×D73—416no—
556C2×D73—42no—
557C2×D73—42no—
558C2×D73C2×#11714yescomplemented
559C4×C73—22no—
560C4×C73—22no—
561C4×C73—22no—
562C4×C73—22no—
563C4×C73—24no—
564C4×C73—42no—
565C4×C73—42no—
566C4×C73—42no—
567Dic73—22no—
568Dic73—22no—
569Dic73—22no—
570Dic73—24no—
571Dic73—42no—
572Dic73—42no—
573Dic73—42no—
574Dic73C2×#11714yescomplemented
575Dic73C2×C4×D414yes—
576Dic73C2×C4×D414yes—
577D4×#117—731nomaximal, Sylow
578C2×C73—24no—
579C2×C73—24no—
580C2×C73—42no—
581C2×C73C22×#11711yescharacteristic
582C2×C73C22×C4×D411yescharacteristic
583C2×C73#342811yescharacteristic
584C2×C73D4×#4112yes—
585C2×C73#347512yes—
586D73—24no—
587D73—42no—
588C22×C4×D4—731no—
589C22×#117—731no—
590C22×#117—731no—
591#2354—732no—
592#2352—732no—
593#2352—732no—
594D4×C4⋊C4—732no—
595#2344—731no—
596#2344—731no—
597#2342—731no—
598#2342—731no—
599#2342—731no—
600#2342D7311yescharacteristic, complemented
601D4×C22⋊C4—731no—
602D4×C22⋊C4—731no—
603#2293—732no—
604#2290—732no—
605#2290—732no—
606#2285—731no—
607#2280—731no—
608#2280—731no—
609C42×D4—732no—
610C4×#117—731no—
611C73D4×#11711yescharacteristic, complemented, Sylow
612C23×D4—731no—
613C24×C4—731no—
614C24×C4—731no—
615C2×C4×D4—732no—
616C2×C4×D4—7316no—
617C2×C4×D4—731no—
618C2×C4×D4—731no—
619C2×C4×D4—731no—
620C2×C4×D4—731no—
621C2×C4×D4—731no—
622C2×C4×D4—731no—
623C2×C4×D4—731no—
624C2×C4×D4—731no—
625C2×C4×D4—732no—
626C2×#117—731no—
627C2×#117—732no—
628C2×#117—731no—
629C2×#117—731no—
630C2×#117—731no—
631C2×#117—732no—
632C2×#117—731no—
633C2×#117—731no—
634C2×#117—732no—
635C2×#117—731no—
636C2×#117—732no—
637C2×#117—1468no—
638C2×#117—1468no—
639C2×#117C2×D7311yescharacteristic
640C22×C4⋊C4—731no—
641C22×C4⋊C4—732no—
642C22×C4⋊C4—732no—
643C22×C22⋊C4—731no—
644C22×C22⋊C4—731no—
645C22×C22⋊C4—731no—
646C22×C22⋊C4—731no—
647C22×C22⋊C4C2×D7311yescharacteristic
648C22×C22⋊C4C2×D7311yescharacteristic
649C22×C42—731no—
650C22×C42—732no—
651C22×C42—732no—
652#390—732no—
653#390—732no—
654#389—732no—
655#389—732no—
656#388—732no—
657#388—732no—
658#388—732no—
659#388—732no—
660#388—732no—
661#388—732no—
662#388C2×D7312yescomplemented
663#388C2×D7312yescomplemented
664#387—732no—
665#387—732no—
666#387—732no—
667#387—732no—
668#386—732no—
669#386—732no—
670#386—732no—
671#386—732no—
672#385—732no—
673#385—732no—
674#385—732no—
675#385C2×D7312yescomplemented
676#384—732no—
677#382—732no—
678#381—731no—
679#381—731no—
680#381—731no—
681#381C2×D7311yescharacteristic
682#380—731no—
683#380—731no—
684#380—731no—
685#380—732no—
686#380—732no—
687#380—732no—
688#380—732no—
689#380C2×D7311yescharacteristic
690#379—731no—
691#379—731no—
692#379—731no—
693#379C2×D7311yescharacteristic
694C4×C4⋊C4—732no—
695C4×C4⋊C4—732no—
696C4×C4⋊C4—732no—
697C4×C4⋊C4—732no—
698C4×C4⋊C4—732no—
699C4×C4⋊C4—732no—
700C4×C22⋊C4—731no—
701C4×C22⋊C4—731no—
702C4×C22⋊C4—731no—
703C4×C22⋊C4—732no—
704C4×C22⋊C4—732no—
