Finite Group Databasebeta

← #2610×D73 #33256826

Subgroups — #2610×D73 #33256826

Order 18688.

3286 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
1C2×#124×D73C211yesmaximal, characteristic, complemented
2C2×#117×D73C211yesmaximal, characteristic, complemented
3#22615621C211yesmaximal, characteristic, complemented
4#22615620C211yesmaximal, characteristic, complemented
5#22615619C211yesmaximal, characteristic, complemented
6#22615618C211yesmaximal, characteristic, complemented
7#22615617C212yesmaximal, complemented
8#22615616C212yesmaximal, complemented
9#22615615C212yesmaximal, complemented
10#22615614C212yesmaximal, complemented
11#22615613C211yesmaximal, characteristic, complemented
12#22615612C211yesmaximal, characteristic, complemented
13#22615611C211yesmaximal, characteristic, complemented
14#395×D73C211yesmaximal, characteristic, complemented
15#394×D73C211yesmaximal, characteristic, complemented
16#393×D73C211yesmaximal, characteristic, complemented
17#392×D73C211yesmaximal, characteristic
18#390×D73C212yesmaximal, complemented
19#388×D73C212yesmaximal, complemented
20#388×D73C212yesmaximal, complemented
21#386×D73C212yesmaximal, complemented
22#376×D73C211yesmaximal, characteristic, complemented
23C73×#2610C211yesmaximal, characteristic, complemented
24C22×Q8×D73C2211yescharacteristic
25C22×D4×D73C2212yes—
26C22×D4×D73C2211yescharacteristic
27C23×C4×D73C2211yescharacteristic
28C2×#14556580C2211yescharacteristic, complemented
29C2×#14556579C2211yescharacteristic, complemented
30C2×#14556578C2211yescharacteristic, complemented
31C2×#14556577C2212yescomplemented
32C2×#14556577C2212yescomplemented
33#124×D73—28no—
34C2×#14556550C2211yescharacteristic, complemented
35C2×#14556549C2211yescharacteristic, complemented
36C2×#14556549C2211yescharacteristic, complemented
37C2×#14556548C2211yescharacteristic, complemented
38C2×#14556548C2211yescharacteristic, complemented
39C2×#14556547C2211yescharacteristic, complemented
40C2×#14556547C2211yescharacteristic, complemented
41#117×D73—28no—
42C2×C4⋊C4×D73C2211yescharacteristic
43C2×C4⋊C4×D73C2211yescharacteristic
44C2×C4⋊C4×D73C2212yes—
45C2×C22⋊C4×D73C2211yescharacteristic
46C2×C22⋊C4×D73C2211yescharacteristic
47C2×C22⋊C4×D73C2212yes—
48C2×C22⋊C4×D73C2212yes—
49C2×C22⋊C4×D73C2212yes—
50C2×C22⋊C4×D73C2212yes—
51C2×C22⋊C4×D73C2212yes—
52C2×C22⋊C4×D73C2212yes—
53C2×C42×D73C2212yes—
54C2×C42×D73C2211yescharacteristic
55C2×C42×D73C2211yescharacteristic
56#17988508C2211yescharacteristic, complemented
57#17988508C2212yescomplemented
58#17988507C2212yescomplemented
59#17988507C2211yescharacteristic, complemented
60#17988506C2211yescharacteristic, complemented
61#17988505C2211yescharacteristic, complemented
62#17988504C2211yescharacteristic, complemented
63#17988503C2212yescomplemented
64#17988502C2212yescomplemented
65#17988501C2211yescharacteristic, complemented
66#17988500C2211yescharacteristic, complemented
67#17988500C2212yescomplemented
68#17988499C2211yescharacteristic, complemented
69#17988499C2212yescomplemented
70#17988498C2211yescharacteristic, complemented
71#17988497C2211yescharacteristic
72#17988496C2212yes—
73#17988496C2211yescharacteristic
74#17988495C2212yes—
75#17988495C2211yescharacteristic
76#17988490C2212yescomplemented
77#17988489C2212yescomplemented
78#17988488C2212yescomplemented
79#17988487C2212yescomplemented
80#17988487C2212yescomplemented
81#17988487C2212yescomplemented
82#17988487C2212yescomplemented
83#17988481C2212yescomplemented
84#17988481C2212yescomplemented
85#17988480C2212yescomplemented
86#17988480C2212yescomplemented
87#17988479C2212yescomplemented
88#17988479C2212yescomplemented
