Finite Group Databasebeta

← #33008951

Subgroups — #33008951

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988467C211yesmaximal, characteristic
2C2×#17988450C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
5#22608193C211yesmaximal, characteristic, complemented
6#22608176C211yesmaximal, characteristic, complemented
7#22608176C211yesmaximal, characteristic, complemented
8#22608172C211yesmaximal, characteristic
9#22608168C211yesmaximal, characteristic, complemented
10#22608168C211yesmaximal, characteristic, complemented
11#22608165C211yesmaximal, characteristic, complemented
12#22608156C211yesmaximal, characteristic, complemented
13#22608156C211yesmaximal, characteristic, complemented
14#22608153C211yesmaximal, characteristic, complemented
15C2×#386×C73C211yesmaximal, characteristic
16C24×Dic73C2211yescharacteristic
17C22×C4⋊Dic73C2211yescharacteristic
18C22×C22⋊Dic73C2211yescharacteristic
19C22×C22⋊Dic73C2211yescharacteristic
20C22×C22⋊Dic73C2211yescharacteristic
21C22×C22⋊Dic73C2211yescharacteristic
22C22×C22⋊Dic73C2211yescharacteristic
23C22×C22⋊Dic73C2211yescharacteristic
24C22×C22⋊Dic73C2211yescharacteristic
25C22×C4×Dic73C2211yescharacteristic
26C22×C4×Dic73C2211yescharacteristic
27C22×C4×Dic73C2211yescharacteristic
28#17988467—24no—
29#17988450—24no—
30C22⋊C4×Dic73—24no—
31C4×C22⋊Dic73—24no—
32C2×#14556498C2211yescharacteristic
33C2×#14556498C2211yescharacteristic
34C2×#14556498C2211yescharacteristic
35C2×#14556498C2211yescharacteristic
36C2×#14556498C2211yescharacteristic
37C2×#14556498C2211yescharacteristic
38C2×#14556498C2211yescharacteristic
39C2×#14556498C2211yescharacteristic
40C2×#14556498C2211yescharacteristic
41C2×#14556498C2211yescharacteristic
42C2×#14556498C2211yescharacteristic
43C2×#14556498C2211yescharacteristic
44C2×#14556498C2211yescharacteristic
45C2×#14556498C2211yescharacteristic
46C2×#14556498C2211yescharacteristic
47C2×#14556498C2211yescharacteristic
48C23×D4×C73C2211yescharacteristic
49C24×C4×C73C2211yescharacteristic
50C22×C22⋊C4×C73C2211yescharacteristic
51C22×C22⋊C4×C73C2211yescharacteristic
52C22×C22⋊C4×C73C2211yescharacteristic
53#386×C73C418yescomplemented
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C23×Dic73—22no—
57C23×Dic73—22no—
58C23×Dic73—22no—
59C23×Dic73—22no—
60C23×Dic73—22no—
61C23×Dic73—41no—
62C23×Dic73—41no—
63C23×Dic73C2311yescharacteristic
64C23×Dic73C2311yescharacteristic
65C23×Dic73C2311yescharacteristic
66C23×Dic73C2311yescharacteristic
67C23×Dic73C2311yescharacteristic
68C23×Dic73C2311yescharacteristic
69C23×Dic73C2311yescharacteristic
70C23×Dic73C2311yescharacteristic
71C2×C4⋊Dic73—22no—
72C2×C4⋊Dic73—41no—
73C2×C4⋊Dic73—41no—
74C2×C22⋊Dic73—22no—
75C2×C22⋊Dic73—22no—
76C2×C22⋊Dic73—22no—
77C2×C22⋊Dic73—22no—
78C2×C22⋊Dic73—22no—
79C2×C22⋊Dic73—22no—
80C2×C22⋊Dic73—22no—
81C2×C22⋊Dic73—22no—