705C4×C22⋊C4—732no—
706C4×C22⋊C4—732no—
707C4×C22⋊C4—732no—
708C4×C22⋊C4—732no—
709C4×C22⋊C4—732no—
710C4×C22⋊C4C2×D7311yescharacteristic
711C4×C22⋊C4C2×D7312yescomplemented
712#376—732no—
713C43—732no—
714C25—731no—
715C25C22×D7311yescharacteristic
716C22×D4—731no—
717C22×D4—738no—
718C22×D4—731no—
719C22×D4—731no—
720C22×D4—731no—
721C22×D4—1468no—
722C23×C4—732no—
723C23×C4—732no—
724C23×C4—732no—
725C23×C4—731no—
726C23×C4—738no—
727C23×C4—731no—
728C23×C4—731no—
729C23×C4—731no—
730C23×C4—731no—
731C23×C4—731no—
732C23×C4—731no—
733C23×C4—738no—
734C23×C4—731no—
735C23×C4—731no—
736C23×C4—731no—
737C23×C4—731no—
738C23×C4—1464no—
739C23×C4—1464no—
740C23×C4—1464no—
741C23×C4—1464no—
742C23×C4C22×D7312yes—
743C23×C4C22×D7311yescharacteristic
744C23×C4C22×D7311yescharacteristic
745C4×D4—738no—
746C4×D4—738no—
747C4×D4—738no—
748C4×D4—738no—
749C4×D4—738no—
750C4×D4—738no—
751C4×D4—738no—
752C4×D4—738no—
753C4×D4—1468no—
754C4×D4—1468no—
755#117—24no—
756#117—738no—
757#117—1468no—
758#117—1468no—
759#117—1468no—
760#117—1464no—
761#117—1468no—
762#117—1464no—
763#117—1464no—
764#117—1464no—
765#117—1464no—
766#117—1464no—
767C2×C4⋊C4—732no—
768C2×C4⋊C4—738no—
769C2×C4⋊C4—732no—
770C2×C4⋊C4—731no—
771C2×C4⋊C4—731no—
772C2×C4⋊C4—731no—
773C2×C4⋊C4—731no—
774C2×C4⋊C4—732no—
775C2×C4⋊C4—732no—
776C2×C4⋊C4—732no—
777C2×C4⋊C4—732no—
778C2×C4⋊C4—732no—
779C2×C4⋊C4—732no—
780C2×C4⋊C4—732no—
781C2×C4⋊C4—732no—
782C2×C4⋊C4—1468no—
783C2×C4⋊C4—1468no—
784C2×C4⋊C4C22×D7312yes—
785C2×C4⋊C4C22×D7312yes—
786C2×C22⋊C4—24no—
787C2×C22⋊C4—732no—
788C2×C22⋊C4—732no—
789C2×C22⋊C4—732no—
790C2×C22⋊C4—731no—
791C2×C22⋊C4—738no—
792C2×C22⋊C4—731no—
793C2×C22⋊C4—731no—
794C2×C22⋊C4—731no—
795C2×C22⋊C4—731no—
796C2×C22⋊C4—731no—
797C2×C22⋊C4—731no—
798C2×C22⋊C4—732no—
799C2×C22⋊C4—731no—
800C2×C22⋊C4—732no—
801C2×C22⋊C4—732no—
802C2×C22⋊C4—732no—
803C2×C22⋊C4—732no—
804C2×C22⋊C4—732no—
805C2×C22⋊C4—1464no—
806C2×C22⋊C4—1464no—
807C2×C22⋊C4—1464no—
808C2×C22⋊C4C4×D7318yescomplemented
809C2×C22⋊C4C22×D7311yescharacteristic
810C2×C22⋊C4C22×D7311yescharacteristic
811C2×C22⋊C4C22×D7312yes—
812C2×C22⋊C4C22×D7311yescharacteristic
813C2×C22⋊C4C22×D7312yes—
814C2×C22⋊C4C22×D7312yes—
815C2×C22⋊C4C22×D7311yescharacteristic
816C2×C22⋊C4C22×D7311yescharacteristic
817C2×C22⋊C4C22×D7311yescharacteristic
818C2×C22⋊C4C22×D7311yescharacteristic
819C2×C22⋊C4C22×D7311yescharacteristic
820C2×C42—732no—
821C2×C42—738no—
822C2×C42—732no—
823C2×C42—731no—
824C2×C42—731no—
825C2×C42—731no—
826C2×C42—731no—
827C2×C42—732no—
828C2×C42—732no—
829C2×C42—732no—
830C2×C42—732no—
831C2×C42—732no—
832C2×C42—732no—
833C2×C42—732no—
834C2×C42—732no—
835C2×C42—1468no—
836C2×C42—1468no—
837C2×C42C22×D7312yes—
838C2×C42C22×D7312yes—
839#95—732no—
840#95—732no—
841#95—732no—
842#95—732no—
843#95—732no—
844#95—732no—
845#95—732no—
846#95—732no—
847#95—732no—
848#95—732no—
849#95—732no—
