Finite Group Databasebeta

← C2×C73×#3343 #32970639

Subgroups — C2×C73×#3343 #32970639

Order 18688.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C73C211yesmaximal, characteristic, complemented
2C2×#547×C73C211yesmaximal, characteristic
3C73×#3343C2116yesmaximal, direct product factor
4C2×#501×C73C211yesmaximal, characteristic, complemented
5C2×#484×C73C211yesmaximal, characteristic, complemented
6C2×#482×C73C211yesmaximal, characteristic, complemented
7C2×#483×C73C211yesmaximal, characteristic, complemented
8C2×#480×C73C211yesmaximal, characteristic, complemented
9C2×#477×C73C211yesmaximal, characteristic, complemented
10C2×#478×C73C211yesmaximal, characteristic, complemented
11C2×#468×C73C211yesmaximal, characteristic, complemented
12C2×#465×C73C211yesmaximal, characteristic, complemented
13C2×#440×C73C211yesmaximal, characteristic, complemented
14C2×#435×C73C211yesmaximal, characteristic, complemented
15C2×#428×C73C211yesmaximal, characteristic, complemented
16C22×#107×C73C211yesmaximal, characteristic, complemented
17C22×#41×C73—21no—
18C22×SD16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C23×C8×C73C2211yescharacteristic
21#552×C73—24no—
22#552×C73C2218yescomplemented
23#547×C73—24no—
24#547×C73C2218yes—
25C2×C4⋊Q8×C73C2211yescharacteristic
26C2×#126×C73—21no—
27C2×#125×C73—21no—
28C2×#125×C73C2211yescharacteristic
29C2×#123×C73—21no—
30C2×#123×C73—21no—
31C2×#123×C73—21no—
32C2×C22⋊Q8×C73—21no—
33C2×C22⋊Q8×C73C2211yescharacteristic
34C2×C22⋊Q8×C73C2211yescharacteristic
35C2×#121×C73C2211yescharacteristic
36C2×#121×C73C2211yescharacteristic
37C2×C4×Q8×C73C2211yescharacteristic
38C2×C4×D4×C73C2211yescharacteristic
39C2×C4×D4×C73C2211yescharacteristic
40C2×#117×C73—21no—
41C2×#117×C73C2211yescharacteristic
42C22×C4⋊C4×C73C2211yescharacteristic
43C22×C4⋊C4×C73C2211yescharacteristic
44C22×C4⋊C4×C73C2211yescharacteristic
45#501×C73C2218yescomplemented
46#484×C73C2218yescomplemented
47#483×C73C2218yescomplemented
48#482×C73C2218yescomplemented
49#480×C73C2218yescomplemented
50#478×C73C2218yescomplemented
51#477×C73C2218yescomplemented
52#468×C73C2218yescomplemented
53#465×C73C2218yescomplemented
54#440×C73C2218yescomplemented
55#435×C73C2218yescomplemented
56#428×C73C2218yescomplemented
57C2×#107×C73C2211yescharacteristic
58C2×#107×C73C2211yescharacteristic
59C2×#107×C73C2211yescharacteristic
60C2×#107×C73C2211yescharacteristic
61C2×#107×C73C2211yescharacteristic
62C2×#107×C73C2211yescharacteristic
63C2×#107×C73C2218yescomplemented
64C2×#106×C73C2211yescharacteristic
65C2×#106×C73C2211yescharacteristic
66C2×#106×C73C2211yescharacteristic
67C2×C4⋊C8×C73C2211yescharacteristic
68C2×#103×C73C2211yescharacteristic
69C2×#103×C73C2211yescharacteristic
70C2×#103×C73C2211yescharacteristic
71C2×#102×C73C2211yescharacteristic
72C2×#102×C73C2211yescharacteristic
73C2×#102×C73C2211yescharacteristic
74C2×C22⋊C8×C73C2211yescharacteristic
75C2×C22⋊C8×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#41×C73—28no—
78C2×#41×C73—48no—
79C22×Q8×C73—21no—
80C22×Q8×C73C2311yescharacteristic