82C2×C22⋊Dic73—22no—
83C2×C22⋊Dic73—22no—
84C2×C22⋊Dic73—22no—
85C2×C22⋊Dic73—22no—
86C2×C22⋊Dic73—22no—
87C2×C22⋊Dic73—22no—
88C2×C22⋊Dic73—22no—
89C2×C22⋊Dic73—22no—
90C2×C22⋊Dic73—41no—
91C2×C22⋊Dic73—41no—
92C2×C22⋊Dic73—41no—
93C2×C22⋊Dic73—41no—
94C2×C22⋊Dic73D414yes—
95C2×C4×Dic73—22no—
96C2×C4×Dic73—22no—
97C2×C4×Dic73—22no—
98C2×C4×Dic73—22no—
99C2×C4×Dic73—22no—
100C2×C4×Dic73—22no—
101C2×C4×Dic73—41no—
102C2×C4×Dic73—41no—
103C2×C4×Dic73—41no—
104#14556498—22no—
105#14556498—22no—
106#14556498—22no—
107#14556498—22no—
108#14556498—22no—
109#14556498—22no—
110#14556498—22no—
111#14556498—22no—
112#14556498—22no—
113#14556498—22no—
114#14556498—41no—
115#14556498—41no—
116#14556498—41no—
117#14556498—41no—
118#14556498—41no—
119#14556498D414yescomplemented
120C25×C73C2311yescharacteristic
121C25×C73C2311yescharacteristic
122C22×D4×C73—22no—
123C22×D4×C73—22no—
124C22×D4×C73—22no—
125C22×D4×C73—22no—
126C22×D4×C73—41no—
127C22×D4×C73—41no—
128C22×D4×C73C2×C414yes—
129C23×C4×C73—22no—
130C23×C4×C73—22no—
131C23×C4×C73—22no—
132C23×C4×C73—22no—
133C23×C4×C73—41no—
134C23×C4×C73—41no—
135C23×C4×C73C2×C414yescomplemented
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C23×C4×C73C2311yescharacteristic
139C23×C4×C73C2311yescharacteristic
140C23×C4×C73C2311yescharacteristic
141C2×C22⋊C4×C73—22no—
142C2×C22⋊C4×C73—22no—
143C2×C22⋊C4×C73—41no—
144C2×C22⋊C4×C73—41no—
145C2×C22⋊C4×C73—41no—
146C2×C22⋊C4×C73—41no—
147C2×C22⋊C4×C73C2×C414yes—
148C2×C22⋊C4×C73C2×C414yes—
149C2×C22⋊C4×C73C2×C414yescomplemented
150#95×C73C2×C414yescomplemented
151#95×C73C2×C414yescomplemented
152C22×Dic73—21no—
153C22×Dic73—21no—
154C22×Dic73—21no—
155C22×Dic73—21no—
156C22×Dic73—28no—
157C22×Dic73—21no—
158C22×Dic73—21no—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—21no—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73—21no—
177C22×Dic73—21no—
178C22×Dic73—21no—
179C22×Dic73—21no—
180C22×Dic73—21no—
181C22×Dic73—21no—
182C22×Dic73—21no—
183C22×Dic73—21no—
184C22×Dic73—21no—
185C22×Dic73—21no—
186C22×Dic73—21no—
187C22×Dic73—21no—
188C22×Dic73—21no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73—21no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73—21no—
198C22×Dic73—21no—
199C22×Dic73—21no—
200C22×Dic73—21no—
201C22×Dic73—44no—
202C22×Dic73—44no—
203C22×Dic73—44no—
204C22×Dic73—44no—
205C22×Dic73—44no—
206C22×Dic73—44no—
207C22×Dic73C2×D412yes—
208C22×Dic73C2×D412yes—
209C22×Dic73C2×D412yes—
210C22×Dic73C2×D412yes—
211C22×Dic73#4112yes—
212C22×Dic73#4112yes—
213C22×Dic73#4112yes—
214C22×Dic73#4112yes—
215C4⋊Dic73—44no—
216C22⋊Dic73—28no—
217C22⋊Dic73—28no—
218C22⋊Dic73—28no—
219C22⋊Dic73—44no—
220C22⋊Dic73—44no—
221C22⋊Dic73—44no—
222C22⋊Dic73—44no—
223C4×Dic73—44no—
224C4×Dic73—44no—
225C4×Dic73—44no—
226C24×C73—21no—
227C24×C73—21no—
228C24×C73—21no—
