Finite Group Databasebeta

← C2×#22612598 #33244710

Subgroups — C2×#22612598 #33244710

Order 18688.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556573C211yesmaximal, characteristic
2C22×C4×C22⋊D73C211yesmaximal, characteristic
3C22×C4⋊C4×D73C211yesmaximal, characteristic, complemented
4#22612598C2116yesmaximal, direct product factor
5C2×#17988484C211yesmaximal, characteristic, complemented
6C2×#17988483C211yesmaximal, characteristic, complemented
7C2×#17988480C211yesmaximal, characteristic, complemented
8C2×#17988475C211yesmaximal, characteristic, complemented
9C2×#17988472C211yesmaximal, characteristic, complemented
10C2×#17988468C211yesmaximal, characteristic, complemented
11C2×#17988463C211yesmaximal, characteristic
12C2×#17988460C211yesmaximal, characteristic, complemented
13C2×#17988458C211yesmaximal, characteristic, complemented
14C2×#17988449C211yesmaximal, characteristic, complemented
15C2×#17988434C211yesmaximal, characteristic, complemented
16C2×#385×C73C211yesmaximal, characteristic, complemented
17C23×C22⋊D73C2211yescharacteristic
18C23×C4×D73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C23×C4×D73C2211yescharacteristic
21C2×#14556573C4116yescomplemented
22C2×#14556573C2218yes—
23C2×C4×C22⋊D73—28no—
24C2×C4×C22⋊D73C2218yes—
25C22×C4⋊Dic73C2211yescharacteristic
26C22×C4⋊Dic73C2211yescharacteristic
27C22×#11924007C2211yescharacteristic
28C22×#11924007C2211yescharacteristic
29C22×#11924007C2211yescharacteristic
30C22×#11924007C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C2×C4⋊C4×D73—28no—
33C2×C4⋊C4×D73C2218yescomplemented
34C22×C22⋊Dic73C2211yescharacteristic
35C22×C22⋊Dic73C2211yescharacteristic
36C22×C22⋊Dic73C2211yescharacteristic
37C22×#11924005C2211yescharacteristic
38C22×#11924005C2211yescharacteristic
39C22×#11924005C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42C22×C4×Dic73C2211yescharacteristic
43#17988484C2218yescomplemented
44#17988483C2218yescomplemented
45#17988480C2218yescomplemented
46#17988475C2218yescomplemented
47#17988472C2218yescomplemented
48#17988468C2218yescomplemented
49#17988463C2218yes—
50#17988460C2218yescomplemented
51#17988458C2218yescomplemented
52#17988449C2218yescomplemented
53#17988434C2218yescomplemented
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2211yescharacteristic
61C2×#14556498C2211yescharacteristic
62C24×C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65C22×C22⋊C4×C73C2211yescharacteristic
66C22×C22⋊C4×C73C2211yescharacteristic
67#385×C73C2218yescomplemented
68C2×#95×C73C2211yescharacteristic
69C2×#95×C73C2211yescharacteristic
70C24×D73C2311yescharacteristic
71C22×C22⋊D73—24no—
72C22×C22⋊D73—24no—
73C22×C22⋊D73C2×C418yes—
74C22×C22⋊D73C2314yes—
75C23×Dic73C2311yescharacteristic
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C22×C4×D73—24no—
83C22×C4×D73—24no—
84C22×C4×D73—24no—
85C22×C4×D73—42no—
86C22×C4×D73—42no—
87C22×C4×D73—42no—
88C22×C4×D73—42no—
89C22×C4×D73C2×C418yescomplemented
90C22×C4×D73D418yes—
91C22×C4×D73C2314yes—
92C22×C4×D73C2314yes—
93C22×C4×D73C2314yes—
