Finite Group Databasebeta

← C2×#22613059 #33245696

Subgroups — C2×#22613059 #33245696

Order 18688.

3094 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556573C211yesmaximal, characteristic
2#22613059C2116yesmaximal, direct product factor
3C2×#17988487C211yesmaximal, characteristic
4C2×#17988477C211yesmaximal, characteristic, complemented
5C2×#17988476C211yesmaximal, characteristic, complemented
6C2×#17988475C211yesmaximal, characteristic, complemented
7C2×#17988472C211yesmaximal, characteristic, complemented
8C2×#17988469C211yesmaximal, characteristic, complemented
9C2×#17988464C211yesmaximal, characteristic
10C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C2×C4×#11924007C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
14C2×C4×#11924005C211yesmaximal, characteristic, complemented
15C2×#17988434C211yesmaximal, characteristic, complemented
16C2×#388×C73C211yesmaximal, characteristic, complemented
17C23×C22⋊D73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C2×#14556573C4116yescomplemented
21C2×#14556573C2218yes—
22C22×C4⋊Dic73C2211yescharacteristic
23C22×#11924007C2211yescharacteristic
24C22×#11924007C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C22×C4×Dic73C2211yescharacteristic
36C22×C4×Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39#17988487C2218yes—
40#17988477C2218yescomplemented
41#17988476C2218yescomplemented
42#17988475C2218yescomplemented
43#17988472C2218yescomplemented
44#17988469C2218yescomplemented
45#17988464C2218yes—
46C4⋊C4×Dic73C2218yescomplemented
47C4×#11924007C2218yescomplemented
48C22⋊C4×Dic73C2218yescomplemented
49C22⋊C4×Dic73C2218yescomplemented
50C4×#11924005C2218yescomplemented
51#17988434C2218yescomplemented
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C22⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C42×C73C2211yescharacteristic
65#388×C73C2218yescomplemented
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C24×D73C2311yescharacteristic
69C22×C22⋊D73—42no—
70C22×C22⋊D73—42no—
71C22×C22⋊D73C2×C418yes—
72C22×C22⋊D73C2314yes—
73C23×Dic73—24no—
74C23×Dic73—24no—
75C23×Dic73—42no—
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2314yes—
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C22×C4×D73—42no—
85C22×C4×D73—42no—
86C22×C4×D73C2×C418yescomplemented
87C22×C4×D73C2314yes—
88#14556573C2×C4164yescomplemented
89C2×C4⋊Dic73C2×C418yescomplemented
90C2×C4⋊Dic73C2314yes—
91C2×#11924007—24no—
92C2×#11924007—42no—
93C2×#11924007C2×C418yescomplemented
94C2×#11924007C2314yes—
95C2×#11924007C2314yes—
96C2×#11924007C2314yes—
97C2×C22⋊Dic73—24no—
98C2×C22⋊Dic73C2×C418yes—
99C2×C22⋊Dic73C2314yes—
100C2×C22⋊Dic73C2314yes—
101C2×#11924005—24no—
102C2×#11924005—24no—
103C2×#11924005—24no—
104C2×#11924005—24no—
105C2×#11924005C2×C418yescomplemented
106C2×#11924005C2314yes—
107C2×#11924005C2314yes—
108C2×#11924005C2314yes—
109C2×#11924005C2314yes—
110C2×#11924005C2314yes—
111C2×C4×Dic73—24no—
112C2×C4×Dic73—24no—
113C2×C4×Dic73—42no—
114C2×C4×Dic73—42no—
115C2×C4×Dic73—42no—
116C2×C4×Dic73—42no—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119C2×C4×Dic73C2314yes—
120C2×C4×Dic73C2314yes—
121C2×C4×Dic73C2314yes—
