Finite Group Databasebeta

← C73×#22660 #32932064

Subgroups — C73×#22660 #32932064

Order 18688.

970 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C73C211yesmaximal, characteristic
2C2×#428×C73C211yesmaximal, characteristic, complemented
3C2×#427×C73C211yesmaximal, characteristic, complemented
4C73×#2354C211yesmaximal, characteristic
5C73×#2352C211yesmaximal, characteristic
6C73×#1949C211yesmaximal, characteristic, complemented
7C73×#1947C211yesmaximal, characteristic, complemented
8C73×#1854C211yesmaximal, characteristic, complemented
9C73×#1854C211yesmaximal, characteristic, complemented
10C73×#1854C211yesmaximal, characteristic, complemented
11C73×#1852C211yesmaximal, characteristic, complemented
12C73×#1847C211yesmaximal, characteristic, complemented
13C73×#1809C211yesmaximal, characteristic, complemented
14C73×#1808C211yesmaximal, characteristic, complemented
15C73×#1776C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C4×D4×C73C2211yescharacteristic
19C2×#117×C73C2211yescharacteristic
20C2×#117×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#435×C73C418yescomplemented
24#428×C73—24no—
25#427×C73—24no—
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#107×C73C2211yescharacteristic
31C2×#107×C73C2211yescharacteristic
32C2×#106×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×#106×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40#390×C73—21no—
41#388×C73—21no—
42#388×C73—21no—
43#388×C73—21no—
44#387×C73—21no—
45#386×C73—21no—
46#384×C73C2211yescharacteristic
47#382×C73C2211yescharacteristic
48#380×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52C4×C4⋊C4×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55C4×C22⋊C4×C73—21no—
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62C22×D4×C73D411yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66C2×M16×C73—22no—
67C2×M16×C73—22no—
68C2×M16×C73C2×C414yes—
69C22×C8×C73—22no—
70C22×C8×C73—22no—
71C22×C8×C73C2×C414yescomplemented
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C4×D4×C73C2×C414yes—
77C4×D4×C73Q814yes—
78#117×C73—22no—
79#117×C73—22no—
80#117×C73—22no—
81#117×C73—41no—
82#117×C73—41no—
83#117×C73—41no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—41no—
89C2×C4⋊C4×C73D411yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73C2311yescharacteristic
113#107×C73—22no—
114#107×C73—22no—
115#107×C73—22no—
116#107×C73—22no—
117#107×C73—22no—
118#107×C73—41no—
119#106×C73—22no—
120#106×C73—22no—
121#106×C73—41no—
122#106×C73D414yescomplemented
123C4⋊C8×C73C2×C414yescomplemented
124C22⋊C8×C73C2×C414yes—
125C22⋊C8×C73C2×C414yescomplemented
126#97×C73C2×C414yescomplemented
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135C24×C73C2×D411yescharacteristic
136C24×C73C2×D411yescharacteristic
137C2×D4×C73—41no—
138C2×D4×C73—41no—
139C2×D4×C73C4⋊C414yes—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—42no—
157C22×C4×C73—42no—
158C22×C4×C73—81no—
159C22×C4×C73C22×C412yes—
160C22×C4×C73C22×C412yes—
161C22×C4×C73C2×D411yescharacteristic
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×Q812yes—
166C22×C4×C73C2×Q812yes—
167C22×C4×C73C2411yescharacteristic
168M16×C73—28no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—28no—
176C2×C8×C73C22×C412yes—
177C2×C8×C73C22×C412yes—
178C2×C8×C73C22×C412yes—
179C2×C8×C73C22×C412yes—
180C2×C8×C73C2×D412yes—
181C2×C8×C73#4112yes—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73C4⋊C414yes—
200C4⋊C4×C73C2×D412yes—
201C4⋊C4×C73C2×D412yes—
202C22⋊C4×C73—42no—
203C22⋊C4×C73—42no—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—81no—
207C22⋊C4×C73—81no—
208C22⋊C4×C73—81no—
209C22⋊C4×C73C4⋊C414yes—
210C22⋊C4×C73C4⋊C414yes—
211C42×C73—42no—
212C42×C73—42no—
213C42×C73—42no—
214C42×C73—42no—
215C42×C73—81no—
216C42×C73C22×C412yes—
217C42×C73C2×Q812yes—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73C2×C4⋊C412yes—
231C23×C73C2×C4⋊C412yes—
232C23×C73C22×D411yescharacteristic
233D4×C73—44no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—84no—
275C2×C4×C73C2×C4⋊C412yes—
276C2×C4×C73C2×C4⋊C412yes—
277C2×C4×C73C2×C4⋊C412yes—
278C2×C4×C73C2×C4⋊C412yes—
279C2×C4×C73C23×C411yescharacteristic
280C2×C4×C73C22×D411yescharacteristic