229C24×C73—21no—
230C24×C73—21no—
231C24×C73—21no—
232C24×C73—21no—
233C24×C73—21no—
234C24×C73—21no—
235C24×C73—21no—
236C24×C73—21no—
237C24×C73—21no—
238C24×C73—21no—
239C24×C73—21no—
240C24×C73—21no—
241C24×C73—21no—
242C24×C73—21no—
243C24×C73—21no—
244C24×C73—21no—
245C24×C73—21no—
246C24×C73—21no—
247C24×C73—21no—
248C24×C73—21no—
249C24×C73—21no—
250C24×C73C22×C412yes—
251C24×C73C22×C412yes—
252C24×C73C2×D412yes—
253C24×C73#4112yes—
254C24×C73#4112yes—
255C24×C73#4112yes—
256C24×C73C2411yescharacteristic
257C2×D4×C73—28no—
258C2×D4×C73—28no—
259C2×D4×C73—44no—
260C2×D4×C73—44no—
261C2×D4×C73—44no—
262C2×D4×C73—44no—
263C2×D4×C73—44no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—28no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—28no—
294C22×C4×C73—44no—
295C22×C4×C73—44no—
296C22×C4×C73—44no—
297C22×C4×C73—44no—
298C22×C4×C73—44no—
299C22×C4×C73C22×C412yes—
300C22×C4×C73C22×C412yes—
301C22×C4×C73C22×C412yes—
302C22×C4×C73C22×C412yes—
303C22×C4×C73C22×C412yes—
304C22×C4×C73C2×D412yes—
305C22×C4×C73#4112yes—
306C22⋊C4×C73—28no—
307C22⋊C4×C73—44no—
308C22⋊C4×C73—44no—
309C23×C73—22no—
310C23×C73—22no—
311C23×C73—22no—
312C23×C73—22no—
313C23×C73—22no—
314C23×C73—22no—
315C23×C73—22no—
316C23×C73—22no—
317C23×C73—22no—
318C23×C73—22no—
319C23×C73—22no—
320C23×C73—22no—
321C23×C73—22no—
322C23×C73—22no—
323C23×C73—22no—
324C23×C73—22no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—22no—
328C23×C73—22no—
329C23×C73—22no—
330C23×C73—22no—
331C23×C73—22no—
332C23×C73—22no—
333C23×C73—22no—
334C23×C73—22no—
335C23×C73—22no—
336C23×C73—22no—
337C23×C73—22no—
338C23×C73—22no—
339C23×C73—22no—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—41no—
346C23×C73—41no—
347C23×C73—41no—
348C23×C73—41no—
349C23×C73—41no—
350C23×C73—41no—
351C23×C73—41no—
352C23×C73—41no—
353C23×C73—41no—
354C23×C73—41no—
355C23×C73—41no—
356C23×C73—41no—
357C23×C73—41no—
358C23×C73—41no—
359C23×C73—41no—
360C23×C73—41no—
361C23×C73—41no—
362C23×C73—41no—
363C23×C73—41no—
364C23×C73—41no—
365C23×C73—41no—
366C23×C73—41no—
367C23×C73—41no—
368C23×C73—41no—
369C23×C73—41no—
370C23×C73—41no—
371C23×C73—41no—
372C23×C73—41no—
373C23×C73—41no—
374C23×C73—41no—
375C23×C73—41no—
376C23×C73—41no—
377C23×C73#11714yes—
378C23×C73C4×D414yes—
379C23×C73C23×C411yescharacteristic
380C23×C73C22×D411yescharacteristic
381C23×C73C22×D411yescharacteristic
382C23×C73C2×#4111yescharacteristic
383C23×C73C2×#4111yescharacteristic
384C23×C73C2×#4111yescharacteristic
385C23×C73C2×#4111yescharacteristic
386C23×C73C2×#4111yescharacteristic
387C23×C73C2×#4111yescharacteristic
388C23×C73C2×#4111yescharacteristic
389C23×C73C2×#4111yescharacteristic
390C23×C73H(5,𝔽2)11yescharacteristic
391C23×C73H(5,𝔽2)11yescharacteristic
392C23×C73H(5,𝔽2)11yescharacteristic
393C23×C73H(5,𝔽2)11yescharacteristic
394D4×C73—416no—