122C2×C4×Dic73C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130#14556498C2314yes—
131C25×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73—24no—
139C2×C4⋊C4×C73C2314yes—
140C2×C22⋊C4×C73—24no—
141C2×C22⋊C4×C73—42no—
142C2×C22⋊C4×C73C2×C418yes—
143C2×C22⋊C4×C73C2314yes—
144C2×C22⋊C4×C73C2314yes—
145C2×C22⋊C4×C73C2314yes—
146C2×C42×C73—42no—
147C2×C42×C73C2314yes—
148#95×C73C2314yes—
149#95×C73C2314yes—
150C23×D73—22no—
151C23×D73—22no—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—22no—
156C23×D73C22×C414yes—
157C23×D73C2412yes—
158C2×C22⋊D73—416no—
159C2×C22⋊D73—44no—
160C2×C22⋊D73—44no—
161C2×C22⋊D73C22×C4116yes—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—28no—
178C22×Dic73—28no—
179C22×Dic73—44no—
180C22×Dic73—416no—
181C22×Dic73C22×C414yes—
182C22×Dic73C22×C414yes—
183C22×Dic73C22×C414yes—
184C22×Dic73#4114yes—
185C22×Dic73#4114yes—
186C22×Dic73#4114yes—
187C22×Dic73C2412yes—
188C22×Dic73C2412yes—
189C22×Dic73C2412yes—
190C22×Dic73C2412yes—
191C22×Dic73C2412yes—
192C22×Dic73C2412yes—
193C22×Dic73C2412yes—
194C2×C4×D73—416no—
195C2×C4×D73—44no—
196C2×C4×D73—44no—
197C2×C4×D73C22×C4116yescomplemented
198C4⋊Dic73C22×C4116yescomplemented
199#11924007—28no—
200#11924007—44no—
201#11924007C22×C4116yescomplemented
202C22⋊Dic73—28no—
203C22⋊Dic73C22×C4116yes—
204#11924005—28no—
205#11924005—28no—
206#11924005—28no—
207#11924005—28no—
208#11924005C22×C4116yescomplemented
209C4×Dic73—28no—
210C4×Dic73—28no—
211C4×Dic73—44no—
212C4×Dic73—44no—
213C4×Dic73—44no—
214C4×Dic73—44no—
215C24×C73—22no—
216C24×C73—22no—
217C24×C73—22no—
218C24×C73—22no—
219C24×C73—22no—
220C24×C73—22no—
221C24×C73C22×C414yes—
222C24×C73C2412yes—
223C24×C73C2411yescharacteristic
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—22no—
234C22×C4×C73—22no—
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73—22no—
239C22×C4×C73C22×C414yes—
240C22×C4×C73C22×C414yes—
241C22×C4×C73#4114yes—
242C22×C4×C73C2412yes—
243C22×C4×C73C2412yes—
244C22×C4×C73C2412yes—
245C22×C4×C73C2412yes—
246C22×C4×C73C2412yes—
247C22×C4×C73C2412yes—
248C4⋊C4×C73—28no—
249C22⋊C4×C73—28no—
250C22⋊C4×C73—44no—
251C22⋊C4×C73C22×C4116yes—
252C42×C73—44no—
253C23×C73—28no—
254C23×C73—28no—
255C23×C73—28no—
256C23×C73—22no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—22no—
261C23×C73—22no—
262C23×C73—44no—
263C23×C73—44no—
264C23×C73—44no—
265C23×C73—44no—
266C23×C73C23×C414yes—
267C23×C73C23×C412yes—
268C23×C73C2×#4112yes—
269C23×C73C2×#4112yes—
270C23×C73C2×#4112yes—
271C23×C73C2×#4112yes—
272C23×C73H(5,𝔽2)12yes—
273C23×C73H(5,𝔽2)12yes—
274C23×C73C2511yescharacteristic
275C22×D73—28no—
276C22×D73—28no—
277C22×D73—28no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73—44no—
287C22×D73—44no—
288C22×D73C23×C414yes—
289C2×C4×C73—28no—
290C2×C4×C73—28no—
291C2×C4×C73—28no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—44no—
308C2×C4×C73—44no—
309C2×C4×C73—44no—
310C2×C4×C73C23×C414yes—
311C2×C4×C73C23×C414yes—
312C2×C4×C73C2×#4114yes—
313C22⋊D73—416no—
314C2×Dic73—28no—
315C2×Dic73—28no—
316C2×Dic73—28no—
317C2×Dic73—28no—
318C2×Dic73—28no—
319C2×Dic73—28no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—416no—
336C2×Dic73—44no—
337C2×Dic73C23×C414yes—
