Finite Group Databasebeta

← C2×C73×#3350 #32970646

Subgroups — C2×C73×#3350 #32970646

Order 18688.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C73C211yesmaximal, characteristic, complemented
2C2×#553×C73C211yesmaximal, characteristic
3C73×#3350C2116yesmaximal, direct product factor
4C2×#501×C73C211yesmaximal, characteristic, complemented
5C2×#485×C73C211yesmaximal, characteristic, complemented
6C2×#482×C73C211yesmaximal, characteristic, complemented
7C2×#482×C73C211yesmaximal, characteristic, complemented
8C2×#483×C73C211yesmaximal, characteristic, complemented
9C2×#479×C73C211yesmaximal, characteristic, complemented
10C2×#476×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
16C2×#427×C73C211yesmaximal, characteristic, complemented
17C22×SD16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20#556×C73—24no—
21#556×C73C2218yescomplemented
22#553×C73—24no—
23#553×C73C2218yes—
24C2×C4⋊Q8×C73C2211yescharacteristic
25C2×#126×C73—21no—
26C2×#126×C73—21no—
27C2×#126×C73—21no—
28C2×#125×C73C2211yescharacteristic
29C2×#124×C73—21no—
30C2×#123×C73—21no—
31C2×C22⋊Q8×C73C2211yescharacteristic
32C2×C22⋊Q8×C73C2211yescharacteristic
33C2×#121×C73—21no—
34C2×#121×C73C2211yescharacteristic
35C2×#121×C73C2211yescharacteristic
36C2×C4×Q8×C73—21no—
37C2×C4×Q8×C73C2211yescharacteristic
38C2×C4×D4×C73—21no—
39C2×C4×D4×C73C2211yescharacteristic
40C2×C4×D4×C73C2211yescharacteristic
41C2×#117×C73C2211yescharacteristic
42C2×#117×C73C2211yescharacteristic
43C2×#117×C73C2211yescharacteristic
44C22×C4⋊C4×C73C2211yescharacteristic
45#501×C73C2218yescomplemented
46#485×C73C2218yescomplemented
47#483×C73C2218yescomplemented
48#482×C73C2218yescomplemented
49#482×C73C2218yescomplemented
50#479×C73C2218yescomplemented
51#476×C73C2218yescomplemented
52#468×C73C2218yescomplemented
53#465×C73C2218yescomplemented
54#440×C73C2218yescomplemented
55#435×C73C2218yescomplemented
56#428×C73C2218yescomplemented
57#427×C73C2218yescomplemented
58C2×#107×C73C2211yescharacteristic
59C2×#107×C73C2211yescharacteristic
60C2×#107×C73C2211yescharacteristic
61C2×#107×C73C2211yescharacteristic
62C2×#106×C73C2211yescharacteristic
63C2×#106×C73C2211yescharacteristic
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
77C22×Q8×C73—21no—
78C22×Q8×C73C2311yescharacteristic
79C22×D4×C73—21no—
80C22×D4×C73—21no—
81C22×D4×C73D411yescharacteristic
82C22×D4×C73C2311yescharacteristic
83C23×C4×C73—21no—
84C23×C4×C73—21no—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C2×SD16×C73—24no—
88C2×SD16×C73C2314yes—
89C2×M16×C73—24no—
90C2×M16×C73C2314yes—
91C22×C8×C73—24no—
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2314yes—
96C22×C8×C73C2311yescharacteristic
97C4⋊Q8×C73—22no—
98C4⋊Q8×C73C2314yes—
99#126×C73—28no—
100#126×C73—28no—
101#126×C73—28no—
102#125×C73—22no—
103#125×C73C2314yes—
104#124×C73—28no—
105#123×C73—28no—
106C22⋊Q8×C73—22no—
107C22⋊Q8×C73—22no—
108C22⋊Q8×C73C2314yes—
109C22⋊Q8×C73C2314yes—
110#121×C73—28no—
111#121×C73—22no—
112#121×C73—22no—
113#121×C73C2314yes—
114#121×C73C2314yes—
115C4×Q8×C73—28no—
116C4×Q8×C73—22no—
117C4×Q8×C73C2314yes—
118C4×D4×C73—28no—
119C4×D4×C73—22no—
120C4×D4×C73D414yes—
121C4×D4×C73C2314yes—
122C4×D4×C73C2314yes—
123#117×C73—22no—
124#117×C73—22no—
125#117×C73—22no—
126#117×C73C2314yes—
127#117×C73C2314yes—
128#117×C73C2314yes—
129C2×C4⋊C4×C73—21no—
130C2×C4⋊C4×C73—22no—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—21no—