89#17988478C2212yescomplemented
90#17988478C2212yescomplemented
91#17988477C2212yescomplemented
92#17988477C2212yescomplemented
93#17988476C2212yescomplemented
94#17988476C2212yescomplemented
95#17988475C2212yescomplemented
96#17988475C2212yescomplemented
97#17988467C2212yescomplemented
98#17988466C2212yescomplemented
99#17988465C2212yescomplemented
100#17988465C2212yescomplemented
101#17988464C2212yescomplemented
102#17988463C2212yescomplemented
103#17988463C2212yescomplemented
104#17988433C2212yescomplemented
105#17988433C2211yescharacteristic, complemented
106#17988432C2211yescharacteristic, complemented
107#17988432C2212yescomplemented
108#17988432C2211yescharacteristic, complemented
109#95×D73C2212yes—
110#95×D73C2211yescharacteristic
111#95×D73C2211yescharacteristic
112#95×D73C2212yes—
113#95×D73C2212yes—
114C2×#124×C73C2211yescharacteristic, complemented
115C2×#117×C73C2211yescharacteristic, complemented
116#395×C73C2211yescharacteristic, complemented
117#394×C73C2211yescharacteristic, complemented
118#393×C73C2211yescharacteristic, complemented
119#392×C73C2211yescharacteristic
120#390×C73C2212yescomplemented
121#388×C73C2212yescomplemented
122#388×C73C2212yescomplemented
123#386×C73C2212yescomplemented
124#376×C73C2211yescharacteristic, complemented
125C24×D73C2312yes—
126C24×D73C2311yescharacteristic
127C22×Dic146C2312yes—
128C22×Dic146C2311yescharacteristic
129C2×Q8×D73—24no—
130C2×Q8×D73—44no—
131C22×D292C2312yes—
132C22×D292C2311yescharacteristic
133C22×C22⋊D73C2312yes—
134C22×C22⋊D73C2312yes—
135C22×C22⋊D73C2312yes—
136C2×D4×D73—28no—
137C2×D4×D73—24no—
138C2×D4×D73—28no—
139C2×D4×D73—44no—
140C2×D4×D73—44no—
141C23×Dic73C2311yescharacteristic
142C22×C4×D73—24no—
143C22×C4×D73—24no—
144C22×C4×D73—24no—
145C22×C4×D73C2311yescharacteristic
146C22×C4×D73C2311yescharacteristic
147C22×C4×D73C2312yes—
148C22×C4×D73C2312yes—
149C22×C4×D73C2311yescharacteristic
150C22×C4×D73C2311yescharacteristic
151C22×C4×D73C2311yescharacteristic
152C22×C4×D73C2311yescharacteristic
153C22×C4×D73C2311yescharacteristic
154C22×C4×D73C2311yescharacteristic
155C22×C4×D73C2312yes—
156#14556580—24no—
157#14556579—24no—
158#14556578—24no—
159#14556577—28no—
160#14556577—28no—
161#14556550—24no—
162#14556549—24no—
163#14556549—24no—
164#14556548—24no—
165#14556548—24no—
166#14556547—24no—
167#14556547—24no—
168C2×C4⋊Dic73C2311yescharacteristic
169C2×C4⋊Dic73C2311yescharacteristic
170C2×C4⋊Dic73C2312yes—
171C2×#11924007C2311yescharacteristic
172C2×#11924007C2311yescharacteristic
173C2×#11924007C2311yescharacteristic
174C2×#11924007C2311yescharacteristic
175C2×#11924007C2312yes—
176C2×#11924007C2312yes—
177C4⋊C4×D73—24no—
178C4⋊C4×D73—24no—
179C4⋊C4×D73—44no—
180C2×C22⋊Dic73C2312yes—
181C2×C22⋊Dic73C2312yes—
182C2×C22⋊Dic73C2312yes—
183C2×C22⋊Dic73C2312yes—
184C2×C22⋊Dic73C2311yescharacteristic
185C2×C22⋊Dic73C2311yescharacteristic
186C2×C22⋊Dic73C2312yes—
187C2×C22⋊Dic73C2312yes—
188C2×#11924005C2312yes—
189C2×#11924005C2312yes—
190C2×#11924005C2312yes—
191C2×#11924005C2312yes—
192C2×#11924005C2312yes—
193C2×#11924005C2312yes—
194C2×#11924005C2312yes—
195C2×#11924005C2312yes—
196C2×#11924005C2311yescharacteristic
197C2×#11924005C2311yescharacteristic
198C2×#11924005C2311yescharacteristic
199C2×#11924005C2311yescharacteristic
200C2×#11924005C2312yes—
201C2×#11924005C2312yes—
202C2×#11924005C2312yes—
203C2×#11924005C2312yes—
204C22⋊C4×D73—24no—
205C22⋊C4×D73—24no—
206C22⋊C4×D73—28no—
207C22⋊C4×D73—28no—
208C22⋊C4×D73—28no—
209C22⋊C4×D73—28no—
210C22⋊C4×D73—44no—
211C22⋊C4×D73—44no—
212C2×C4×Dic73C2312yes—
213C2×C4×Dic73C2312yes—
214C2×C4×Dic73C2312yes—