338C2×Dic73C23×C414yes—
339C2×Dic73C23×C414yes—
340C2×Dic73C2×#4114yes—
341C2×Dic73C2×#4114yes—
342C2×Dic73C2×#4114yes—
343C4×D73—416no—
344C22×C73—24no—
345C22×C73—24no—
346C22×C73—24no—
347C22×C73—416no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73C4×#4114yes—
353C22×C73C4×#4114yes—
354C22×C73#51814yes—
355C22×C73#55114yes—
356C22×C73#55314yes—
357C22×C73#55314yes—
358C22×C73#55914yes—
359C22×C73C24×C411yescharacteristic
360C22×C73C22×#4111yescharacteristic
361C22×C73C22×#4111yescharacteristic
362C22×C73C22×#4111yescharacteristic
363C22×C73C22×#4111yescharacteristic
364C22×C73C2×H(5,𝔽2)11yescharacteristic
365C22×C73C2×H(5,𝔽2)11yescharacteristic
366C2×D73—24no—
367C2×D73—24no—
368C2×D73—24no—
369C2×D73—416no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C4×C73—24no—
375C4×C73—24no—
376C4×C73—24no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—42no—
380Dic73—24no—
381Dic73—24no—
382Dic73—24no—
383Dic73—24no—
384Dic73—24no—
385Dic73—24no—
386Dic73—42no—
387C2×#2374—731nomaximal, Sylow
388C2×C73—44no—
389C2×C73#237418yescomplemented
390C2×C73C2×C4×#4111yescharacteristic
391C2×C73C2×C4×#4111yescharacteristic
392C2×C73C2×#51811yescharacteristic
393C2×C73C2×#55111yescharacteristic
394C2×C73C2×#55311yescharacteristic
395C2×C73C2×#55311yescharacteristic
396C2×C73C2×#55911yescharacteristic
397D73—44no—
398C22×#123—731no—
399#2374—7316no—
400C2×#390—731no—
401C2×#388—731no—
402C2×#388—731no—
403C2×#388—731no—
404C2×#388D7311yescharacteristic, complemented
405C2×#387—731no—
406C2×#387—731no—
407C2×#386—731no—
408C2×C4×C4⋊C4—731no—
409C2×C4×C4⋊C4—731no—
410C2×C4×C22⋊C4—731no—
411C2×C4×C22⋊C4—731no—
412C2×C4×C22⋊C4—731no—
413C2×C4×C22⋊C4—731no—
414C73C2×#237411yescharacteristic, complemented, Sylow
415C23×D4—731no—
416C24×C4—731no—
417C24×C4—731no—
418C2×#123—7316no—
419C2×#123—738no—
420C22×C4⋊C4—731no—
421C22×C4⋊C4—731no—
422C22×C4⋊C4—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4C2×D7311yescharacteristic
425C22×C22⋊C4—731no—
426C22×C22⋊C4—731no—
427C22×C22⋊C4—731no—
428C22×C22⋊C4—731no—
429C22×C22⋊C4—731no—
430C22×C22⋊C4—731no—
431C22×C22⋊C4—731no—
432C22×C22⋊C4C2×D7311yescharacteristic
433C22×C22⋊C4C2×D7311yescharacteristic
434C22×C22⋊C4C2×D7311yescharacteristic
435C22×C42—731no—
436C22×C42—731no—
437C22×C42—731no—
438C22×C42—731no—
439C22×C42—731no—
440C22×C42—731no—
441C22×C42C2×D7311yescharacteristic
442#390—738no—
443#388—738no—
444#388—738no—
445#388—738no—
446#388C2×D7318yescomplemented
447#387—738no—
448#387—738no—
449#386—738no—
450C4×C4⋊C4—738no—
451C4×C4⋊C4—738no—
452C4×C22⋊C4—738no—
453C4×C22⋊C4—738no—
454C4×C22⋊C4—738no—
455C4×C22⋊C4—738no—
456C2×#95—731no—
457C2×#95—731no—
458C2×#95—731no—
459C2×#95—731no—
460C2×#95—731no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95C2×D7311yescharacteristic
465C2×#95C2×D7311yescharacteristic
466C25—731no—
467C25C22×D7311yescharacteristic
468C22×D4—2922no—
469C22×D4—2922no—
470C22×D4—738no—
471C22×D4—734no—
472C23×C4—2922no—
473C23×C4—2922no—
474C23×C4—2922no—
475C23×C4—738no—
476C23×C4—734no—
477C23×C4—734no—
478C23×C4—731no—
479C23×C4—731no—
480C23×C4—731no—
481C23×C4—731no—
482C23×C4—731no—
483C23×C4—731no—
484C23×C4—731no—
485C23×C4—1464no—