81C22×D4×C73—21no—
82C22×D4×C73—21no—
83C22×D4×C73D411yescharacteristic
84C22×D4×C73C2311yescharacteristic
85C23×C4×C73—21no—
86C23×C4×C73—21no—
87C23×C4×C73—21no—
88C23×C4×C73—21no—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C2×SD16×C73—24no—
92C2×SD16×C73C2314yes—
93C2×M16×C73—24no—
94C2×M16×C73C2314yes—
95C22×C8×C73—24no—
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99C22×C8×C73C2314yes—
100C22×C8×C73C2311yescharacteristic
101C4⋊Q8×C73—22no—
102C4⋊Q8×C73C2314yes—
103#126×C73—28no—
104#125×C73—28no—
105#125×C73—22no—
106#125×C73C2314yes—
107#123×C73—28no—
108#123×C73—28no—
109#123×C73—28no—
110C22⋊Q8×C73—22no—
111C22⋊Q8×C73—22no—
112C22⋊Q8×C73—28no—
113C22⋊Q8×C73C2314yes—
114C22⋊Q8×C73C2314yes—
115#121×C73—22no—
116#121×C73—22no—
117#121×C73C2314yes—
118#121×C73C2314yes—
119C4×Q8×C73—22no—
120C4×Q8×C73C2314yes—
121C4×D4×C73—22no—
122C4×D4×C73D414yes—
123C4×D4×C73C2314yes—
124C4×D4×C73C2314yes—
125#117×C73—22no—
126#117×C73—28no—
127#117×C73C2314yes—
128C2×C4⋊C4×C73—21no—
129C2×C4⋊C4×C73—21no—
130C2×C4⋊C4×C73—21no—
131C2×C4⋊C4×C73—22no—
132C2×C4⋊C4×C73—22no—
133C2×C4⋊C4×C73—22no—
134C2×C4⋊C4×C73—21no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—21no—
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73—21no—
139C2×C4⋊C4×C73—21no—
140C2×C4⋊C4×C73D411yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C2×C4⋊C4×C73C2311yescharacteristic
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C4⋊C4×C73C2311yescharacteristic
147C2×C4⋊C4×C73C2314yes—
148C2×C4⋊C4×C73C2314yes—
149C2×C4⋊C4×C73C2314yes—
150C2×C22⋊C4×C73—21no—
151C2×C22⋊C4×C73—21no—
152C2×C22⋊C4×C73—21no—
153C2×C22⋊C4×C73—21no—
154C2×C22⋊C4×C73—21no—
155C2×C22⋊C4×C73—21no—
156C2×C22⋊C4×C73D411yescharacteristic
157C2×C22⋊C4×C73D411yescharacteristic
158C2×C42×C73—21no—
159C2×C42×C73—21no—
160C2×C42×C73C2311yescharacteristic
161#107×C73C2314yes—
162#107×C73C2314yes—
163#107×C73C2314yes—
164#107×C73C2314yes—
165#107×C73C2314yes—
166#107×C73C2314yes—
167#106×C73C2314yes—
168#106×C73C2314yes—
169#106×C73C2314yes—
170C4⋊C8×C73C2314yes—
171#103×C73C2314yes—
172#103×C73C2314yes—
173#103×C73C2314yes—
174#102×C73C2314yes—
175#102×C73C2314yes—
176#102×C73C2314yes—
177C22⋊C8×C73C2314yes—
178C22⋊C8×C73C2314yes—
179#97×C73C2314yes—
180C24×C73—21no—
181C24×C73C2×D411yescharacteristic
182C24×C73C2×D411yescharacteristic
183#41×C73—432no—
184C2×Q8×C73—21no—
185C2×Q8×C73—24no—
186C2×Q8×C73—22no—
187C2×Q8×C73—22no—
188C2×Q8×C73—44no—
189C2×Q8×C73C2412yes—
190C2×D4×C73—24no—
191C2×D4×C73—24no—
192C2×D4×C73—24no—
193C2×D4×C73—21no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—44no—
197C2×D4×C73—44no—
198C2×D4×C73C2×D414yes—
199C2×D4×C73C2412yes—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—22no—
203C22×C4×C73—22no—
204C22×C4×C73—24no—
205C22×C4×C73—24no—
206C22×C4×C73—24no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—24no—
215C22×C4×C73—44no—
216C22×C4×C73—44no—
217C22×C4×C73—44no—
218C22×C4×C73—44no—
219C22×C4×C73C2×D412yes—
220C22×C4×C73C2×D412yes—