135C2×C4⋊C4×C73—21no—
136C2×C4⋊C4×C73—21no—
137C2×C4⋊C4×C73D411yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C4⋊C4×C73C2311yescharacteristic
142C2×C4⋊C4×C73C2311yescharacteristic
143C2×C4⋊C4×C73C2311yescharacteristic
144C2×C4⋊C4×C73C2314yes—
145C2×C22⋊C4×C73—21no—
146C2×C22⋊C4×C73—21no—
147C2×C22⋊C4×C73—21no—
148C2×C22⋊C4×C73—21no—
149C2×C22⋊C4×C73—21no—
150C2×C22⋊C4×C73—21no—
151C2×C22⋊C4×C73—21no—
152C2×C22⋊C4×C73—21no—
153C2×C22⋊C4×C73D411yescharacteristic
154C2×C22⋊C4×C73D411yescharacteristic
155C2×C42×C73—21no—
156C2×C42×C73—21no—
157C2×C42×C73—21no—
158C2×C42×C73—21no—
159C2×C42×C73C2311yescharacteristic
160#107×C73C2314yes—
161#107×C73C2314yes—
162#107×C73C2314yes—
163#107×C73C2314yes—
164#106×C73C2314yes—
165#106×C73C2314yes—
166#106×C73C2314yes—
167#106×C73C2314yes—
168#106×C73C2314yes—
169C4⋊C8×C73C2314yes—
170#103×C73C2314yes—
171#103×C73C2314yes—
172#103×C73C2314yes—
173#102×C73C2314yes—
174#102×C73C2314yes—
175#102×C73C2314yes—
176C22⋊C8×C73C2314yes—
177C22⋊C8×C73C2314yes—
178#97×C73C2314yes—
179C24×C73—21no—
180C24×C73C2×D411yescharacteristic
181C24×C73C2×D411yescharacteristic
182C2×Q8×C73—21no—
183C2×Q8×C73—24no—
184C2×Q8×C73—22no—
185C2×Q8×C73—22no—
186C2×Q8×C73—44no—
187C2×Q8×C73C2412yes—
188C2×D4×C73—24no—
189C2×D4×C73—24no—
190C2×D4×C73—21no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—42no—
194C2×D4×C73—44no—
195C2×D4×C73—82no—
196C2×D4×C73C2×D414yes—
197C2×D4×C73C2412yes—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—24no—
210C22×C4×C73—24no—
211C22×C4×C73—82no—
212C22×C4×C73—82no—
213C22×C4×C73C2×D412yes—
214C22×C4×C73C2×D412yes—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2412yes—
220C22×C4×C73C2412yes—
221C22×C4×C73C2411yescharacteristic
222SD16×C73—28no—
223M16×C73—28no—
224C2×C8×C73—22no—
225C2×C8×C73—22no—
226C2×C8×C73—22no—
227C2×C8×C73—28no—
228C2×C8×C73#4114yes—
229C2×C8×C73C2412yes—
230C2×C8×C73C2412yes—
231C2×C8×C73C2412yes—
232C2×C8×C73C2412yes—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—24no—
236C4⋊C4×C73—24no—
237C4⋊C4×C73—24no—
238C4⋊C4×C73—24no—
239C4⋊C4×C73—24no—
240C4⋊C4×C73—24no—
241C4⋊C4×C73—24no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73C2×D414yes—
247C4⋊C4×C73C2412yes—
248C4⋊C4×C73C2412yes—
249C4⋊C4×C73C2412yes—
250C4⋊C4×C73C2412yes—
251C4⋊C4×C73C2412yes—
252C4⋊C4×C73C2412yes—
253C22⋊C4×C73—24no—
254C22⋊C4×C73—24no—
255C22⋊C4×C73—24no—
256C22⋊C4×C73—24no—
257C22⋊C4×C73—24no—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—24no—
260C22⋊C4×C73—24no—
261C22⋊C4×C73C2×D414yes—
262C22⋊C4×C73C2×D414yes—
263C42×C73—24no—
264C42×C73—24no—
265C42×C73—24no—
266C42×C73—24no—
267C42×C73C2×D412yes—
268C42×C73C2412yes—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—42no—
277C23×C73—42no—
278C23×C73—42no—
279C23×C73C22×D412yes—
280C23×C73C22×D412yes—
281C23×C73C22×D411yescharacteristic
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—48no—
285Q8×C73—42no—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—44no—
289D4×C73—48no—
290D4×C73—42no—
291D4×C73—84no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—24no—
297C2×C4×C73—24no—
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—22no—
308C2×C4×C73—22no—
309C2×C4×C73—42no—
310C2×C4×C73—42no—
311C2×C4×C73—42no—
312C2×C4×C73—42no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—84no—
317C2×C4×C73—84no—
318C2×C4×C73C22×D412yes—