395C2×C4×C73—22no—
396C2×C4×C73—22no—
397C2×C4×C73—22no—
398C2×C4×C73—22no—
399C2×C4×C73—22no—
400C2×C4×C73—22no—
401C2×C4×C73—22no—
402C2×C4×C73—22no—
403C2×C4×C73—22no—
404C2×C4×C73—22no—
405C2×C4×C73—22no—
406C2×C4×C73—22no—
407C2×C4×C73—22no—
408C2×C4×C73—22no—
409C2×C4×C73—22no—
410C2×C4×C73—22no—
411C2×C4×C73—22no—
412C2×C4×C73—22no—
413C2×C4×C73—416no—
414C2×C4×C73—41no—
415C2×C4×C73—41no—
416C2×C4×C73—41no—
417C2×C4×C73—41no—
418C2×C4×C73—41no—
419C2×C4×C73—41no—
420C2×C4×C73—41no—
421C2×C4×C73—41no—
422C2×C4×C73—41no—
423C2×C4×C73—41no—
424C2×C4×C73—41no—
425C2×C4×C73—41no—
426C2×C4×C73—41no—
427C2×C4×C73—41no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73C4×D414yes—
431C2×Dic73—22no—
432C2×Dic73—22no—
433C2×Dic73—22no—
434C2×Dic73—22no—
435C2×Dic73—22no—
436C2×Dic73—22no—
437C2×Dic73—22no—
438C2×Dic73—22no—
439C2×Dic73—22no—
440C2×Dic73—22no—
441C2×Dic73—22no—
442C2×Dic73—22no—
443C2×Dic73—22no—
444C2×Dic73—22no—
445C2×Dic73—22no—
446C2×Dic73—22no—
447C2×Dic73—22no—
448C2×Dic73—22no—
449C2×Dic73—22no—
450C2×Dic73—22no—
451C2×Dic73—22no—
452C2×Dic73—416no—
453C2×Dic73—41no—
454C2×Dic73—41no—
455C2×Dic73—41no—
456C2×Dic73—41no—
457C2×Dic73—41no—
458C2×Dic73—41no—
459C2×Dic73—41no—
460C2×Dic73—41no—
461C2×Dic73—41no—
462C2×Dic73—41no—
463C2×Dic73—41no—
464C2×Dic73—41no—
465C2×Dic73—41no—
466C2×Dic73—41no—
467C2×Dic73—41no—
468C2×Dic73—41no—
469C2×Dic73—41no—
470C2×Dic73—41no—
471C2×Dic73—41no—
472C2×Dic73—41no—
473C2×Dic73—41no—
474C2×Dic73—41no—
475C2×Dic73—41no—
476C2×Dic73—41no—
477C2×Dic73—41no—
478C2×Dic73—41no—
479C2×Dic73—41no—
480C2×Dic73—41no—
481C2×Dic73—41no—
482C2×Dic73—41no—
483C2×Dic73—41no—
484C2×Dic73—41no—
485C2×Dic73—41no—
486C2×Dic73—41no—
487C2×Dic73#12314yes—
488C22×C73—24no—
489C22×C73—24no—
490C22×C73—24no—
491C22×C73—24no—
492C22×C73—24no—
493C22×C73—24no—
494C22×C73—42no—
495C22×C73—42no—
496C22×C73—42no—
497C22×C73—42no—
498C22×C73—42no—
499C22×C73—42no—
500C22×C73—42no—
501C22×C73—42no—
502C22×C73—42no—
503C22×C73—42no—
504C22×C73—42no—
505C22×C73—42no—
506C22×C73—42no—
507C22×C73—42no—
508C22×C73—42no—
509C22×C73—42no—
510C22×C73—42no—
511C22×C73—42no—
512C22×C73—42no—
513C22×C73—42no—
514C22×C73—42no—
515C22×C73—42no—
516C22×C73—42no—
517C22×C73—42no—
518C22×C73C2×#11711yescharacteristic
519C22×C73C2×C4×D411yescharacteristic
520C22×C73C2×C4×D411yescharacteristic
521C22×C73C4×#4111yescharacteristic
522C22×C73C4×#4111yescharacteristic
523C22×C73#51811yescharacteristic
524C22×C73#51811yescharacteristic
525C22×C73C2×#12311yescharacteristic
526C22×C73#52511yescharacteristic
527C22×C73#52511yescharacteristic
528C22×C73#52511yescharacteristic
529C22×C73#52911yescharacteristic
530C22×C73#52911yescharacteristic
531C22×C73#52911yescharacteristic
532C22×C73#52911yescharacteristic
533C22×C73#53811yescharacteristic