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2412yes—
226C22×C4×C73C2412yes—
227C22×C4×C73C2411yescharacteristic
228SD16×C73—28no—
229M16×C73—28no—
230C2×C8×C73—22no—
231C2×C8×C73—22no—
232C2×C8×C73—22no—
233C2×C8×C73—28no—
234C2×C8×C73#4114yescomplemented
235C2×C8×C73C2412yes—
236C2×C8×C73C2412yes—
237C2×C8×C73C2412yes—
238C2×C8×C73C2412yes—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—24no—
244C4⋊C4×C73—24no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—24no—
247C4⋊C4×C73—24no—
248C4⋊C4×C73—24no—
249C4⋊C4×C73—24no—
250C4⋊C4×C73—24no—
251C4⋊C4×C73—24no—
252C4⋊C4×C73—24no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73C2×D414yes—
255C4⋊C4×C73C2412yes—
256C4⋊C4×C73C2412yes—
257C4⋊C4×C73C2412yes—
258C4⋊C4×C73C2412yes—
259C4⋊C4×C73C2412yes—
260C4⋊C4×C73C2412yes—
261C22⋊C4×C73—24no—
262C22⋊C4×C73—24no—
263C22⋊C4×C73—24no—
264C22⋊C4×C73—24no—
265C22⋊C4×C73—24no—
266C22⋊C4×C73—24no—
267C22⋊C4×C73C2×D414yes—
268C22⋊C4×C73C2×D414yes—
269C42×C73—24no—
270C42×C73—24no—
271C42×C73C2×D412yes—
272C42×C73C2412yes—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—42no—
280C23×C73—42no—
281C23×C73—42no—
282C23×C73AGL(1,ℤ/8)14yes—
283C23×C73C22×D412yes—
284C23×C73C22×D412yes—
285C23×C73C22×D411yescharacteristic
286Q8×C73—22no—
287Q8×C73—22no—
288Q8×C73—48no—
289Q8×C73—42no—
290D4×C73—28no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—48no—
294D4×C73—48no—
295D4×C73—42no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—24no—
301C2×C4×C73—24no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
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—48no—
314C2×C4×C73—48no—
315C2×C4×C73—42no—
316C2×C4×C73—48no—
317C2×C4×C73—42no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—42no—
321C2×C4×C73—42no—
322C2×C4×C73—48no—
323C2×C4×C73—42no—
324C2×C4×C73C22×D412yes—
325C2×C4×C73C22×D412yes—
326C2×C4×C73C22×D412yes—
327C2×C4×C73C22×D412yes—
328C2×C4×C73C22×D411yescharacteristic
329C2×C4×C73C2×#4112yes—
330C2×C4×C732−1+412yes—
331C2×C4×C73C2511yescharacteristic
332C8×C73—22no—
333C8×C73—22no—
334C8×C73—22no—
335C8×C73C2×#4114yescomplemented
336C22×C73—28no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—22no—
340C22×C73—22no—
341C22×C73—22no—
342C22×C73—44no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—84no—
347C22×C73#54712yes—
348C22×C73C2×AGL(1,ℤ/8)14yes—
349C22×C73C2×AGL(1,ℤ/8)12yes—
350C22×C73#57812yes—
351C22×C73C23×D411yescharacteristic
352C4×C73—22no—
353C4×C73—22no—
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—42no—
357C4×C73—42no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73—42no—
362C4×C73—42no—
363C4×C73#54712yes—
364C4×C73C22×#4111yescharacteristic
365C4×C73C2×2−1+411yescharacteristic
366C2×#3343C7311yesmaximal, characteristic, direct product factor, Sylow
367C2×C73—24no—
368C2×C73—42no—
369C2×C73—82no—
370C2×C73#334314yesdirect product factor
371C2×C73C2×#54711yescharacteristic
372C2×C73C22×AGL(1,ℤ/8)11yescharacteristic
373C2×C73C2×#57811yescharacteristic
374C2×#552C2×C7311yescharacteristic, complemented