319C2×C4×C73C22×D412yes—
320C2×C4×C73C22×D412yes—
321C2×C4×C73C22×D412yes—
322C2×C4×C73C22×D411yescharacteristic
323C2×C4×C73C2×#4112yes—
324C2×C4×C732−1+412yes—
325C2×C4×C73C2511yescharacteristic
326C8×C73—22no—
327C8×C73—22no—
328C8×C73—22no—
329C8×C73C2×#4114yes—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—44no—
337C22×C73—44no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—84no—
342C22×C73#54712yes—
343C22×C73#57512yes—
344C22×C73#57712yes—
345C22×C73C23×D411yescharacteristic
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—22no—
349C4×C73—22no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73—42no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73#54712yes—
358C4×C73C22×#4111yescharacteristic
359C4×C73C2×2−1+411yescharacteristic
360C2×#3350C7311yesmaximal, characteristic, direct product factor, Sylow
361C2×C73—42no—
362C2×C73—42no—
363C2×C73—82no—
364C2×C73#335014yesdirect product factor
365C2×C73C2×#54711yescharacteristic
366C2×C73C2×#57511yescharacteristic
367C2×C73C2×#57711yescharacteristic
368C2×#556C2×C7311yescharacteristic, complemented
369C2×#553C2×C7311yescharacteristic
370#3350C2×C73116yesdirect product factor
371C2×#501C2×C7311yescharacteristic, complemented
372C2×#485C2×C7311yescharacteristic, complemented
373C2×#482C2×C7311yescharacteristic, complemented
374C2×#482C2×C7311yescharacteristic, complemented
375C2×#483C2×C7311yescharacteristic, complemented
376C2×#479C2×C7311yescharacteristic, complemented
377C2×#476C2×C7311yescharacteristic, complemented
378C2×#468C2×C7311yescharacteristic, complemented
379C2×#465C2×C7311yescharacteristic, complemented
380C2×#440C2×C7311yescharacteristic, complemented
381C2×#435C2×C7311yescharacteristic, complemented
382C2×#428C2×C7311yescharacteristic, complemented
383C2×#427C2×C7311yescharacteristic, complemented
384C73C2×#335011yescharacteristic, direct product factor, Sylow
385C22×SD16C22×C7311yescharacteristic
386C22×M16C22×C7311yescharacteristic
387C23×C8C22×C7311yescharacteristic
388#556—24no—
389#556C22×C7318yescomplemented
390#553—24no—
391#553C22×C7318yes—
392C2×C4⋊Q8C22×C7311yescharacteristic
393C2×#126—21no—
394C2×#126—21no—
395C2×#126—21no—
396C2×#125C22×C7311yescharacteristic
397C2×#124—21no—
398C2×#123—21no—
399C2×C22⋊Q8C22×C7311yescharacteristic
400C2×C22⋊Q8C22×C7311yescharacteristic
401C2×#121—21no—
402C2×#121C22×C7311yescharacteristic
403C2×#121C22×C7311yescharacteristic
404C2×C4×Q8—21no—
405C2×C4×Q8C22×C7311yescharacteristic
406C2×C4×D4—21no—
407C2×C4×D4C22×C7311yescharacteristic
408C2×C4×D4C22×C7311yescharacteristic
409C2×#117C22×C7311yescharacteristic
410C2×#117C22×C7311yescharacteristic
411C2×#117C22×C7311yescharacteristic
412C22×C4⋊C4C22×C7311yescharacteristic
413#501C22×C7318yescomplemented
414#485C22×C7318yescomplemented
415#483C22×C7318yescomplemented
416#482C22×C7318yescomplemented
417#482C22×C7318yescomplemented
418#479C22×C7318yescomplemented
419#476C22×C7318yescomplemented
420#468C22×C7318yescomplemented
421#465C22×C7318yescomplemented
422#440C22×C7318yescomplemented
423#435C22×C7318yescomplemented
424#428C22×C7318yescomplemented
425#427C22×C7318yescomplemented
426C2×#107C22×C7311yescharacteristic
427C2×#107C22×C7311yescharacteristic
428C2×#107C22×C7311yescharacteristic
429C2×#107C22×C7311yescharacteristic
430C2×#106C22×C7311yescharacteristic
431C2×#106C22×C7311yescharacteristic