850#95—732no—
851#95C22×D7312yes—
852#95C22×D7312yes—
853#95C22×D7312yes—
854#95C22×D7312yes—
855C24—22no—
856C24—22no—
857C24—24no—
858C24—42no—
859C24—2922no—
860C24—734no—
861C24—731no—
862C24—731no—
863C24—1464no—
864C24—1462no—
865C24—1462no—
866C24C2×C4×D7314yes—
867C24C23×D7311yescharacteristic
868C24C23×D7311yescharacteristic
869C24C23×D7311yescharacteristic
870C2×D4—734no—
871C2×D4—738no—
872C2×D4—734no—
873C2×D4—734no—
874C2×D4—734no—
875C2×D4—1464no—
876C2×D4—14632no—
877C2×D4—1464no—
878C2×D4—1464no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—2922no—
886C22×C4—2922no—
887C22×C4—2922no—
888C22×C4—734no—
889C22×C4—734no—
890C22×C4—734no—
891C22×C4—731no—
892C22×C4—731no—
893C22×C4—731no—
894C22×C4—734no—
895C22×C4—734no—
896C22×C4—734no—
897C22×C4—734no—
898C22×C4—734no—
899C22×C4—734no—
900C22×C4—731no—
901C22×C4—731no—
902C22×C4—731no—
903C22×C4—732no—
904C22×C4—734no—
905C22×C4—734no—
906C22×C4—734no—
907C22×C4—734no—
908C22×C4—732no—
909C22×C4—732no—
910C22×C4—732no—
911C22×C4—1464no—
912C22×C4—1464no—
913C22×C4—1464no—
914C22×C4—1462no—
915C22×C4—1462no—
916C22×C4—1462no—
917C22×C4—1462no—
918C22×C4—1462no—
919C22×C4—1462no—
920C22×C4—1462no—
921C22×C4—1462no—
922C22×C4—14632no—
923C22×C4—1464no—
924C22×C4—1464no—
925C22×C4—1464no—
926C22×C4—1462no—
927C22×C4—1462no—
928C22×C4—1462no—
929C22×C4—1462no—
930C22×C4—1462no—
931C22×C4—1462no—
932C22×C4—1462no—
933C22×C4—1462no—
934C22×C4—14632no—
935C22×C4—1464no—
936C22×C4—1462no—
937C22×C4—1462no—
938C22×C4C2×C4×D7314yes—
939C22×C4C2×C4×D7314yes—
940C22×C4C23×D7312yes—
941C22×C4C23×D7312yes—
942C22×C4C23×D7312yes—
943C22×C4C23×D7311yescharacteristic
944C22×C4C23×D7311yescharacteristic
945C22×C4C23×D7311yescharacteristic
946C22×C4C23×D7311yescharacteristic
947C22×C4C23×D7312yes—
948C4⋊C4—24no—
949C4⋊C4—42no—
950C4⋊C4—2922no—
951C4⋊C4—734no—
952C4⋊C4—734no—
953C4⋊C4—734no—
954C4⋊C4—734no—
955C4⋊C4—738no—
956C4⋊C4—1464no—
957C4⋊C4—1464no—
958C4⋊C4—1464no—
959C4⋊C4—1464no—
960C4⋊C4—1464no—
961C4⋊C4—1464no—
962C4⋊C4—1464no—
963C4⋊C4—1464no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—42no—
970C22⋊C4—2922no—
971C22⋊C4—2922no—
972C22⋊C4—2922no—
973C22⋊C4—734no—
974C22⋊C4—734no—
975C22⋊C4—734no—
976C22⋊C4—734no—
977C22⋊C4—734no—
978C22⋊C4—1464no—
979C22⋊C4—1464no—
980C22⋊C4—1464no—
981C22⋊C4—1464no—
982C22⋊C4—1462no—
983C22⋊C4—1462no—
984C22⋊C4—1462no—
985C22⋊C4—1464no—
986C22⋊C4—1464no—
987C22⋊C4C2×C4×D7314yes—
988C22⋊C4C2×C4×D7314yes—
989C22⋊C4C2×C4×D7314yes—
990C22⋊C4C2×C4×D7314yes—
991C22⋊C4D4×D7314yes—
992C42—24no—
993C42—42no—
994C42—2922no—
995C42—734no—
996C42—734no—
997C42—734no—
998C42—734no—
999C42—738no—
1000C42—1464no—
1001C42—1464no—
1002C42—1464no—
1003C42—1464no—
1004C42—1464no—
1005C42—1464no—
1006C42—1464no—
1007C42—1464no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—21no—
1014C23—21no—
1015C23—22no—
1016C23—22no—
1017C23—28no—
1018C23—28no—