375C2×#547C2×C7311yescharacteristic
376#3343C2×C73116yesdirect product factor
377C2×#501C2×C7311yescharacteristic, complemented
378C2×#484C2×C7311yescharacteristic, complemented
379C2×#482C2×C7311yescharacteristic, complemented
380C2×#483C2×C7311yescharacteristic, complemented
381C2×#480C2×C7311yescharacteristic, complemented
382C2×#477C2×C7311yescharacteristic, complemented
383C2×#478C2×C7311yescharacteristic, complemented
384C2×#468C2×C7311yescharacteristic, complemented
385C2×#465C2×C7311yescharacteristic, complemented
386C2×#440C2×C7311yescharacteristic, complemented
387C2×#435C2×C7311yescharacteristic, complemented
388C2×#428C2×C7311yescharacteristic, complemented
389C22×#107C2×C7311yescharacteristic, complemented
390C73C2×#334311yescharacteristic, direct product factor, Sylow
391C22×#41—21no—
392C22×SD16C22×C7311yescharacteristic
393C22×M16C22×C7311yescharacteristic
394C23×C8C22×C7311yescharacteristic
395#552—24no—
396#552C22×C7318yescomplemented
397#547—24no—
398#547C22×C7318yes—
399C2×C4⋊Q8C22×C7311yescharacteristic
400C2×#126—21no—
401C2×#125—21no—
402C2×#125C22×C7311yescharacteristic
403C2×#123—21no—
404C2×#123—21no—
405C2×#123—21no—
406C2×C22⋊Q8—21no—
407C2×C22⋊Q8C22×C7311yescharacteristic
408C2×C22⋊Q8C22×C7311yescharacteristic
409C2×#121C22×C7311yescharacteristic
410C2×#121C22×C7311yescharacteristic
411C2×C4×Q8C22×C7311yescharacteristic
412C2×C4×D4C22×C7311yescharacteristic
413C2×C4×D4C22×C7311yescharacteristic
414C2×#117—21no—
415C2×#117C22×C7311yescharacteristic
416C22×C4⋊C4C22×C7311yescharacteristic
417C22×C4⋊C4C22×C7311yescharacteristic
418C22×C4⋊C4C22×C7311yescharacteristic
419#501C22×C7318yescomplemented
420#484C22×C7318yescomplemented
421#483C22×C7318yescomplemented
422#482C22×C7318yescomplemented
423#480C22×C7318yescomplemented
424#478C22×C7318yescomplemented
425#477C22×C7318yescomplemented
426#468C22×C7318yescomplemented
427#465C22×C7318yescomplemented
428#440C22×C7318yescomplemented
429#435C22×C7318yescomplemented
430#428C22×C7318yescomplemented
431C2×#107C22×C7311yescharacteristic
432C2×#107C22×C7311yescharacteristic
433C2×#107C22×C7311yescharacteristic
434C2×#107C22×C7311yescharacteristic
435C2×#107C22×C7311yescharacteristic
436C2×#107C22×C7311yescharacteristic
437C2×#107C22×C7318yescomplemented
438C2×#106C22×C7311yescharacteristic
439C2×#106C22×C7311yescharacteristic
440C2×#106C22×C7311yescharacteristic
441C2×C4⋊C8C22×C7311yescharacteristic
442C2×#103C22×C7311yescharacteristic
443C2×#103C22×C7311yescharacteristic
444C2×#103C22×C7311yescharacteristic
445C2×#102C22×C7311yescharacteristic
446C2×#102C22×C7311yescharacteristic
447C2×#102C22×C7311yescharacteristic
448C2×C22⋊C8C22×C7311yescharacteristic
449C2×C22⋊C8C22×C7311yescharacteristic
450C2×#97C22×C7311yescharacteristic
451C2×#41—28no—
452C2×#41—48no—
453C22×Q8—21no—
454C22×Q8C23×C7311yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4D4×C7311yescharacteristic
458C22×D4C23×C7311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C7311yescharacteristic
464C23×C4C23×C7311yescharacteristic
465C2×SD16—24no—