534C22×C73#53811yescharacteristic
535C22×C73#54011yescharacteristic
536C22×C73#54011yescharacteristic
537C22×C73D4211yescharacteristic
538C22×C73#54611yescharacteristic
539C22×C73#54611yescharacteristic
540C22×C73#54611yescharacteristic
541C22×C73#54611yescharacteristic
542C22×C73#54611yescharacteristic
543C22×C73#55011yescharacteristic
544C22×C73#55111yescharacteristic
545C22×C73#55111yescharacteristic
546C22×C73#55111yescharacteristic
547C22×C73#55111yescharacteristic
548C22×C73#55111yescharacteristic
549C22×C73#55311yescharacteristic
550C22×C73#55311yescharacteristic
551C22×C73#55311yescharacteristic
552C22×C73#55511yescharacteristic
553C4×C73—24no—
554C4×C73—42no—
555C4×C73—42no—
556C4×C73—42no—
557C4×C73—42no—
558Dic73—24no—
559Dic73—42no—
560Dic73—42no—
561Dic73—42no—
562Dic73—42no—
563Dic73—42no—
564Dic73—81no—
565Dic73—81no—
566#13984—731nomaximal, Sylow
567C2×C73—44no—
568C2×C73—44no—
569C2×C73#229011yescharacteristic
570C2×C73C4×#12311yescharacteristic
571C2×C73#233311yescharacteristic
572C2×C73#234211yescharacteristic
573C2×C73#235311yescharacteristic
574C2×C73#235811yescharacteristic
575C2×C73#236311yescharacteristic
576C2×C73#241811yescharacteristic
577C2×C73#242011yescharacteristic
578C2×C73#245611yescharacteristic
579C2×C73#245711yescharacteristic
580C2×C73#245711yescharacteristic
581C2×C73#247111yescharacteristic
582C2×C73#257211yescharacteristic
583C2×C73#257611yescharacteristic
584C2×#386—731no—
585C2×#386D7311yescharacteristic
586C2×#381—731no—
587C2×C4×C22⋊C4—731no—
588C2×C4×C22⋊C4—731no—
589#1443—731no—
590#1439—731no—
591#1439—731no—
592#1438—731no—
593#1437—731no—
594#1437—731no—
595#1436—731no—
596#1434—731no—
597#1434—731no—
598C22⋊#95—731no—
599C73#1398411yescharacteristic, complemented, Sylow
600C23×D4C2×D7311yescharacteristic
601C24×C4—731no—
602C24×C4C2×D7311yescharacteristic
603C22×C4⋊C4—731no—
604C22×C22⋊C4—731no—
605C22×C22⋊C4—731no—
606C22×C22⋊C4—731no—
607C22×C22⋊C4—731no—
608C22×C22⋊C4—731no—
609C22×C22⋊C4—731no—
610C22×C22⋊C4—731no—
611C22×C22⋊C4C2×D7311yescharacteristic
612C22×C22⋊C4C2×D7311yescharacteristic
613C22×C22⋊C4C2×D7311yescharacteristic
614C22×C42—731no—
615C22×C42—731no—
616C22×C42—731no—
617#386—1464no—
618#386Dic7318yescomplemented
619#381—1464no—
620C4×C22⋊C4—1464no—
621C4×C22⋊C4—1464no—
622C2×#95—731no—
623C2×#95—731no—
624C2×#95—731no—
625C2×#95—731no—
626C2×#95—731no—
627C2×#95—731no—
628C2×#95—731no—
629C2×#95—731no—
630C2×#95—731no—
631C2×#95—731no—
632C2×#95—731no—
633C2×#95—731no—
634C2×#95—731no—
635C2×#95—731no—
636C2×#95—731no—
637C2×#95—731no—
638C2×#95C2×D7311yescharacteristic
639C2×#95C2×D7311yescharacteristic
640C25C22×D7311yescharacteristic
641C25C22×D7311yescharacteristic
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—41no—
647C22×D4—41no—
648C22×D4C2×Dic7314yes—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—41no—