1019C23—44no—
1020C23—48no—
1021C23—48no—
1022C23—2928no—
1023C23—2928no—
1024C23—2924no—
1025C23—732no—
1026C23—734no—
1027C23—732no—
1028C23—1468no—
1029C23—1461no—
1030C23—1461no—
1031C23—1462no—
1032C23—1462no—
1033C23—1468no—
1034C23—1461no—
1035C23—1461no—
1036C23—1462no—
1037C23C22×C4×D7312yes—
1038C23C22×C4×D7312yes—
1039C23C22×C4×D7312yes—
1040C23C2×D4×D7312yes—
1041C23#41×D7314yes—
1042C23#41×D7312yes—
1043C23C24×D7311yescharacteristic
1044D4—7316no—
1045D4—1468no—
1046D4—1468no—
1047D4—1468no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—28no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—2928no—
1069C2×C4—2928no—
1070C2×C4—2928no—
1071C2×C4—732no—
1072C2×C4—732no—
1073C2×C4—732no—
1074C2×C4—732no—
1075C2×C4—732no—
1076C2×C4—734no—
1077C2×C4—732no—
1078C2×C4—732no—
1079C2×C4—7316no—
1080C2×C4—732no—
1081C2×C4—732no—
1082C2×C4—732no—
1083C2×C4—734no—
1084C2×C4—1468no—
1085C2×C4—1468no—
1086C2×C4—1468no—
1087C2×C4—1468no—
1088C2×C4—1462no—
1089C2×C4—1462no—
1090C2×C4—1462no—
1091C2×C4—1462no—
1092C2×C4—1462no—
1093C2×C4—1462no—
1094C2×C4—1462no—
1095C2×C4—1462no—
1096C2×C4—1462no—
1097C2×C4—1468no—
1098C2×C4—1468no—
1099C2×C4—1468no—
1100C2×C4—1468no—
1101C2×C4—1468no—
1102C2×C4—1461no—
1103C2×C4—1461no—
1104C2×C4—1462no—
1105C2×C4—1461no—
1106C2×C4—1461no—
1107C2×C4—1462no—
1108C2×C4—1462no—
1109C2×C4—1468no—
1110C2×C4C22×C4×D7312yes—
1111C2×C4C22×C4×D7312yes—
1112C2×C4C22×C4×D7312yes—
1113C2×C4C22×C4×D7312yes—
1114C2×C4C2×D4×D7314yes—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—416no—
1127C22—42no—
1128C22—42no—
1129C22—29216no—
1130C22—2922no—
1131C22—2922no—
1132C22—734no—
1133C22—1462no—
1134C22—1462no—
1135C22—1462no—
1136C22—1462no—
1137C22—1462no—
1138C22—1464no—
1139C22—1464no—
1140C22#117×D7314yescomplemented
1141C22C4×D4×D7314yes—
1142C22C23×C4×D7311yescharacteristic
1143C22C22×D4×D7311yescharacteristic
1144C22C2×#41×D7312yes—
1145C22C2×#41×D7311yescharacteristic
1146C22#1798942212yes—
1147C4—22no—
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—24no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—2922no—
1156C4—2922no—
1157C4—2922no—
1158C4—734no—
1159C4—734no—
1160C4—734no—
1161C4—1462no—
1162C4—1462no—
1163C4—1462no—
1164C4—1464no—
1165C2—24no—
1166C2—24no—
1167C2—42no—
1168C2—2922no—
1169C2—1464no—
1170C2C2×#117×D7311yescharacteristic
1171C2C2×C4×D4×D7311yescharacteristic
1172C2#2262312911yescharacteristic
1173C2#2262341512yes—
1174C2#2262348612yes—
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2342C2
socle, cosocleC23×C73C25
prime radicalC23×C22⋊D73C22
hypercenter#2342D73
hypocenterC73D4×#117
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. C22×#14556547C2semidirect
3. C2×#117×D73C2semidirect
4. #22612877C2semidirect
5. #22612859C2semidirect
6. #22612854C2semidirect
7. #22612829C2semidirect
8. #22612801C2semidirect
9. #22612795C2semidirect
10. #22612783C2semidirect