215C2×C4×Dic73C2311yescharacteristic
216C2×C4×Dic73C2311yescharacteristic
217C2×C4×Dic73C2311yescharacteristic
218C2×C4×Dic73C2311yescharacteristic
219C2×C4×Dic73C2311yescharacteristic
220C2×C4×Dic73C2311yescharacteristic
221C42×D73—24no—
222C42×D73—28no—
223C42×D73D418yescomplemented
224#14556498C2312yes—
225#14556498C2312yes—
226#14556498C2312yes—
227#14556498C2311yescharacteristic
228#14556498C2312yes—
229#14556498C2311yescharacteristic
230#14556498C2312yes—
231#14556498C2312yes—
232#14556498C2312yes—
233#14556498C2312yes—
234#14556498C2312yes—
235#14556498C2312yes—
236#14556498C2312yes—
237C22×Q8×C73C2311yescharacteristic
238C22×D4×C73C2312yes—
239C22×D4×C73C2311yescharacteristic
240C23×C4×C73C2311yescharacteristic
241#124×C73—24no—
242#117×C73—24no—
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2312yes—
246C2×C22⋊C4×C73C2312yes—
247C2×C22⋊C4×C73C2312yes—
248C2×C22⋊C4×C73C2312yes—
249C2×C22⋊C4×C73C2312yes—
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73C2312yes—
253C2×C22⋊C4×C73C2312yes—
254C2×C42×C73C2311yescharacteristic
255C2×C42×C73C2312yes—
256C2×C42×C73C2311yescharacteristic
257#95×C73C2312yes—
258#95×C73C2312yes—
259#95×C73C2312yes—
260#95×C73C2311yescharacteristic
261#95×C73C2311yescharacteristic
262C23×D73—22no—
263C23×D73—22no—
264C23×D73—24no—
265C23×D73—24no—
266C23×D73—24no—
267C23×D73—24no—
268C23×D73—24no—
269C23×D73—24no—
270C23×D73—24no—
271C23×D73—24no—
272C23×D73—24no—
273C23×D73#4114yes—
274C23×D73C2412yes—
275C23×D73C2411yescharacteristic
276C23×D73C2411yescharacteristic
277C2×Dic146—22no—
278C2×Dic146—24no—
279C2×Dic146—42no—
280C2×Dic146—42no—
281C2×Dic146—42no—
282Q8×D73—416no—
283C2×D292—24no—
284C2×D292—22no—
285C2×D292—24no—
286C2×D292—42no—
287C2×D292—42no—
288C2×C22⋊D73—24no—
289C2×C22⋊D73—24no—
290C2×C22⋊D73—24no—
291C2×C22⋊D73—24no—
292C2×C22⋊D73—24no—
293C2×C22⋊D73—42no—
294C2×C22⋊D73—42no—
295C2×C22⋊D73—42no—
296C2×C22⋊D73—42no—
297D4×D73—432no—
298D4×D73—416no—
299C22×Dic73—22no—
300C22×Dic73—22no—
301C22×Dic73—22no—
302C22×Dic73C2412yes—
303C22×Dic73C2411yescharacteristic
304C22×Dic73C2412yes—
305C22×Dic73C2411yescharacteristic
306C22×Dic73C2411yescharacteristic
307C22×Dic73C2411yescharacteristic
308C22×Dic73C2411yescharacteristic
309C22×Dic73C2412yes—
310C22×Dic73C2411yescharacteristic
311C2×C4×D73—232no—
312C2×C4×D73—22no—
313C2×C4×D73—24no—
314C2×C4×D73—22no—
315C2×C4×D73—22no—
316C2×C4×D73—22no—
317C2×C4×D73—22no—
318C2×C4×D73—22no—
319C2×C4×D73—24no—
320C2×C4×D73—24no—
321C2×C4×D73—24no—
322C2×C4×D73—22no—
323C2×C4×D73—22no—
324C2×C4×D73—22no—
325C2×C4×D73—22no—
326C2×C4×D73—22no—
327C2×C4×D73—22no—
328C2×C4×D73—24no—
329C2×C4×D73—24no—
330C2×C4×D73—24no—
331C2×C4×D73—24no—
332C2×C4×D73—24no—
333C2×C4×D73—24no—
334C2×C4×D73—24no—
335C2×C4×D73—24no—
336C2×C4×D73C2×D414yes—
337C2×C4×D73C2×D414yes—
338C2×C4×D73C2×D414yes—
339C2×C4×D73#4118yes—
340C2×C4×D73#4114yes—
341C4⋊Dic73—22no—
342C4⋊Dic73—22no—
343C4⋊Dic73—42no—
344#11924007—22no—
345#11924007—22no—
346#11924007—22no—
347#11924007—22no—
348#11924007—42no—
349#11924007—42no—
350C22⋊Dic73—22no—
351C22⋊Dic73—22no—
352C22⋊Dic73—24no—
353C22⋊Dic73—24no—
354C22⋊Dic73—24no—
355C22⋊Dic73—24no—
356C22⋊Dic73—42no—
357C22⋊Dic73—42no—
358#11924005—22no—
359#11924005—22no—
360#11924005—24no—
361#11924005—24no—
362#11924005—24no—
363#11924005—24no—
364#11924005—22no—
365#11924005—22no—
366#11924005—24no—
367#11924005—24no—
368#11924005—24no—
369#11924005—24no—
370#11924005—42no—
371#11924005—42no—
372#11924005—42no—
373#11924005—42no—
374C4×Dic73—22no—
375C4×Dic73—24no—
376C4×Dic73—22no—
377C4×Dic73—22no—
378C4×Dic73—24no—
379C4×Dic73—24no—
380C4×Dic73C2×D414yescomplemented