486C23×C4—1464no—
487C23×C4C22×D7311yescharacteristic
488C23×C4C22×D7311yescharacteristic
489C23×C4C22×D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7311yescharacteristic
493#123—7364no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—2922no—
496C2×C4⋊C4—734no—
497C2×C4⋊C4—738no—
498C2×C4⋊C4—738no—
499C2×C4⋊C4—734no—
500C2×C4⋊C4—734no—
501C2×C4⋊C4—734no—
502C2×C4⋊C4—1464no—
503C2×C4⋊C4C22×D7314yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—738no—
507C2×C22⋊C4—734no—
508C2×C22⋊C4—738no—
509C2×C22⋊C4—734no—
510C2×C22⋊C4—734no—
511C2×C22⋊C4—734no—
512C2×C22⋊C4—734no—
513C2×C22⋊C4—734no—
514C2×C22⋊C4—734no—
515C2×C22⋊C4—1464no—
516C2×C22⋊C4—1464no—
517C2×C22⋊C4—1464no—
518C2×C22⋊C4—1464no—
519C2×C22⋊C4—1464no—
520C2×C22⋊C4C4×D7318yes—
521C2×C22⋊C4C22×D7314yes—
522C2×C22⋊C4C22×D7314yes—
523C2×C22⋊C4C22×D7314yes—
524C2×C42—42no—
525C2×C42—2922no—
526C2×C42—2922no—
527C2×C42—2922no—
528C2×C42—2922no—
529C2×C42—734no—
530C2×C42—734no—
531C2×C42—734no—
532C2×C42—734no—
533C2×C42—734no—
534C2×C42—734no—
535C2×C42—1464no—
536C2×C42—1464no—
537C2×C42C22×D7314yes—
538#95—734no—
539#95—734no—
540#95—734no—
541#95—734no—
542#95—734no—
543#95—734no—
544#95—734no—
545#95—734no—
546#95C22×D7314yes—
547#95C22×D7314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—734no—
555C24—732no—
556C24—1462no—
557C24—1462no—
558C24—1462no—
559C24—1462no—
560C24—1462no—
561C24—1462no—
562C24C2×C4×D7314yes—
563C24C23×D7312yes—
564C24C23×D7311yescharacteristic
565C2×D4—2924no—
566C2×D4—2924no—
567C2×D4—29216no—
568C2×D4—7316no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—2924no—
585C22×C4—2924no—
586C22×C4—29216no—
587C22×C4—2924no—
588C22×C4—29216no—
589C22×C4—7316no—
590C22×C4—734no—
591C22×C4—734no—
592C22×C4—734no—
593C22×C4—734no—
594C22×C4—734no—
595C22×C4—734no—
596C22×C4—732no—
597C22×C4—732no—
598C22×C4—732no—
599C22×C4—732no—
600C22×C4—732no—
601C22×C4—732no—
602C22×C4—732no—
603C22×C4—1468no—
604C22×C4—1468no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4—1462no—
608C22×C4—1462no—
609C22×C4—1462no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1462no—
613C22×C4—1462no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4—1462no—
620C22×C4C2×C4×D7314yes—
621C22×C4C2×C4×D7314yes—
622C22×C4#1192402714yes—
623C22×C4C23×D7312yes—
624C22×C4C23×D7312yes—
625C22×C4C23×D7312yes—
626C22×C4C23×D7312yes—
627C22×C4C23×D7312yes—
628C22×C4C23×D7312yes—
629C4⋊C4—28no—
630C4⋊C4—2924no—
631C4⋊C4—7316no—
632C4⋊C4—7316no—
633C4⋊C4—1468no—
634C22⋊C4—28no—
635C22⋊C4—44no—
636C22⋊C4—7316no—
637C22⋊C4—7316no—
638C22⋊C4—1468no—
639C22⋊C4—1468no—
640C22⋊C4—1468no—
641C22⋊C4—1468no—
642C22⋊C4—1468no—
643C22⋊C4C2×C4×D73116yes—
644C42—44no—
645C42—2924no—
646C42—2924no—
647C42—2924no—
648C42—2924no—
649C42—1468no—
650C42—1468no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—2924no—
665C23—2924no—
666C23—2924no—
667C23—2924no—
668C23—734no—
669C23—1462no—
670C23—1462no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1468no—
676C23—1468no—
677C23—1468no—
678C23C22×C4×D7314yes—
679C23C22×C4×D7312yes—
680C23#41×D7312yes—
681C23#41×D7312yes—
682C23#41×D7312yes—
683C23C2×#1192402712yes—
684C23#1455663612yes—