94#14556573C2×C4164yescomplemented
95C4×C22⋊D73—232no—
96C2×C4⋊Dic73—24no—
97C2×C4⋊Dic73C2×C418yescomplemented
98C2×C4⋊Dic73C2314yes—
99C2×C4⋊Dic73C2314yes—
100C2×#11924007—24no—
101C2×#11924007—24no—
102C2×#11924007—24no—
103C2×#11924007—42no—
104C2×#11924007C2×C418yescomplemented
105C2×#11924007C2314yes—
106C2×#11924007C2314yes—
107C2×#11924007C2314yes—
108C2×#11924007C2314yes—
109C2×#11924007C2314yes—
110C4⋊C4×D73—232no—
111C2×C22⋊Dic73—24no—
112C2×C22⋊Dic73—42no—
113C2×C22⋊Dic73C2×C418yescomplemented
114C2×C22⋊Dic73C2314yes—
115C2×C22⋊Dic73C2314yes—
116C2×C22⋊Dic73C2314yes—
117C2×#11924005—24no—
118C2×#11924005—24no—
119C2×#11924005C2×C418yescomplemented
120C2×#11924005C2314yes—
121C2×#11924005C2314yes—
122C2×#11924005C2314yes—
123C2×C4×Dic73—24no—
124C2×C4×Dic73—42no—
125C2×C4×Dic73—42no—
126C2×C4×Dic73C2314yes—
127C2×C4×Dic73C2314yes—
128C2×C4×Dic73C2314yes—
129#14556498C2314yes—
130#14556498C2314yes—
131#14556498C2314yes—
132#14556498C2314yes—
133#14556498C2314yes—
134#14556498C2314yes—
135#14556498C2314yes—
136#14556498C2314yes—
137C25×C73C2311yescharacteristic
138C23×C4×C73—24no—
139C23×C4×C73—42no—
140C23×C4×C73—42no—
141C23×C4×C73C2311yescharacteristic
142C23×C4×C73C2311yescharacteristic
143C23×C4×C73C2311yescharacteristic
144C23×C4×C73C2311yescharacteristic
145C23×C4×C73C2311yescharacteristic
146C23×C4×C73C2311yescharacteristic
147C23×C4×C73C2314yes—
148C2×C4⋊C4×C73—24no—
149C2×C4⋊C4×C73—42no—
150C2×C4⋊C4×C73C2314yes—
151C2×C4⋊C4×C73C2314yes—
152C2×C22⋊C4×C73—42no—
153C2×C22⋊C4×C73C2×C418yescomplemented
154C2×C22⋊C4×C73C2314yes—
155C2×C22⋊C4×C73C2314yes—
156#95×C73C2314yes—
157#95×C73C2314yes—
158C23×D73—22no—
159C23×D73—22no—
160C23×D73—22no—
161C23×D73—22no—
162C23×D73C22×C414yes—
163C23×D73C2×D414yes—
164C23×D73#4114yes—
165C23×D73C2412yes—
166C2×C22⋊D73—232no—
167C2×C22⋊D73—28no—
168C2×C22⋊D73—28no—
169C2×C22⋊D73C22×C4116yes—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—22no—
179C22×Dic73—22no—
180C22×Dic73—22no—
181C22×Dic73—22no—
182C22×Dic73—22no—
183C22×Dic73—22no—
184C22×Dic73—22no—
185C22×Dic73—22no—
186C22×Dic73—22no—
187C22×Dic73C22×C414yes—
188C22×Dic73C22×C414yes—
189C22×Dic73C22×C414yes—
190C22×Dic73C2×D414yes—
191C22×Dic73C2412yes—
192C22×Dic73C2412yes—
193C22×Dic73C2412yes—
194C22×Dic73C2412yes—
195C22×Dic73C2412yes—
196C22×Dic73C2412yes—
197C22×Dic73C2412yes—
198C2×C4×D73—232no—
199C2×C4×D73—28no—
200C2×C4×D73—28no—
201C2×C4×D73—28no—
202C2×C4×D73—416no—
203C2×C4×D73—44no—
204C2×C4×D73—44no—
205C2×C4×D73—44no—
206C2×C4×D73—44no—
207C2×C4×D73—416no—
208C2×C4×D73C22×C4116yescomplemented
209C2×C4×D73C2×D4116yes—
210C4⋊Dic73—28no—
211C4⋊Dic73C22×C4116yescomplemented
212#11924007—28no—
213#11924007—28no—
214#11924007—28no—
215#11924007—44no—
216#11924007C22×C4116yescomplemented
217C22⋊Dic73—28no—
218C22⋊Dic73—44no—
219C22⋊Dic73C22×C4116yescomplemented
220#11924005—28no—
221#11924005—28no—
222#11924005C22×C4116yescomplemented
223C4×Dic73—28no—
224C4×Dic73—44no—
225C4×Dic73—44no—
226C24×C73—22no—
227C24×C73—22no—
228C24×C73—22no—
229C24×C73—22no—
230C24×C73—22no—
231C24×C73—22no—