381C4×Dic73C2×D414yescomplemented
382C4×Dic73C2×D414yescomplemented
383C24×C73C2412yes—
384C24×C73C2411yescharacteristic
385C2×Q8×C73—22no—
386C2×Q8×C73—42no—
387C2×D4×C73—24no—
388C2×D4×C73—22no—
389C2×D4×C73—24no—
390C2×D4×C73—42no—
391C2×D4×C73—42no—
392C22×C4×C73—22no—
393C22×C4×C73—22no—
394C22×C4×C73—22no—
395C22×C4×C73C2412yes—
396C22×C4×C73C2411yescharacteristic
397C22×C4×C73C2412yes—
398C22×C4×C73C2411yescharacteristic
399C22×C4×C73C2411yescharacteristic
400C22×C4×C73C2411yescharacteristic
401C22×C4×C73C2411yescharacteristic
402C22×C4×C73C2412yes—
403C22×C4×C73C2411yescharacteristic
404C4⋊C4×C73—22no—
405C4⋊C4×C73—22no—
406C4⋊C4×C73—42no—
407C22⋊C4×C73—22no—
408C22⋊C4×C73—22no—
409C22⋊C4×C73—24no—
410C22⋊C4×C73—24no—
411C22⋊C4×C73—24no—
412C22⋊C4×C73—24no—
413C22⋊C4×C73—42no—
414C22⋊C4×C73—42no—
415C42×C73—22no—
416C42×C73—24no—
417C42×C73C2×D414yescomplemented
418C23×C73—21no—
419C23×C73—21no—
420C23×C73—22no—
421C23×C73—22no—
422C23×C73—22no—
423C23×C73—22no—
424C23×C73—22no—
425C23×C73—22no—
426C23×C73—22no—
427C23×C73—22no—
428C23×C73—22no—
429C23×C73C2×#4112yes—
430C23×C73C2511yescharacteristic
431C22×D73—21no—
432C22×D73—21no—
433C22×D73—22no—
434C22×D73—22no—
435C22×D73—28no—
436C22×D73—216no—
437C22×D73—22no—
438C22×D73—22no—
439C22×D73—22no—
440C22×D73—22no—
441C22×D73—22no—
442C22×D73—22no—
443C22×D73—22no—
444C22×D73—44no—
445C22×D73—44no—
446C22×D73—48no—
447C22×D73—48no—
448C22×D73—48no—
449C22×D73—48no—
450C22×D73—48no—
451C22×D73—48no—
452C22×D73—48no—
453C22×D73—48no—
454C22×D73C22×D412yes—
455C22×D73C2×#4112yes—
456C22×D73C2×#4112yes—
457C22×D73C2×#4112yes—
458C22×D73C2×#4114yes—
459C22×D73H(5,𝔽2)14yes—
460Q8×C73—44no—
461D4×C73—48no—
462D4×C73—44no—
463C2×C4×C73—28no—
464C2×C4×C73—21no—
465C2×C4×C73—22no—
466C2×C4×C73—21no—
467C2×C4×C73—21no—
468C2×C4×C73—21no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—21no—
473C2×C4×C73—21no—
474C2×C4×C73—22no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—22no—
480C2×C4×C73—22no—
481C2×C4×C73—22no—
482C2×C4×C73C22×D412yes—
483C2×C4×C73C22×D412yes—
484C2×C4×C73C22×D412yes—
485C2×C4×C73C2×#4114yes—
486C2×C4×C73C2×#4112yes—
487C22⋊D73—48no—
488C22⋊D73—48no—
489C22⋊D73—48no—
490C2×Dic73—28no—
491C2×Dic73—21no—
492C2×Dic73—22no—
493C2×Dic73—21no—
494C2×Dic73—21no—
495C2×Dic73—21no—
496C2×Dic73—22no—
497C2×Dic73—22no—
498C2×Dic73—22no—
499C2×Dic73—21no—
500C2×Dic73—21no—
501C2×Dic73—22no—
502C2×Dic73—22no—
503C2×Dic73—22no—
504C2×Dic73—22no—
505C2×Dic73—22no—
506C2×Dic73—22no—
507C2×Dic73—22no—
508C2×Dic73—22no—
509C2×Dic73C22×D412yes—
510C2×Dic73C22×D412yes—
511C2×Dic73C22×D412yes—
512C2×Dic73C2×#4114yes—
513C2×Dic73C2×#4112yes—
514D292—48no—
515D292—44no—
516C4×D73—28no—
517C4×D73—28no—
518C4×D73—28no—
519C4×D73—28no—
520C4×D73—28no—
521C4×D73—28no—
522C4×D73—216no—
523C4×D73—44no—
524C4×D73—44no—
525C4×D73—48no—
526C4×D73—48no—
527Dic146—48no—
528Dic146—44no—
529C22×C73—22no—
530C22×C73—24no—
531C22×C73—41no—
532C22×C73—41no—
533C22×C73—42no—
534C22×C73—42no—
535C22×C73—42no—
536C22×C73—42no—
537C22×C73—42no—
538C22×C73—42no—
539C22×C73—42no—
540C22×C73—42no—
541C22×C73C23×D411yescharacteristic
542C22×C73C22×#4111yescharacteristic
543C22×C73C22×#4111yescharacteristic
544C22×C73C22×#4112yes—
545C22×C73C2×H(5,𝔽2)12yes—
546C2×D73—22no—
547C2×D73—24no—
548C2×D73—41no—
549C2×D73—41no—
550C2×D73—42no—
551C2×D73—416no—
552C2×D73—42no—
553C2×D73—42no—
554C2×D73—42no—
555C2×D73—42no—
556C2×D73—42no—
557C2×D73—42no—
558C2×D73—42no—
559C2×D73—816no—
560C2×D73#52514yes—
561C2×D73#53214yes—
562C2×D73#53514yes—
563C2×D73#55118yes—
564C2×D73#55518yes—
565C4×C73—22no—
566C4×C73—22no—