432C2×#106C22×C7311yescharacteristic
433C2×#106C22×C7311yescharacteristic
434C2×#106C22×C7311yescharacteristic
435C2×C4⋊C8C22×C7311yescharacteristic
436C2×#103C22×C7311yescharacteristic
437C2×#103C22×C7311yescharacteristic
438C2×#103C22×C7311yescharacteristic
439C2×#102C22×C7311yescharacteristic
440C2×#102C22×C7311yescharacteristic
441C2×#102C22×C7311yescharacteristic
442C2×C22⋊C8C22×C7311yescharacteristic
443C2×C22⋊C8C22×C7311yescharacteristic
444C2×#97C22×C7311yescharacteristic
445C22×Q8—21no—
446C22×Q8C23×C7311yescharacteristic
447C22×D4—21no—
448C22×D4—21no—
449C22×D4D4×C7311yescharacteristic
450C22×D4C23×C7311yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4C23×C7311yescharacteristic
454C23×C4C23×C7311yescharacteristic
455C2×SD16—24no—
456C2×SD16C23×C7314yes—
457C2×M16—24no—
458C2×M16C23×C7314yes—
459C22×C8—24no—
460C22×C8C23×C7311yescharacteristic
461C22×C8C23×C7314yes—
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464C22×C8C23×C7311yescharacteristic
465C4⋊Q8—22no—
466C4⋊Q8C23×C7314yes—
467#126—28no—
468#126—28no—
469#126—28no—
470#125—22no—
471#125C23×C7314yes—
472#124—28no—
473#123—28no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8C23×C7314yes—
477C22⋊Q8C23×C7314yes—
478#121—28no—
479#121—22no—
480#121—22no—
481#121C23×C7314yes—
482#121C23×C7314yes—
483C4×Q8—28no—
484C4×Q8—22no—
485C4×Q8C23×C7314yes—
486C4×D4—28no—
487C4×D4—22no—
488C4×D4D4×C7314yes—
489C4×D4C23×C7314yes—
490C4×D4C23×C7314yes—
491#117—22no—
492#117—22no—
493#117—22no—
494#117C23×C7314yes—
495#117C23×C7314yes—
496#117C23×C7314yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4D4×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
507C2×C4⋊C4C23×C7311yescharacteristic
508C2×C4⋊C4C23×C7314yes—
509C2×C4⋊C4C23×C7311yescharacteristic
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C4⋊C4C23×C7311yescharacteristic
512C2×C4⋊C4C23×C7311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4D4×C7311yescharacteristic
522C2×C22⋊C4D4×C7311yescharacteristic
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42C23×C7311yescharacteristic
528#107C23×C7314yes—
529#107C23×C7314yes—
530#107C23×C7314yes—
531#107C23×C7314yes—
532#106C23×C7314yes—
533#106C23×C7314yes—
534#106C23×C7314yes—
535#106C23×C7314yes—
536#106C23×C7314yes—
537C4⋊C8C23×C7314yes—
538#103C23×C7314yes—
539#103C23×C7314yes—
540#103C23×C7314yes—
541#102C23×C7314yes—
542#102C23×C7314yes—
543#102C23×C7314yes—
544C22⋊C8C23×C7314yes—
545C22⋊C8C23×C7314yes—
546#97C23×C7314yes—
547C24—21no—
548C24C2×D4×C7311yescharacteristic
549C24C2×D4×C7311yescharacteristic
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8C24×C7312yes—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—42no—
562C2×D4—44no—
563C2×D4—82no—
564C2×D4C2×D4×C7314yes—
565C2×D4C24×C7312yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4C2×D4×C7311yescharacteristic
582C22×C4C2×D4×C7311yescharacteristic
583C22×C4C2×D4×C7311yescharacteristic
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7312yes—
586C22×C4C2×D4×C7312yes—
587C22×C4C24×C7312yes—
588C22×C4C24×C7312yes—
589C22×C4C24×C7311yescharacteristic
590SD16—28no—
591M16—28no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—28no—
596C2×C8#41×C7314yes—
597C2×C8C24×C7312yes—
598C2×C8C24×C7312yes—
599C2×C8C24×C7312yes—
600C2×C8C24×C7312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4C2×D4×C7314yes—
615C4⋊C4C24×C7312yes—
616C4⋊C4C24×C7312yes—