232C24×C73C22×C414yes—
233C24×C73C2412yes—
234C24×C73C2411yescharacteristic
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73—22no—
241C22×C4×C73—22no—
242C22×C4×C73—22no—
243C22×C4×C73—22no—
244C22×C4×C73—22no—
245C22×C4×C73—22no—
246C22×C4×C73—22no—
247C22×C4×C73—22no—
248C22×C4×C73—22no—
249C22×C4×C73—22no—
250C22×C4×C73—28no—
251C22×C4×C73—44no—
252C22×C4×C73—44no—
253C22×C4×C73—416no—
254C22×C4×C73C22×C414yes—
255C22×C4×C73C22×C414yes—
256C22×C4×C73C2×D414yes—
257C22×C4×C73C2412yes—
258C22×C4×C73C2412yes—
259C22×C4×C73C2412yes—
260C22×C4×C73C2412yes—
261C22×C4×C73C2412yes—
262C22×C4×C73C2412yes—
263C4⋊C4×C73—28no—
264C4⋊C4×C73—44no—
265C22⋊C4×C73—44no—
266C22⋊C4×C73C22×C4116yescomplemented
267C23×C73—28no—
268C23×C73—28no—
269C23×C73—28no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—44no—
277C23×C73—44no—
278C23×C73—44no—
279C23×C73—44no—
280C23×C73C23×C414yes—
281C23×C73C23×C412yes—
282C23×C73C22×D412yes—
283C23×C73C2×#4112yes—
284C23×C73H(5,𝔽2)12yes—
285C23×C73H(5,𝔽2)12yes—
286C23×C732−1+412yes—
287C23×C732−1+412yes—
288C23×C73C2511yescharacteristic
289C22×D73—28no—
290C22×D73—28no—
291C22×D73—28no—
292C22×D73—28no—
293C22×D73—28no—
294C22×D73—28no—
295C22×D73—22no—
296C22×D73—22no—
297C22×D73—22no—
298C22×D73—22no—
299C22×D73C4×D4116yes—
300C22×D73C23×C414yes—
301C22×D73C22×D414yes—
302C22×D73C2×#4114yes—
303C2×C4×C73—28no—
304C2×C4×C73—28no—
305C2×C4×C73—28no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—22no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—416no—
322C2×C4×C73—44no—
323C2×C4×C73—44no—
324C2×C4×C73—44no—
325C2×C4×C73C23×C414yes—
326C2×C4×C73C23×C414yes—
327C2×C4×C73C22×D414yes—
328C22⋊D73—232no—
329C2×Dic73—28no—
330C2×Dic73—28no—
331C2×Dic73—28no—
332C2×Dic73—28no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—22no—
336C2×Dic73—22no—
337C2×Dic73—22no—
338C2×Dic73—22no—
339C2×Dic73—22no—
340C2×Dic73—22no—
341C2×Dic73—22no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—44no—
351C2×Dic73—44no—
352C2×Dic73—44no—
353C2×Dic73C23×C414yes—
354C2×Dic73C23×C414yes—
355C2×Dic73C23×C414yes—
356C2×Dic73C22×D414yes—
357C4×D73—232no—
358C4×D73—416no—
359C4×D73—416no—
360C22×C73—24no—
361C22×C73—24no—
362C22×C73—24no—
363C22×C73—416no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73C2×C4×D414yes—
369C22×C73#52014yes—
370C22×C73#52014yes—
371C22×C73#53414yes—
372C22×C73#53614yes—
373C22×C73#53914yes—
374C22×C73#53914yes—
375C22×C73C24×C411yescharacteristic
376C22×C73C23×D411yescharacteristic
377C22×C73C22×#4111yescharacteristic
378C22×C73C2×H(5,𝔽2)11yescharacteristic
379C22×C73C2×H(5,𝔽2)11yescharacteristic
380C22×C73C2×2−1+411yescharacteristic
381C22×C73C2×2−1+411yescharacteristic
382C2×D73—232no—
383C2×D73—24no—
384C2×D73—24no—
385C2×D73—24no—
386C2×D73—24no—
387C2×D73—24no—
388C2×D73—24no—
389C2×D73C2×C4×D418yes—
390C4×C73—24no—
391C4×C73—24no—
392C4×C73—24no—
393C4×C73—42no—
394C4×C73—42no—
395C4×C73—42no—
396Dic73—24no—
397Dic73—24no—
398Dic73—24no—
399Dic73—24no—
400Dic73—42no—
401Dic73—42no—
402Dic73—42no—
403C2×#2322—731nomaximal, Sylow