567C4×C73—22no—
568C4×C73—22no—
569C4×C73—24no—
570C4×C73—41no—
571C4×C73—42no—
572C4×C73—41no—
573C4×C73—42no—
574Dic73—22no—
575Dic73—22no—
576Dic73—22no—
577Dic73—22no—
578Dic73—24no—
579Dic73—41no—
580Dic73—42no—
581Dic73—41no—
582Dic73—42no—
583C2×#2610—731nomaximal, Sylow
584C2×C73—42no—
585C2×C73—82no—
586C2×C73C2×#52511yescharacteristic
587C2×C73C2×#53211yescharacteristic
588C2×C73C2×#53511yescharacteristic
589C2×C73C2×#55112yes—
590C2×C73C2×#55512yes—
591D73—42no—
592D73—82no—
593D73#261018yesdirect product factor
594C22×#124—731no—
595C22×#117—731no—
596#2610—731no—
597#2610—731no—
598#2610—731no—
599#2610—731no—
600#2610—732no—
601#2610—732no—
602#2610—732no—
603#2610—732no—
604#2610—731no—
605#2610—731no—
606#2610—731no—
607#2610D7311yescharacteristic, direct product factor
608C2×#395—731no—
609C2×#394—731no—
610C2×#393—731no—
611C2×#392—731no—
612C2×#390—732no—
613C2×#388—732no—
614C2×#388—732no—
615C2×#386—732no—
616C2×#376—731no—
617C73C2×#261011yescharacteristic, complemented, Sylow
618C23×Q8—731no—
619C23×D4—731no—
620C23×D4—732no—
621C24×C4—731no—
622C2×#124—731no—
623C2×#124—731no—
624C2×#124—732no—
625C2×#124—732no—
626C2×#124—731no—
627C2×#124—1468no—
628C2×#124C2×D7311yescharacteristic, complemented
629C2×#117—731no—
630C2×#117—731no—
631C2×#117—731no—
632C2×#117—731no—
633C2×#117—731no—
634C2×#117—731no—
635C2×#117—731no—
636C2×#117—1468no—
637C2×#117C2×D7311yescharacteristic, complemented
638C22×C4⋊C4—732no—
639C22×C4⋊C4—731no—
640C22×C4⋊C4—731no—
641C22×C22⋊C4—732no—
642C22×C22⋊C4—732no—
643C22×C22⋊C4—731no—
644C22×C22⋊C4—732no—
645C22×C22⋊C4—732no—
646C22×C22⋊C4—731no—
647C22×C22⋊C4—732no—
648C22×C22⋊C4—732no—
649C22×C42—731no—
650C22×C42—731no—
651C22×C42—732no—
652#395—731no—
653#395—731no—
654#395—732no—
655#395—732no—
656#395—731no—
657#395C2×D7311yescharacteristic, complemented
658#394—731no—
659#394—731no—
660#394—732no—
661#394—732no—
662#394—731no—
663#394C2×D7311yescharacteristic, complemented
664#393—731no—
665#393—731no—
666#393—732no—
667#393—732no—
668#393—731no—
669#393C2×D7311yescharacteristic, complemented
670#392—732no—
671#392—731no—
672#392—732no—
673#392—731no—
674#392—731no—
675#392C2×D7311yescharacteristic
676#390—732no—
677#390—732no—
678#390—732no—
679#390—732no—
680#390—732no—
681#390—732no—
682#390—732no—
683#390C2×D7312yescomplemented
684#388—732no—
685#388—732no—
686#388—732no—
687#388—732no—
688#388—732no—
689#388—732no—
690#388—732no—
691#388—732no—
692#388—732no—
693#388—732no—
694#388—732no—
695#388—732no—
696#388—732no—
697#388—732no—
698#388C2×D7312yescomplemented
699#388C2×D7312yescomplemented
700#386—732no—
701#386—732no—
702#386—732no—
703#386—732no—
704#386—732no—
705#386—732no—
706#386—732no—
707#386C2×D7312yescomplemented
708#376—732no—
709#376—731no—
710#376—731no—
711#376—731no—
712#376—732no—
713#376C2×D7311yescharacteristic, complemented
714C2×#95—731no—
715C2×#95—731no—
716C2×#95—732no—
717C2×#95—732no—
718C2×#95—732no—
719C25—731no—
720C25—732no—
721C22×Q8—2924no—
722C22×Q8—732no—
723C22×Q8—731no—
724C22×Q8—1464no—
725C22×Q8C22×D7311yescharacteristic
726C22×D4—2924no—
727C22×D4—2924no—
728C22×D4—732no—
729C22×D4—732no—
730C22×D4—732no—
731C22×D4—731no—
732C22×D4—732no—
733C22×D4—1464no—
734C22×D4—1468no—
735C22×D4—1468no—
736C22×D4C22×D7312yes—
737C22×D4C22×D7311yescharacteristic
738C23×C4—731no—
739C23×C4—731no—
740C23×C4—731no—
741C23×C4—731no—
742C23×C4—732no—
743C23×C4—731no—
744C23×C4—731no—
745C23×C4—732no—
746C23×C4—731no—
747C23×C4—732no—
748C23×C4—731no—
749C23×C4—731no—
750C23×C4—1464no—
751C23×C4—1464no—
752C23×C4—1464no—
753C23×C4C22×D7311yescharacteristic
754#124—24no—