685C23#1455663712yes—
686C23C24×D7311yescharacteristic
687D4—29216no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—29216no—
710C2×C4—2924no—
711C2×C4—29216no—
712C2×C4—734no—
713C2×C4—734no—
714C2×C4—734no—
715C2×C4—734no—
716C2×C4—734no—
717C2×C4—734no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1468no—
734C2×C4—1468no—
735C2×C4—1468no—
736C2×C4—1468no—
737C2×C4—1468no—
738C2×C4—1468no—
739C2×C4C22×C4×D7314yes—
740C2×C4C22×C4×D7314yes—
741C2×C4C2×#1192402714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—416no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—2922no—
751C22—29216no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—1464no—
756C22—1464no—
757C22—1464no—
758C22C4×#1192402714yes—
759C22#1798905514yes—
760C22#1798905914yes—
761C22#1798926214yes—
762C22#1798928014yes—
763C22#1798928214yes—
764C22#1798931914yes—
765C22C23×C4×D7311yescharacteristic
766C22C2×#41×D7311yescharacteristic
767C22C2×#41×D7311yescharacteristic
768C22C2×#41×D7311yescharacteristic
769C22C22×#1192402711yescharacteristic
770C22C2×#1455663611yescharacteristic
771C22C2×#1455663711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—2922no—
779C4—1464no—
780C4—1464no—
781C4—1464no—
782C4—1464no—
783C4—1464no—
784C4—1464no—
785C2—44no—
786C2—2924no—
787C2#2261305918yesdirect product factor
788C2C2×C4×#1192402711yescharacteristic
789C2C2×#1798905511yescharacteristic
790C2C2×#1798905911yescharacteristic
791C2C2×#1798926211yescharacteristic
792C2C2×#1798928011yescharacteristic
793C2C2×#1798928211yescharacteristic
794C2C2×#1798931911yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#388×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC2×#388D73
hypocenterC73C2×#2374
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #22613059C2direct (N × H)
4. C2×#17988477C2semidirect
5. C2×#17988476C2semidirect
6. C2×#17988475C2semidirect
7. C2×#17988472C2semidirect
8. C2×#17988469C2semidirect
10. C2×C4⋊C4×Dic73C2semidirect
11. C2×C4×#11924007C2semidirect
12. C2×C22⋊C4×Dic73C2semidirect
13. C2×C22⋊C4×Dic73C2semidirect
14. C2×C4×#11924005C2semidirect
15. C2×#17988434C2semidirect
16. C2×#388×C73C2semidirect
20. C2×#14556573C4semidirect
40. #17988477C22semidirect
41. #17988476C22semidirect
42. #17988475C22semidirect
43. #17988472C22semidirect
44. #17988469C22semidirect
46. C4⋊C4×Dic73C22semidirect
47. C4×#11924007C22semidirect
48. C22⋊C4×Dic73C22semidirect
49. C22⋊C4×Dic73C22semidirect
50. C4×#11924005C22semidirect
51. #17988434C22semidirect
65. #388×C73C22semidirect
86. C22×C4×D73C2×C4semidirect
88. #14556573C2×C4semidirect
89. C2×C4⋊Dic73C2×C4semidirect
93. C2×#11924007C2×C4semidirect
105. C2×#11924005C2×C4semidirect
197. C2×C4×D73C22×C4semidirect
198. C4⋊Dic73C22×C4semidirect
201. #11924007C22×C4semidirect
208. #11924005C22×C4semidirect
389. C2×C73#2374semidirect
404. C2×#388D73semidirect
414. C73C2×#2374semidirect
446. #388C2×D73semidirect
787. C2#22613059direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565732
#226130592
C2×#179884872
C2×#179884772
C2×#179884762
C2×#179884752
C2×#179884722
C2×#179884692
C2×#179884642
C2×C4⋊C4×Dic732
C2×C4×#119240072
C2×C22⋊C4×Dic732
C2×C4×#119240052
C2×#179884342
C2×#388×C732
C2×#237473