404C2×C73—44no—
405C2×C73#232218yescomplemented
406C2×C73C22×C4×D411yescharacteristic
407C2×C73C2×#52011yescharacteristic
408C2×C73C2×#52011yescharacteristic
409C2×C73C2×#53411yescharacteristic
410C2×C73C2×#53611yescharacteristic
411C2×C73C2×#53911yescharacteristic
412C2×C73C2×#53911yescharacteristic
413D73—28no—
414C22×#123—731no—
415C22×C4×D4—731no—
416C23×C4⋊C4—731no—
417#2322—7316no—
418C2×#389—731no—
419C2×#389—731no—
420C2×#388—731no—
421C2×#388—731no—
422C2×#387—731no—
423C2×#387—731no—
424C2×#386—731no—
425C2×#385—731no—
426C2×#385—731no—
427C2×#385D7311yescharacteristic, complemented
428C2×#381—731no—
429C2×C4×C22⋊C4—731no—
430C73C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—731no—
432C24×C4—731no—
433C24×C4—731no—
434C24×C4—731no—
435C24×C4C2×D7311yescharacteristic
436C2×#123—7316no—
437C2×#123—738no—
438C2×C4×D4—738no—
439C2×C4×D4—1468no—
440C22×C4⋊C4—731no—
441C22×C4⋊C4—731no—
442C22×C4⋊C4—731no—
443C22×C4⋊C4—731no—
444C22×C4⋊C4—731no—
445C22×C4⋊C4—731no—
446C22×C4⋊C4—731no—
447C22×C4⋊C4—738no—
448C22×C4⋊C4—1468no—
449C22×C4⋊C4C2×D7311yescharacteristic
450C22×C4⋊C4C2×D7311yescharacteristic
451C22×C22⋊C4—731no—
452C22×C22⋊C4—731no—
453C22×C22⋊C4—731no—
454C22×C22⋊C4—731no—
455C22×C22⋊C4—731no—
456C22×C22⋊C4—731no—
457C22×C22⋊C4C2×D7311yescharacteristic
458C22×C22⋊C4C2×D7311yescharacteristic
459C22×C42—731no—
460C22×C42—731no—
461C22×C42—731no—
462#389—738no—
463#389—738no—
464#388—738no—
465#388—738no—
466#387—738no—
467#387—738no—
468#386—738no—
469#385—738no—
470#385—738no—
471#385C2×D7318yescomplemented
472#381—738no—
473C4×C22⋊C4—738no—
474C2×#95—731no—
475C2×#95—731no—
476C2×#95—731no—
477C2×#95—731no—
478C2×#95—731no—
479C2×#95—731no—
480C2×#95—731no—
481C2×#95—731no—
482C2×#95C2×D7311yescharacteristic
483C2×#95C2×D7311yescharacteristic
484C25—731no—
485C25C22×D7311yescharacteristic
486C22×D4—738no—
487C22×D4—734no—
488C22×D4—1464no—
489C22×D4—1464no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—42no—
493C23×C4—2922no—
494C23×C4—2922no—
495C23×C4—2922no—
496C23×C4—2922no—
497C23×C4—738no—
498C23×C4—734no—
499C23×C4—734no—
500C23×C4—731no—
501C23×C4—731no—
502C23×C4—731no—
503C23×C4—731no—
504C23×C4—738no—
505C23×C4—734no—
506C23×C4—731no—
507C23×C4—731no—
508C23×C4—731no—
509C23×C4—1464no—
510C23×C4—1464no—
511C23×C4—1464no—
512C23×C4C22×D7311yescharacteristic
513C23×C4C22×D7311yescharacteristic
514C23×C4C22×D7311yescharacteristic
515C23×C4C22×D7311yescharacteristic
516C23×C4C22×D7311yescharacteristic
517C23×C4C22×D7311yescharacteristic
518C23×C4C22×D7314yes—
519#123—7364no—
520C4×D4—14632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—2922no—
524C2×C4⋊C4—734no—
525C2×C4⋊C4—738no—
526C2×C4⋊C4—738no—
527C2×C4⋊C4—734no—
528C2×C4⋊C4—734no—
529C2×C4⋊C4—734no—
530C2×C4⋊C4—734no—
531C2×C4⋊C4—734no—
532C2×C4⋊C4—734no—
533C2×C4⋊C4—14632no—
534C2×C4⋊C4—1464no—
535C2×C4⋊C4—1464no—
536C2×C4⋊C4—1464no—
537C2×C4⋊C4—1464no—
538C2×C4⋊C4C22×D7314yes—
539C2×C4⋊C4C22×D7314yes—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—2922no—
542C2×C22⋊C4—734no—