755#124—1468no—
756#124—1468no—
757#124—1464no—
758#124—1464no—
759#124—1464no—
760#117—24no—
761#117—1464no—
762#117—1464no—
763#117—1464no—
764#117—1464no—
765#117—1464no—
766#117—1464no—
767#117—1464no—
768C2×C4⋊C4—2924no—
769C2×C4⋊C4—732no—
770C2×C4⋊C4—732no—
771C2×C4⋊C4—732no—
772C2×C4⋊C4—731no—
773C2×C4⋊C4—731no—
774C2×C4⋊C4—731no—
775C2×C4⋊C4—731no—
776C2×C4⋊C4—731no—
777C2×C4⋊C4—731no—
778C2×C4⋊C4—1464no—
779C2×C4⋊C4—1464no—
780C2×C4⋊C4C22×D7311yescharacteristic
781C2×C4⋊C4C22×D7311yescharacteristic
782C2×C4⋊C4C22×D7312yes—
783C2×C22⋊C4—2924no—
784C2×C22⋊C4—2924no—
785C2×C22⋊C4—732no—
786C2×C22⋊C4—732no—
787C2×C22⋊C4—732no—
788C2×C22⋊C4—732no—
789C2×C22⋊C4—732no—
790C2×C22⋊C4—732no—
791C2×C22⋊C4—731no—
792C2×C22⋊C4—731no—
793C2×C22⋊C4—732no—
794C2×C22⋊C4—732no—
795C2×C22⋊C4—732no—
796C2×C22⋊C4—732no—
797C2×C22⋊C4—731no—
798C2×C22⋊C4—731no—
799C2×C22⋊C4—731no—
800C2×C22⋊C4—731no—
801C2×C22⋊C4—732no—
802C2×C22⋊C4—732no—
803C2×C22⋊C4—732no—
804C2×C22⋊C4—732no—
805C2×C22⋊C4—732no—
806C2×C22⋊C4—732no—
807C2×C22⋊C4—732no—
808C2×C22⋊C4—732no—
809C2×C22⋊C4—1464no—
810C2×C22⋊C4—1464no—
811C2×C22⋊C4—1468no—
812C2×C22⋊C4—1468no—
813C2×C22⋊C4—1468no—
814C2×C22⋊C4—1468no—
815C2×C22⋊C4C22×D7311yescharacteristic
816C2×C22⋊C4C22×D7311yescharacteristic
817C2×C22⋊C4C22×D7312yes—
818C2×C22⋊C4C22×D7312yes—
819C2×C22⋊C4C22×D7312yes—
820C2×C22⋊C4C22×D7312yes—
821C2×C22⋊C4C22×D7312yes—
822C2×C22⋊C4C22×D7312yes—
823C2×C42—731no—
824C2×C42—731no—
825C2×C42—731no—
826C2×C42—738no—
827C2×C42—731no—
828C2×C42—731no—
829C2×C42—731no—
830C2×C42—732no—
831C2×C42—732no—
832C2×C42—732no—
833C2×C42—1464no—
834C2×C42—1468no—
835C2×C42C22×D7311yescharacteristic
836C2×C42C22×D7312yes—
837C2×C42C22×D7311yescharacteristic
838#95—732no—
839#95—732no—
840#95—732no—
841#95—731no—
842#95—732no—
843#95—732no—
844#95—731no—
845#95—732no—
846#95—732no—
847#95—732no—
848#95—732no—
849#95—732no—
850#95—732no—
851#95C22×D7312yes—
852#95C22×D7311yescharacteristic
853#95C22×D7311yescharacteristic
854#95C22×D7312yes—
855#95C22×D7312yes—
856C24—731no—
857C24—734no—
858C24—731no—
859C24—732no—
860C24—1464no—
861C24—1464no—
862C24—1464no—
863C24—1464no—
864C24—1464no—
865C24—1464no—
866C24—1464no—
867C24—1464no—
868C24—1462no—
869C24—1462no—
870C24—1464no—
871C24C23×D7312yes—
872C24C23×D7311yescharacteristic
873C2×Q8—22no—
874C2×Q8—42no—
875C2×Q8—2922no—
876C2×Q8—2922no—
877C2×Q8—2922no—
878C2×Q8—29216no—
879C2×Q8—1464no—
880C2×Q8—1462no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—24no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—2922no—
887C2×D4—2922no—
888C2×D4—29216no—
889C2×D4—29232no—
890C2×D4—2922no—
891C2×D4—2922no—
892C2×D4—2922no—
893C2×D4—2922no—
894C2×D4—1464no—
895C2×D4—1464no—
896C2×D4—1464no—
897C2×D4—1464no—
898C2×D4—1464no—
899C2×D4—1464no—
900C2×D4—1462no—
901C2×D4—1464no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—732no—
906C22×C4—731no—
907C22×C4—731no—
908C22×C4—731no—
909C22×C4—731no—
910C22×C4—734no—
911C22×C4—734no—
912C22×C4—734no—
913C22×C4—738no—
914C22×C4—734no—
915C22×C4—732no—
916C22×C4—731no—
917C22×C4—732no—
918C22×C4—731no—
919C22×C4—1462no—
920C22×C4—1462no—
921C22×C4—1464no—
922C22×C4—1464no—
923C22×C4—1464no—
924C22×C4—1464no—
925C22×C4—1464no—
926C22×C4—1464no—
927C22×C4—1464no—
928C22×C4—1464no—
929C22×C4—1462no—
930C22×C4—1462no—
931C22×C4—1464no—
932C22×C4—1464no—
933C22×C4—1462no—
934C22×C4—1462no—
935C22×C4—1462no—
936C22×C4—1462no—
937C22×C4—1462no—
938C22×C4—1462no—
939C22×C4—1464no—
940C22×C4—1464no—
941C22×C4—14632no—
942C22×C4—1462no—
943C22×C4—1462no—
944C22×C4—1462no—
945C22×C4—1462no—
946C22×C4—1462no—
947C22×C4C23×D7312yes—