617C4⋊C4C24×C7312yes—
618C4⋊C4C24×C7312yes—
619C4⋊C4C24×C7312yes—
620C4⋊C4C24×C7312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4C2×D4×C7314yes—
630C22⋊C4C2×D4×C7314yes—
631C42—24no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42C2×D4×C7312yes—
636C42C24×C7312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×D4×C7312yes—
648C23C22×D4×C7312yes—
649C23C22×D4×C7311yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—48no—
653Q8—42no—
654D4—22no—
655D4—22no—
656D4—44no—
657D4—48no—
658D4—42no—
659D4—84no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4C22×D4×C7312yes—
687C2×C4C22×D4×C7312yes—
688C2×C4C22×D4×C7312yes—
689C2×C4C22×D4×C7312yes—
690C2×C4C22×D4×C7311yescharacteristic
691C2×C4C2×#41×C7312yes—
692C2×C42−1+4×C7312yes—
693C2×C4C25×C7311yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#41×C7314yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#547×C7312yes—
711C22#575×C7312yes—
712C22#577×C7312yes—
713C22C23×D4×C7311yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4#547×C7312yes—
726C4C22×#41×C7311yescharacteristic
727C4C2×2−1+4×C7311yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2C73×#335014yesdirect product factor
732C2C2×#547×C7311yescharacteristic
733C2C2×#575×C7311yescharacteristic
734C2C2×#577×C7311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC2×C4C25×C73
prime radicalC2×#553×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×#556×C73C2semidirect
3. C73×#3350C2direct (N × H)
4. C2×#501×C73C2semidirect
5. C2×#485×C73C2semidirect
6. C2×#482×C73C2semidirect
7. C2×#482×C73C2semidirect
8. C2×#483×C73C2semidirect
9. C2×#479×C73C2semidirect
10. C2×#476×C73C2semidirect
11. C2×#468×C73C2semidirect
12. C2×#465×C73C2semidirect
13. C2×#440×C73C2semidirect
14. C2×#435×C73C2semidirect
15. C2×#428×C73C2semidirect
16. C2×#427×C73C2semidirect
21. #556×C73C22semidirect
45. #501×C73C22semidirect
46. #485×C73C22semidirect
47. #483×C73C22semidirect
48. #482×C73C22semidirect
49. #482×C73C22semidirect
50. #479×C73C22semidirect
51. #476×C73C22semidirect
52. #468×C73C22semidirect
53. #465×C73C22semidirect
54. #440×C73C22semidirect
55. #435×C73C22semidirect
56. #428×C73C22semidirect
57. #427×C73C22semidirect
360. C2×#3350C73direct (N × H)
364. C2×C73#3350direct (N × H)
368. C2×#556C2×C73semidirect
370. #3350C2×C73direct (N × H)
371. C2×#501C2×C73semidirect
372. C2×#485C2×C73semidirect
373. C2×#482C2×C73semidirect
374. C2×#482C2×C73semidirect
375. C2×#483C2×C73semidirect
376. C2×#479C2×C73semidirect
377. C2×#476C2×C73semidirect
378. C2×#468C2×C73semidirect
379. C2×#465C2×C73semidirect
380. C2×#440C2×C73semidirect
381. C2×#435C2×C73semidirect
382. C2×#428C2×C73semidirect
383. C2×#427C2×C73semidirect
384. C73C2×#3350direct (N × H)
389. #556C22×C73semidirect
413. #501C22×C73semidirect
414. #485C22×C73semidirect
415. #483C22×C73semidirect
416. #482C22×C73semidirect
417. #482C22×C73semidirect
418. #479C22×C73semidirect
419. #476C22×C73semidirect
420. #468C22×C73semidirect
421. #465C22×C73semidirect
422. #440C22×C73semidirect
423. #435C22×C73semidirect
424. #428C22×C73semidirect
425. #427C22×C73semidirect
731. C2C73×#3350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C732
C2×#553×C732
C73×#33502
C2×#501×C732
C2×#485×C732
C2×#482×C732
C2×#483×C732
C2×#479×C732
C2×#476×C732
C2×#468×C732
C2×#465×C732
C2×#440×C732
C2×#435×C732
C2×#428×C732
C2×#427×C732
C2×#335073