543C2×C22⋊C4—738no—
544C2×C22⋊C4—734no—
545C2×C22⋊C4—738no—
546C2×C22⋊C4—734no—
547C2×C22⋊C4—734no—
548C2×C22⋊C4—734no—
549C2×C22⋊C4—734no—
550C2×C22⋊C4—1464no—
551C2×C22⋊C4—1464no—
552C2×C22⋊C4—1464no—
553C2×C22⋊C4C4×D7318yescomplemented
554C2×C22⋊C4C22×D7314yes—
555C2×C22⋊C4C22×D7314yes—
556C2×C42—2922no—
557C2×C42—2922no—
558C2×C42—734no—
559C2×C42—734no—
560C2×C42—734no—
561C2×C42—1464no—
562#95—734no—
563#95—734no—
564#95—734no—
565#95—734no—
566#95—734no—
567#95—734no—
568#95—734no—
569#95—734no—
570#95C22×D7314yes—
571#95C22×D7314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—734no—
579C24—734no—
580C24—734no—
581C24—732no—
582C24—1462no—
583C24—1462no—
584C24—1462no—
585C24—1462no—
586C24C2×C4×D7314yes—
587C24C23×D7312yes—
588C24C23×D7311yescharacteristic
589C2×D4—7316no—
590C2×D4—1468no—
591C2×D4—1468no—
592C2×D4—14632no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—29216no—
613C22×C4—2924no—
614C22×C4—2924no—
615C22×C4—2924no—
616C22×C4—2924no—
617C22×C4—29216no—
618C22×C4—7316no—
619C22×C4—734no—
620C22×C4—734no—
621C22×C4—734no—
622C22×C4—734no—
623C22×C4—732no—
624C22×C4—732no—
625C22×C4—732no—
626C22×C4—732no—
627C22×C4—7316no—
628C22×C4—732no—
629C22×C4—732no—
630C22×C4—732no—
631C22×C4—1468no—
632C22×C4—1468no—
633C22×C4—1468no—
634C22×C4—14632no—
635C22×C4—1462no—
636C22×C4—1462no—
637C22×C4—1462no—
638C22×C4—1462no—
639C22×C4—1462no—
640C22×C4—1462no—
641C22×C4—1462no—
642C22×C4—1462no—
643C22×C4—1462no—
644C22×C4—1462no—
645C22×C4—1462no—
646C22×C4—1462no—
647C22×C4—1462no—
648C22×C4—1462no—
649C22×C4—1462no—
650C22×C4—1462no—
651C22×C4—1462no—
652C22×C4C2×C4×D7314yes—
653C22×C4C2×C4×D7314yes—
654C22×C4D4×D7314yes—
655C22×C4C23×D7312yes—
656C22×C4C23×D7312yes—
657C22×C4C23×D7312yes—
658C22×C4C23×D7312yes—
659C22×C4C23×D7312yes—
660C22×C4C23×D7312yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—2924no—
664C4⋊C4—7316no—
665C4⋊C4—7316no—
666C4⋊C4—1468no—
667C4⋊C4—1468no—
668C4⋊C4—1468no—
669C4⋊C4—1468no—
670C22⋊C4—44no—
671C22⋊C4—2924no—
672C22⋊C4—7316no—
673C22⋊C4—7316no—
674C22⋊C4—1468no—
675C22⋊C4—1468no—
676C22⋊C4—1468no—
677C22⋊C4C2×C4×D73116yescomplemented
678C42—2924no—
679C42—2924no—
680C42—1468no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—734no—
695C23—734no—
696C23—734no—
697C23—7316no—
698C23—1468no—
699C23—1468no—
700C23—1462no—
701C23—1462no—
702C23—1462no—
703C23—1462no—
704C23—1468no—
705C23—1468no—
706C23—1468no—
707C23—1468no—
708C23C22×C4×D7314yes—
709C23C22×C4×D7312yes—
710C23C2×D4×D7312yes—
711C23#41×D7312yes—
712C23#1455663612yes—
713C23#1455663612yes—
714C23#1455663812yes—
715C23#1455663912yes—
716C23C24×D7311yescharacteristic
717D4—14632no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—29216no—
741C2×C4—29216no—
742C2×C4—2924no—
743C2×C4—2924no—
744C2×C4—2924no—
745C2×C4—734no—
746C2×C4—734no—
747C2×C4—734no—
748C2×C4—734no—
749C2×C4—14632no—
750C2×C4—1462no—
751C2×C4—1462no—
752C2×C4—1462no—
753C2×C4—1462no—
754C2×C4—1462no—
755C2×C4—1462no—
756C2×C4—1462no—
757C2×C4—1462no—
758C2×C4—1462no—
759C2×C4—1468no—
760C2×C4—1462no—