466C2×SD16C23×C7314yes—
467C2×M16—24no—
468C2×M16C23×C7314yes—
469C22×C8—24no—
470C22×C8C23×C7311yescharacteristic
471C22×C8C23×C7314yes—
472C22×C8C23×C7311yescharacteristic
473C22×C8C23×C7311yescharacteristic
474C22×C8C23×C7311yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8C23×C7314yes—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C23×C7314yes—
481#123—28no—
482#123—28no—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—28no—
487C22⋊Q8C23×C7314yes—
488C22⋊Q8C23×C7314yes—
489#121—22no—
490#121—22no—
491#121C23×C7314yes—
492#121C23×C7314yes—
493C4×Q8—22no—
494C4×Q8C23×C7314yes—
495C4×D4—22no—
496C4×D4D4×C7314yes—
497C4×D4C23×C7314yes—
498C4×D4C23×C7314yes—
499#117—22no—
500#117—28no—
501#117C23×C7314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4D4×C7311yescharacteristic
515C2×C4⋊C4C23×C7311yescharacteristic
516C2×C4⋊C4C23×C7311yescharacteristic
517C2×C4⋊C4C23×C7311yescharacteristic
518C2×C4⋊C4C23×C7311yescharacteristic
519C2×C4⋊C4C23×C7311yescharacteristic
520C2×C4⋊C4C23×C7314yes—
521C2×C4⋊C4C23×C7314yes—
522C2×C4⋊C4C23×C7314yes—
523C2×C4⋊C4C23×C7311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4D4×C7311yescharacteristic
531C2×C22⋊C4D4×C7311yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C23×C7311yescharacteristic
535#107C23×C7314yes—
536#107C23×C7314yes—
537#107C23×C7314yes—
538#107C23×C7314yes—
539#107C23×C7314yes—
540#107C23×C7314yes—
541#106C23×C7314yes—
542#106C23×C7314yes—
543#106C23×C7314yes—
544C4⋊C8C23×C7314yes—
545#103C23×C7314yes—
546#103C23×C7314yes—
547#103C23×C7314yes—
548#102C23×C7314yes—
549#102C23×C7314yes—
550#102C23×C7314yes—
551C22⋊C8C23×C7314yes—
552C22⋊C8C23×C7314yes—
553#97C23×C7314yes—
554C24—21no—
555C24C2×D4×C7311yescharacteristic
556C24C2×D4×C7311yescharacteristic
557#41—432no—
558C2×Q8—21no—
559C2×Q8—24no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—44no—
563C2×Q8C24×C7312yes—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4C2×D4×C7314yes—
573C2×D4C24×C7312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7312yes—
598C22×C4C2×D4×C7312yes—
599C22×C4C24×C7312yes—
600C22×C4C24×C7312yes—
601C22×C4C24×C7311yescharacteristic
602SD16—28no—
603M16—28no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—28no—
608C2×C8#41×C7314yescomplemented
609C2×C8C24×C7312yes—
610C2×C8C24×C7312yes—
611C2×C8C24×C7312yes—
612C2×C8C24×C7312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4C2×D4×C7314yes—
629C4⋊C4C24×C7312yes—
630C4⋊C4C24×C7312yes—
631C4⋊C4C24×C7312yes—
632C4⋊C4C24×C7312yes—
633C4⋊C4C24×C7312yes—
634C4⋊C4C24×C7312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4C2×D4×C7314yes—
642C22⋊C4C2×D4×C7314yes—
643C42—24no—
644C42—24no—
645C42C2×D4×C7312yes—
646C42C24×C7312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23AGL(1,ℤ/8)×C7314yes—
657C23C22×D4×C7312yes—
658C23C22×D4×C7312yes—
659C23C22×D4×C7311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—48no—
663Q8—42no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—48no—
694C2×C4—48no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4C22×D4×C7312yes—