654C23×C4—41no—
655C23×C4—2921no—
656C23×C4—2921no—
657C23×C4—731no—
658C23×C4—731no—
659C23×C4—731no—
660C23×C4—731no—
661C23×C4—731no—
662C23×C4—731no—
663C23×C4—731no—
664C23×C4—731no—
665C23×C4—1462no—
666C23×C4—1462no—
667C23×C4—1462no—
668C23×C4—1462no—
669C23×C4—1462no—
670C23×C4C2×Dic7314yescomplemented
671C23×C4C22×D7311yescharacteristic
672C23×C4C22×D7311yescharacteristic
673C23×C4C22×D7311yescharacteristic
674C23×C4C22×D7311yescharacteristic
675C23×C4C22×D7311yescharacteristic
676C2×C4⋊C4—2921no—
677C2×C4⋊C4—2921no—
678C2×C4⋊C4—1462no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—2921no—
686C2×C22⋊C4—2921no—
687C2×C22⋊C4—2921no—
688C2×C22⋊C4—2921no—
689C2×C22⋊C4—734no—
690C2×C22⋊C4—1462no—
691C2×C22⋊C4—1462no—
692C2×C22⋊C4—1462no—
693C2×C22⋊C4—1462no—
694C2×C22⋊C4—1462no—
695C2×C22⋊C4—1462no—
696C2×C22⋊C4—1462no—
697C2×C22⋊C4—1462no—
698C2×C22⋊C4—1462no—
699C2×C22⋊C4—1462no—
700C2×C22⋊C4—1462no—
701C2×C22⋊C4—1462no—
702C2×C22⋊C4—1462no—
703C2×C22⋊C4—1462no—
704C2×C22⋊C4—1462no—
705C2×C22⋊C4—1462no—
706C2×C22⋊C4C2×Dic7314yes—
707C2×C22⋊C4C2×Dic7314yes—
708C2×C22⋊C4C2×Dic7314yescomplemented
709C2×C42—2921no—
710C2×C42—2921no—
711C2×C42—2921no—
712C2×C42—1462no—
713C2×C42—1462no—
714C2×C42—1462no—
715C2×C42—1462no—
716C2×C42—1462no—
717C2×C42—1462no—
718#95—2921no—
719#95—2921no—
720#95—2921no—
721#95—2921no—
722#95—2921no—
723#95—734no—
724#95—1462no—
725#95—1462no—
726#95—1462no—
727#95—1462no—
728#95—1462no—
729#95—1462no—
730#95—1462no—
731#95—1462no—
732#95—1462no—
733#95—1462no—
734#95C2×Dic7314yescomplemented
735#95C2×Dic7314yescomplemented
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24C22×Dic7312yes—
761C24C22×Dic7312yes—
762C24D4×D7312yes—
763C24#1192402712yes—
764C24#1192402812yes—
765C24#1192402812yes—
766C24C23×D7311yescharacteristic
767C2×D4—28no—
768C2×D4—28no—
769C2×D4—44no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—28no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—28no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—2924no—
810C22×C4—2924no—
811C22×C4—2924no—
812C22×C4—2924no—
813C22×C4—2924no—
814C22×C4—2924no—
815C22×C4—732no—
816C22×C4—732no—
817C22×C4—732no—
818C22×C4—732no—
819C22×C4—732no—
820C22×C4—732no—
821C22×C4—732no—
822C22×C4—732no—
823C22×C4—1461no—
824C22×C4—1461no—
825C22×C4—1461no—
826C22×C4—1461no—
827C22×C4—1461no—
828C22×C4—1461no—
829C22×C4—1461no—
830C22×C4—1461no—
831C22×C4—1461no—
832C22×C4—1461no—
833C22×C4—1461no—
834C22×C4—1461no—
835C22×C4—1461no—
836C22×C4—1461no—
837C22×C4—1468no—
838C22×C4—1461no—
839C22×C4—1461no—
840C22×C4—1461no—
841C22×C4—1461no—
842C22×C4—1461no—
843C22×C4—1461no—
844C22×C4—1461no—
845C22×C4—1461no—
846C22×C4—1461no—
847C22×C4—1461no—
848C22×C4—1461no—
849C22×C4—1461no—
850C22×C4—1461no—
851C22×C4—1461no—
852C22×C4—1461no—
853C22×C4—1461no—