948C22×C4C23×D7311yescharacteristic
949C22×C4C23×D7312yes—
950C22×C4C23×D7311yescharacteristic
951C22×C4C23×D7311yescharacteristic
952C22×C4C23×D7311yescharacteristic
953C22×C4C23×D7311yescharacteristic
954C22×C4C23×D7312yes—
955C22×C4C23×D7311yescharacteristic
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—42no—
959C4⋊C4—2922no—
960C4⋊C4—2922no—
961C4⋊C4—2922no—
962C4⋊C4—1462no—
963C4⋊C4—1462no—
964C4⋊C4—1462no—
965C4⋊C4—1462no—
966C4⋊C4—1462no—
967C4⋊C4—1462no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—24no—
971C22⋊C4—24no—
972C22⋊C4—24no—
973C22⋊C4—24no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—2922no—
977C22⋊C4—2922no—
978C22⋊C4—2922no—
979C22⋊C4—2922no—
980C22⋊C4—2922no—
981C22⋊C4—2922no—
982C22⋊C4—1464no—
983C22⋊C4—1464no—
984C22⋊C4—1462no—
985C22⋊C4—1462no—
986C22⋊C4—1464no—
987C22⋊C4—1464no—
988C22⋊C4—1464no—
989C22⋊C4—1464no—
990C22⋊C4—1462no—
991C22⋊C4—1462no—
992C22⋊C4—1464no—
993C22⋊C4—1464no—
994C22⋊C4—1462no—
995C22⋊C4—1462no—
996C22⋊C4—1464no—
997C22⋊C4—1464no—
998C22⋊C4—1464no—
999C22⋊C4—1464no—
1000C42—22no—
1001C42—24no—
1002C42—734no—
1003C42—734no—
1004C42—734no—
1005C42—1464no—
1006C42—1464no—
1007C42—1462no—
1008C42—1462no—
1009C42—1462no—
1010C42—1464no—
1011C42D4×D7314yescomplemented
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—2924no—
1024C23—2924no—
1025C23—2928no—
1026C23—2928no—
1027C23—2928no—
1028C23—2928no—
1029C23—2928no—
1030C23—2928no—
1031C23—2928no—
1032C23—2928no—
1033C23—732no—
1034C23—732no—
1035C23—734no—
1036C23—732no—
1037C23—734no—
1038C23—732no—
1039C23—1468no—
1040C23—14616no—
1041C23—1462no—
1042C23—1462no—
1043C23—1462no—
1044C23—1462no—
1045C23—1462no—
1046C23—1462no—
1047C23—1462no—
1048C23—1461no—
1049C23—1461no—
1050C23—1462no—
1051C23—1462no—
1052C23#41×D7312yes—
1053C23C24×D7311yescharacteristic
1054Q8—44no—
1055Q8—2924no—
1056Q8—2928no—
1057D4—48no—
1058D4—44no—
1059D4—2924no—
1060D4—2928no—
1061D4—2928no—
1062D4—2928no—
1063D4—2928no—
1064C2×C4—28no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—2928no—
1084C2×C4—2924no—
1085C2×C4—2924no—
1086C2×C4—2928no—
1087C2×C4—732no—
1088C2×C4—732no—
1089C2×C4—732no—
1090C2×C4—734no—
1091C2×C4—732no—
1092C2×C4—1468no—
1093C2×C4—1468no—
1094C2×C4—1468no—
1095C2×C4—14616no—
1096C2×C4—1468no—
1097C2×C4—1468no—
1098C2×C4—1468no—
1099C2×C4—1461no—
1100C2×C4—1461no—
1101C2×C4—1462no—
1102C2×C4—1462no—
1103C2×C4—1462no—
1104C2×C4—1462no—
1105C2×C4—1462no—
1106C2×C4—1462no—
1107C2×C4—1462no—
1108C2×C4—1462no—
1109C2×C4—1468no—
1110C2×C4—1461no—
1111C2×C4—1462no—
1112C2×C4—1461no—
1113C2×C4—1461no—
1114C2×C4—1461no—
1115C2×C4—1462no—
1116C2×C4—1462no—
1117C2×C4—1462no—
1118C2×C4C2×D4×D7312yes—
1119C2×C4C2×D4×D7312yes—
1120C2×C4C2×D4×D7312yes—
1121C2×C4#41×D7314yes—
1122C2×C4#41×D7312yes—
1123C22—22no—
1124C22—24no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—29216no—
1136C22—2921no—
1137C22—2921no—
1138C22—2922no—
1139C22—2922no—
1140C22—2922no—
1141C22—2922no—
1142C22—2922no—
1143C22—2922no—
1144C22—2922no—
1145C22—2922no—
1146C22—58416no—
1147C22—734no—
1148C22—734no—
1149C22—738no—
1150C22—734no—
1151C22—738no—
1152C22—1462no—
1153C22—1464no—
1154C22C22×D4×D7311yescharacteristic
1155C22C2×#41×D7311yescharacteristic
1156C22C2×#41×D7311yescharacteristic
1157C22C2×#41×D7312yes—
1158C22H(5,𝔽2)×D7312yes—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—24no—
1163C4—22no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—2922no—
1169C4—2921no—
1170C4—2921no—
1171C4—2922no—
1172C4—1462no—
1173C4—1462no—
1174C4—1462no—
1175C4—1464no—
1176C4—1462no—
1177C2—42no—
1178C2—82no—
1179C2—2922no—
1180C2—5842no—
1181C2—738no—