699C2×C4C22×D4×C7312yes—
700C2×C4C22×D4×C7312yes—
701C2×C4C22×D4×C7312yes—
702C2×C4C22×D4×C7311yescharacteristic
703C2×C4C2×#41×C7312yes—
704C2×C42−1+4×C7312yes—
705C2×C4C25×C7311yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#41×C7314yescomplemented
710C22—22no—
711C22—22no—
712C22—28no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22#547×C7312yes—
722C22C2×AGL(1,ℤ/8)×C7314yes—
723C22C2×AGL(1,ℤ/8)×C7312yes—
724C22#578×C7312yes—
725C22C23×D4×C7311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4#547×C7312yes—
738C4C22×#41×C7311yescharacteristic
739C4C2×2−1+4×C7311yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2C73×#334314yesdirect product factor
744C2C2×#547×C7311yescharacteristic
745C2C22×AGL(1,ℤ/8)×C7311yescharacteristic
746C2C2×#578×C7311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC2×C4C25×C73
prime radicalC2×#547×C73C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#552×C73C2semidirect
3. C73×#3343C2direct (N × H)
4. C2×#501×C73C2semidirect
5. C2×#484×C73C2semidirect
6. C2×#482×C73C2semidirect
7. C2×#483×C73C2semidirect
8. C2×#480×C73C2semidirect
9. C2×#477×C73C2semidirect
10. C2×#478×C73C2semidirect
11. C2×#468×C73C2semidirect
12. C2×#465×C73C2semidirect
13. C2×#440×C73C2semidirect
14. C2×#435×C73C2semidirect
15. C2×#428×C73C2semidirect
16. C22×#107×C73C2semidirect
22. #552×C73C22semidirect
45. #501×C73C22semidirect
46. #484×C73C22semidirect
47. #483×C73C22semidirect
48. #482×C73C22semidirect
49. #480×C73C22semidirect
50. #478×C73C22semidirect
51. #477×C73C22semidirect
52. #468×C73C22semidirect
53. #465×C73C22semidirect
54. #440×C73C22semidirect
55. #435×C73C22semidirect
56. #428×C73C22semidirect
63. C2×#107×C73C22semidirect
234. C2×C8×C73#41semidirect
335. C8×C73C2×#41semidirect
366. C2×#3343C73direct (N × H)
370. C2×C73#3343direct (N × H)
374. C2×#552C2×C73semidirect
376. #3343C2×C73direct (N × H)
377. C2×#501C2×C73semidirect
378. C2×#484C2×C73semidirect
379. C2×#482C2×C73semidirect
380. C2×#483C2×C73semidirect
381. C2×#480C2×C73semidirect
382. C2×#477C2×C73semidirect
383. C2×#478C2×C73semidirect
384. C2×#468C2×C73semidirect
385. C2×#465C2×C73semidirect
386. C2×#440C2×C73semidirect
387. C2×#435C2×C73semidirect
388. C2×#428C2×C73semidirect
389. C22×#107C2×C73semidirect
390. C73C2×#3343direct (N × H)
396. #552C22×C73semidirect
419. #501C22×C73semidirect
420. #484C22×C73semidirect
421. #483C22×C73semidirect
422. #482C22×C73semidirect
423. #480C22×C73semidirect
424. #478C22×C73semidirect
425. #477C22×C73semidirect
426. #468C22×C73semidirect
427. #465C22×C73semidirect
428. #440C22×C73semidirect
429. #435C22×C73semidirect
430. #428C22×C73semidirect
437. C2×#107C22×C73semidirect
608. C2×C8#41×C73semidirect
709. C8C2×#41×C73semidirect
743. C2C73×#3343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#552×C732
C2×#547×C732
C73×#33432
C2×#501×C732
C2×#484×C732
C2×#482×C732
C2×#483×C732
C2×#480×C732
C2×#477×C732
C2×#478×C732
C2×#468×C732
C2×#465×C732
C2×#440×C732
C2×#435×C732
C2×#428×C732
C22×#107×C732
C2×#334373