854C22×C4—1461no—
855C22×C4—1461no—
856C22×C4—1461no—
857C22×C4—1461no—
858C22×C4—1461no—
859C22×C4—1461no—
860C22×C4—1461no—
861C22×C4—1461no—
862C22×C4—1461no—
863C22×C4—1461no—
864C22×C4—1461no—
865C22×C4—1461no—
866C22×C4—1461no—
867C22×C4—1461no—
868C22×C4—1461no—
869C22×C4—1461no—
870C22×C4—1461no—
871C22×C4—1461no—
872C22×C4C22×Dic7312yes—
873C22×C4C22×Dic7312yes—
874C22×C4C22×Dic7312yes—
875C22×C4C22×Dic7312yes—
876C22×C4C22×Dic7312yes—
877C22×C4D4×D7312yes—
878C22×C4#1192402712yes—
879C4⋊C4—2924no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—2924no—
884C22⋊C4—2924no—
885C22⋊C4—2924no—
886C22⋊C4—2924no—
887C22⋊C4—1468no—
888C22⋊C4—1468no—
889C22⋊C4—1468no—
890C42—2924no—
891C42—2924no—
892C42—2924no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23#1455655014yes—
962C23D4×Dic7314yes—
963C23C23×Dic7311yescharacteristic
964C23C2×D4×D7311yescharacteristic
965C23C2×D4×D7311yescharacteristic
966C23#41×D7311yescharacteristic
967C23#41×D7311yescharacteristic
968C23#41×D7311yescharacteristic
969C23#41×D7311yescharacteristic
970C23C2×#1192402711yescharacteristic
971C23C2×#1192402711yescharacteristic
972C23C2×#1192402811yescharacteristic
973C23C2×#1192402811yescharacteristic
974C23#1455663611yescharacteristic
975C23#1455663611yescharacteristic
976C23#1455663611yescharacteristic
977C23#1455663611yescharacteristic
978D4—416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—416no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—2921no—
1015C2×C4—2921no—
1016C2×C4—2921no—
1017C2×C4—2921no—
1018C2×C4—2921no—
1019C2×C4—2921no—
1020C2×C4—2921no—
1021C2×C4—2921no—
1022C2×C4—2921no—
1023C2×C4—2921no—
1024C2×C4—2921no—
1025C2×C4—2921no—
1026C2×C4—2921no—
1027C2×C4—2921no—
1028C2×C4—2921no—
1029C2×C4—2921no—
1030C2×C4—2921no—
1031C2×C4—2921no—
1032C2×C4—2921no—
1033C2×C4—2921no—
1034C2×C4—29216no—
1035C2×C4—2921no—
1036C2×C4—2921no—
1037C2×C4—2921no—
1038C2×C4—2921no—
1039C2×C4—2921no—
1040C2×C4—2921no—
1041C2×C4—2921no—
1042C2×C4—2921no—
1043C2×C4—2921no—
1044C2×C4—2921no—
1045C2×C4—2921no—
1046C2×C4—2921no—
1047C2×C4—2921no—
1048C2×C4—2921no—
1049C2×C4—734no—
1050C2×C4—1462no—
1051C2×C4—1462no—
1052C2×C4—1462no—
1053C2×C4—1462no—
1054C2×C4—1462no—
1055C2×C4—1462no—
1056C2×C4—1462no—
1057C2×C4—1462no—
1058C2×C4—1462no—
1059C2×C4—1462no—
1060C2×C4—1462no—
1061C2×C4—1462no—
1062C2×C4—1462no—
1063C2×C4—1462no—
1064C2×C4—1462no—
1065C2×C4—1462no—
1066C2×C4—1462no—
1067C2×C4—1462no—
1068C2×C4—1462no—
1069C2×C4—1462no—
1070C2×C4—1462no—
1071C2×C4D4×Dic7314yes—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22C2×#1455655011yescharacteristic
1103C22C2×D4×Dic7311yescharacteristic
1104C22C2×D4×Dic7311yescharacteristic
1105C22#41×Dic7311yescharacteristic
1106C22#41×Dic7311yescharacteristic
1107C22#1798906211yescharacteristic
1108C22#1798906211yescharacteristic