1182C2#525×D7311yescharacteristic
1183C2#532×D7311yescharacteristic
1184C2#535×D7311yescharacteristic
1185C2#551×D7312yes—
1186C2#555×D7312yes—
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2610C2
prime radical#392×D73C2
hypercenter#2610D73
hypocenterC73C2×#2610
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. C2×#124×D73C2semidirect
2. C2×#117×D73C2semidirect
3. #22615621C2semidirect
4. #22615620C2semidirect
5. #22615619C2semidirect
6. #22615618C2semidirect
7. #22615617C2semidirect
8. #22615616C2semidirect
9. #22615615C2semidirect
10. #22615614C2semidirect
11. #22615613C2semidirect
12. #22615612C2semidirect
13. #22615611C2semidirect
14. #395×D73C2semidirect
15. #394×D73C2semidirect
16. #393×D73C2semidirect
18. #390×D73C2semidirect
19. #388×D73C2semidirect
20. #388×D73C2semidirect
21. #386×D73C2semidirect
22. #376×D73C2semidirect
23. C73×#2610C2semidirect
28. C2×#14556580C22semidirect
29. C2×#14556579C22semidirect
30. C2×#14556578C22semidirect
31. C2×#14556577C22semidirect
32. C2×#14556577C22semidirect
34. C2×#14556550C22semidirect
35. C2×#14556549C22semidirect
36. C2×#14556549C22semidirect
37. C2×#14556548C22semidirect
38. C2×#14556548C22semidirect
39. C2×#14556547C22semidirect
40. C2×#14556547C22semidirect
56. #17988508C22semidirect
57. #17988508C22semidirect
58. #17988507C22semidirect
59. #17988507C22semidirect
60. #17988506C22semidirect
61. #17988505C22semidirect
62. #17988504C22semidirect
63. #17988503C22semidirect
64. #17988502C22semidirect
65. #17988501C22semidirect
66. #17988500C22semidirect
67. #17988500C22semidirect
68. #17988499C22semidirect
69. #17988499C22semidirect
70. #17988498C22semidirect
76. #17988490C22semidirect
77. #17988489C22semidirect
78. #17988488C22semidirect
79. #17988487C22semidirect
80. #17988487C22semidirect
81. #17988487C22semidirect
82. #17988487C22semidirect
83. #17988481C22semidirect
84. #17988481C22semidirect
85. #17988480C22semidirect
86. #17988480C22semidirect
87. #17988479C22semidirect
88. #17988479C22semidirect
89. #17988478C22semidirect
90. #17988478C22semidirect
91. #17988477C22semidirect
92. #17988477C22semidirect
93. #17988476C22semidirect
94. #17988476C22semidirect
95. #17988475C22semidirect
96. #17988475C22semidirect
97. #17988467C22semidirect
98. #17988466C22semidirect
99. #17988465C22semidirect
100. #17988465C22semidirect
101. #17988464C22semidirect
102. #17988463C22semidirect
103. #17988463C22semidirect
104. #17988433C22semidirect
105. #17988433C22semidirect
106. #17988432C22semidirect
107. #17988432C22semidirect
108. #17988432C22semidirect
114. C2×#124×C73C22semidirect
115. C2×#117×C73C22semidirect
116. #395×C73C22semidirect
117. #394×C73C22semidirect
118. #393×C73C22semidirect
120. #390×C73C22semidirect
121. #388×C73C22semidirect
122. #388×C73C22semidirect
123. #386×C73C22semidirect
124. #376×C73C22semidirect
223. C42×D73D4semidirect
380. C4×Dic73C2×D4semidirect
381. C4×Dic73C2×D4semidirect
382. C4×Dic73C2×D4semidirect
417. C42×C73C2×D4semidirect
593. D73#2610direct (N × H)
607. #2610D73direct (N × H)
617. C73C2×#2610semidirect
628. C2×#124C2×D73semidirect
637. C2×#117C2×D73semidirect
657. #395C2×D73semidirect
663. #394C2×D73semidirect
669. #393C2×D73semidirect
683. #390C2×D73semidirect
698. #388C2×D73semidirect
699. #388C2×D73semidirect
707. #386C2×D73semidirect
713. #376C2×D73semidirect
1011. C42D4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D732
C2×#117×D732
#226156212
#226156202
#226156192
#226156182
#226156172
#226156162
#226156152
#226156142
#226156132
#226156122
#226156112
#395×D732
#394×D732
#393×D732
#392×D732
#390×D732
#388×D732
#386×D732
#376×D732
C73×#26102
C2×#261073