761C2×C4—1462no—
762C2×C4—1462no—
763C2×C4—1462no—
764C2×C4—1462no—
765C2×C4—1462no—
766C2×C4—1462no—
767C2×C4—1462no—
768C2×C4—1468no—
769C2×C4—1468no—
770C2×C4—1468no—
771C2×C4C22×C4×D7314yes—
772C2×C4C22×C4×D7314yes—
773C2×C4C2×D4×D7314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—738no—
783C22—1464no—
784C22—1464no—
785C22—1464no—
786C22—1464no—
787C22—14632no—
788C22—1464no—
789C22—1464no—
790C22C4×D4×D7314yes—
791C22#1798906614yes—
792C22#1798906814yes—
793C22#1798914714yes—
794C22#1798916014yes—
795C22#1798918014yes—
796C22#1798918314yes—
797C22C23×C4×D7311yescharacteristic
798C22C22×D4×D7311yescharacteristic
799C22C2×#41×D7311yescharacteristic
800C22C2×#1455663611yescharacteristic
801C22C2×#1455663611yescharacteristic
802C22C2×#1455663811yescharacteristic
803C22C2×#1455663911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—2922no—
811C4—2922no—
812C4—2922no—
813C4—1464no—
814C4—1464no—
815C4—1464no—
816C4—1464no—
817C2—44no—
818C2—1468no—
819C2#2261259818yesdirect product factor
820C2C2×C4×D4×D7311yescharacteristic
821C2C2×#1798906611yescharacteristic
822C2C2×#1798906811yescharacteristic
823C2C2×#1798914711yescharacteristic
824C2C2×#1798916011yescharacteristic
825C2C2×#1798918011yescharacteristic
826C2C2×#1798918311yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#385×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC2×#385D73
hypocenterC73C2×#2322
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D73C2semidirect
4. #22612598C2direct (N × H)
5. C2×#17988484C2semidirect
6. C2×#17988483C2semidirect
7. C2×#17988480C2semidirect
8. C2×#17988475C2semidirect
9. C2×#17988472C2semidirect
10. C2×#17988468C2semidirect
12. C2×#17988460C2semidirect
13. C2×#17988458C2semidirect
14. C2×#17988449C2semidirect
15. C2×#17988434C2semidirect
16. C2×#385×C73C2semidirect
21. C2×#14556573C4semidirect
33. C2×C4⋊C4×D73C22semidirect
43. #17988484C22semidirect
44. #17988483C22semidirect
45. #17988480C22semidirect
46. #17988475C22semidirect
47. #17988472C22semidirect
48. #17988468C22semidirect
50. #17988460C22semidirect
51. #17988458C22semidirect
52. #17988449C22semidirect
53. #17988434C22semidirect
67. #385×C73C22semidirect
89. C22×C4×D73C2×C4semidirect
94. #14556573C2×C4semidirect
97. C2×C4⋊Dic73C2×C4semidirect
104. C2×#11924007C2×C4semidirect
113. C2×C22⋊Dic73C2×C4semidirect
119. C2×#11924005C2×C4semidirect
153. C2×C22⋊C4×C73C2×C4semidirect
208. C2×C4×D73C22×C4semidirect
211. C4⋊Dic73C22×C4semidirect
216. #11924007C22×C4semidirect
219. C22⋊Dic73C22×C4semidirect
222. #11924005C22×C4semidirect
266. C22⋊C4×C73C22×C4semidirect
405. C2×C73#2322semidirect
427. C2×#385D73semidirect
430. C73C2×#2322semidirect
471. #385C2×D73semidirect
553. C2×C22⋊C4C4×D73semidirect
677. C22⋊C4C2×C4×D73semidirect
819. C2#22612598direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145565732
C22×C4×C22⋊D732
C22×C4⋊C4×D732
#226125982
C2×#179884842
C2×#179884832
C2×#179884802
C2×#179884752
C2×#179884722
C2×#179884682
C2×#179884632
C2×#179884602
C2×#179884582
C2×#179884492
C2×#179884342
C2×#385×C732
C2×#232273