1109C22#123×D7311yescharacteristic
1110C22#1798909511yescharacteristic
1111C22#1798909611yescharacteristic
1112C22#1798909611yescharacteristic
1113C22#1798911411yescharacteristic
1114C22#1798911411yescharacteristic
1115C22#1798911711yescharacteristic
1116C22#1798911711yescharacteristic
1117C22#1798916911yescharacteristic
1118C22#1798916911yescharacteristic
1119C22#1798918711yescharacteristic
1120C22#1798918711yescharacteristic
1121C22#1798921911yescharacteristic
1122C22#1798922411yescharacteristic
1123C22#1798922411yescharacteristic
1124C22#1798922711yescharacteristic
1125C22#1798922711yescharacteristic
1126C22#1798923411yescharacteristic
1127C22#1798925511yescharacteristic
1128C22#1798926311yescharacteristic
1129C22#1798926311yescharacteristic
1130C22#1798926611yescharacteristic
1131C22#1798926611yescharacteristic
1132C22#1798926811yescharacteristic
1133C22#1798928411yescharacteristic
1134C22#1798928611yescharacteristic
1135C22#1798928611yescharacteristic
1136C22#1798930111yescharacteristic
1137C4—24no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—2922no—
1143C4—2922no—
1144C4—2922no—
1145C4—2922no—
1146C4—2922no—
1147C4—5841no—
1148C4—5841no—
1149C4—1464no—
1150C2—44no—
1151C2—44no—
1152C2#2261237611yescharacteristic
1153C2#123×Dic7311yescharacteristic
1154C2#2261269811yescharacteristic
1155C2#2261278011yescharacteristic
1156C2#2261287111yescharacteristic
1157C2#2261291511yescharacteristic
1158C2#2261297311yescharacteristic
1159C2#2261339211yescharacteristic
1160C2#2261342011yescharacteristic
1161C2#2261382711yescharacteristic
1162C2#2261383511yescharacteristic
1163C2#2261384211yescharacteristic
1164C2#2261404611yescharacteristic
1165C2#2261518211yescharacteristic
1166C2#2261523911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D73
commutatorC23×C73C23×C4
FittingC2×#386×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D4×C73C22
hypercenterC2×#386D73
hypocenterC73#13984
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#17988450C2semidirect
3. C2×C22⋊C4×Dic73C2semidirect
4. C2×C4×C22⋊Dic73C2semidirect
5. #22608193C2semidirect
6. #22608176C2semidirect
7. #22608176C2semidirect
9. #22608168C2semidirect
10. #22608168C2semidirect
11. #22608165C2semidirect
12. #22608156C2semidirect
13. #22608156C2semidirect
14. #22608153C2semidirect
53. #386×C73C4semidirect
119. #14556498D4semidirect
135. C23×C4×C73C2×C4semidirect
149. C2×C22⋊C4×C73C2×C4semidirect
150. #95×C73C2×C4semidirect
151. #95×C73C2×C4semidirect
599. C73#13984semidirect
618. #386Dic73semidirect
670. C23×C4C2×Dic73semidirect
708. C2×C22⋊C4C2×Dic73semidirect
734. #95C2×Dic73semidirect
735. #95C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179884672
C2×#179884502
C2×C22⋊C4×Dic732
C2×C4×C22⋊Dic732
#226081932
#226081762
#226081722
#226081682
#226081652
#226081562
#226081532
C2×#386×C732
#1398473