11. #22612780C2semidirect
12. #22612777C2semidirect
15. #22612391C2semidirect
16. #22612373C2semidirect
17. #22612367C2semidirect
18. #22612333C2semidirect
19. #22612311C2semidirect
20. #22612309C2semidirect
21. C4×#14556551C2semidirect
22. C4×#14556547C2semidirect
23. C73×#2342C2semidirect
28. C2×#14556551C4semidirect
39. C2×#14556549C22semidirect
40. C2×#14556548C22semidirect
48. C2×#14556547C22semidirect
49. C2×#14556547C22semidirect
52. C22×#11924007C22semidirect
53. C2×C4⋊C4×D73C22semidirect
59. C22×C4×Dic73C22semidirect
60. C2×C42×D73C22semidirect
63. #17988484C22semidirect
64. #17988482C22semidirect
65. #17988480C22semidirect
66. #17988480C22semidirect
67. #17988479C22semidirect
68. #17988478C22semidirect
69. #17988477C22semidirect
70. #17988476C22semidirect
71. #17988474C22semidirect
72. #17988471C22semidirect
73. #17988469C22semidirect
74. #17988468C22semidirect
79. #17988462C22semidirect
80. #17988461C22semidirect
81. #17988458C22semidirect
82. #17988456C22semidirect
83. #17988451C22semidirect
88. #17988446C22semidirect
89. #17988446C22semidirect
92. #17988445C22semidirect
93. #17988445C22semidirect
97. C4⋊C4×Dic73C22semidirect
98. C4×#11924007C22semidirect
99. C4×#11924007C22semidirect
100. #17988438C22semidirect
101. #17988438C22semidirect
102. #17988438C22semidirect
105. C22⋊C4×Dic73C22semidirect
106. C22⋊C4×Dic73C22semidirect
107. C22⋊C4×Dic73C22semidirect
108. C4×#11924005C22semidirect
110. #17988434C22semidirect
111. #17988434C22semidirect
112. #17988434C22semidirect
113. #17988432C22semidirect
114. C42×Dic73C22semidirect
118. #388×C73C22semidirect
119. #388×C73C22semidirect
120. #385×C73C22semidirect
125. C4×C22⋊C4×C73C22semidirect
135. C23×Dic73C2×C4semidirect
146. C22×C4×D73C2×C4semidirect
157. #14556551C2×C4semidirect
158. #14556551C2×C4semidirect
159. #14556551C2×C4semidirect
160. #14556551C2×C4semidirect
161. #14556551C2×C4semidirect
162. #14556551C2×C4semidirect
173. #14556547D4semidirect
177. C2×#11924007C2×C4semidirect
199. C2×#11924005C2×C4semidirect
213. C2×C4×Dic73C2×C4semidirect
249. C2×C22⋊C4×C73C2×C4semidirect
349. #11924007C2×D4semidirect
380. C4×Dic73C2×D4semidirect
484. C22⋊D73#117semidirect
508. C2×Dic73C4×D4semidirect
541. C22×C73C2×#117semidirect
558. C2×D73C2×#117semidirect
574. Dic73C2×#117semidirect
600. #2342D73semidirect
611. C73D4×#117semidirect
662. #388C2×D73semidirect
663. #388C2×D73semidirect
675. #385C2×D73semidirect
711. C4×C22⋊C4C2×D73semidirect
808. C2×C22⋊C4C4×D73semidirect
1140. C22#117×D73semidirect

Maximal subgroups

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

subgroupindex
C22×#145565512
C22×#145565472
C2×#117×D732
#226128772
#226128592
#226128542
#226128292
#226128012
#226127952
#226127832
#226127802
#226127772
C22⋊C4×C22⋊D732
#226127472
#226123912
#226123732
#226123672
#226123332
#226123112
#226123092
C4×#145565512
C4×#145565472
C73×#23422
D4×#11773