281C2×C4×C73C22×Q811yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73H(5,𝔽2)11yescharacteristic
284C2×C4×C732−1+411yescharacteristic
285C8×C73—22no—
286C8×C73—22no—
287C8×C73—22no—
288C8×C73C4×D414yes—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—22no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73C22×C4⋊C411yescharacteristic
304C22×C73D4211yescharacteristic
305C22×C73#54711yescharacteristic
306C22×C73#57511yescharacteristic
307C22×C73#57511yescharacteristic
308C22×C73#57611yescharacteristic
309C22×C73#57811yescharacteristic
310C4×C73—22no—
311C4×C73—22no—
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—42no—
315C4×C73—42no—
316C4×C73—81no—
317C4×C73—81no—
318C4×C73—81no—
319C4×C73—81no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73C2×C4×D411yescharacteristic
323C4×C73#52011yescharacteristic
324C4×C73D4×Q811yescharacteristic
325C4×C73#55411yescharacteristic
326#22660C7311yesmaximal, characteristic, direct product factor, Sylow
327C2×C73—42no—
328C2×C73—42no—
329C2×C73D4×C4⋊C411yescharacteristic
330C2×C73#291111yescharacteristic
331C2×C73#291311yescharacteristic
332C2×C73#326811yescharacteristic
333C2×C73#326911yescharacteristic
334C2×C73#334711yescharacteristic
335C2×C73#334911yescharacteristic
336C2×#435C2×C7311yescharacteristic
337C2×#428C2×C7311yescharacteristic, complemented
338C2×#427C2×C7311yescharacteristic, complemented
339#2354C2×C7311yescharacteristic
340#2352C2×C7311yescharacteristic
341#1949C2×C7311yescharacteristic, complemented
342#1947C2×C7311yescharacteristic, complemented
343#1854C2×C7311yescharacteristic, complemented
344#1854C2×C7311yescharacteristic, complemented
345#1854C2×C7311yescharacteristic, complemented
346#1852C2×C7311yescharacteristic, complemented
347#1847C2×C7311yescharacteristic, complemented
348#1809C2×C7311yescharacteristic, complemented
349#1808C2×C7311yescharacteristic, complemented
350#1776C2×C7311yescharacteristic, complemented
351C73#2266011yescharacteristic, direct product factor, Sylow
352C22×M16C22×C7311yescharacteristic
353C23×C8C22×C7311yescharacteristic
354C2×C4×D4C22×C7311yescharacteristic
355C2×#117C22×C7311yescharacteristic
356C2×#117C22×C7311yescharacteristic
357C2×#117C22×C7311yescharacteristic
358C22×C4⋊C4C22×C7311yescharacteristic
359#435C4×C7318yescomplemented
360#428—24no—
361#427—24no—
362C2×#107C22×C7311yescharacteristic
363C2×#107C22×C7311yescharacteristic
364C2×#107C22×C7311yescharacteristic
365C2×#107C22×C7311yescharacteristic
366C2×#107C22×C7311yescharacteristic
367C2×#107C22×C7311yescharacteristic
368C2×#106C22×C7311yescharacteristic
369C2×#106C22×C7311yescharacteristic
370C2×#106C22×C7311yescharacteristic
371C2×#106C22×C7311yescharacteristic
372C2×C4⋊C8C22×C7311yescharacteristic
373C2×C22⋊C8C22×C7311yescharacteristic
374C2×C22⋊C8C22×C7311yescharacteristic
375C2×#97C22×C7311yescharacteristic
376#390—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#387—21no—
381#386—21no—
382#384C22×C7311yescharacteristic
383#382C22×C7311yescharacteristic
384#380C22×C7311yescharacteristic
385#380C22×C7311yescharacteristic
386#380C22×C7311yescharacteristic
387#380C22×C7311yescharacteristic
388C4×C4⋊C4—21no—
389C4×C4⋊C4C22×C7311yescharacteristic
390C4×C4⋊C4C22×C7311yescharacteristic
391C4×C22⋊C4—21no—
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398C22×D4D4×C7311yescharacteristic
399C23×C4—21no—
400C23×C4C23×C7311yescharacteristic
401C23×C4C23×C7311yescharacteristic
402C2×M16—22no—
403C2×M16—22no—
404C2×M16C2×C4×C7314yes—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8C2×C4×C7314yescomplemented
408C22×C8C23×C7311yescharacteristic
409C22×C8C23×C7311yescharacteristic
410C22×C8C23×C7311yescharacteristic
411C22×C8C23×C7311yescharacteristic
412C4×D4C2×C4×C7314yes—
413C4×D4Q8×C7314yes—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—41no—
418#117—41no—
419#117—41no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4D4×C7311yescharacteristic
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C4⋊C4C23×C7311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4D4×C7311yescharacteristic
442C2×C22⋊C4D4×C7311yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C7311yescharacteristic
449#107—22no—
450#107—22no—
451#107—22no—
452#107—22no—
453#107—22no—
454#107—41no—
455#106—22no—
456#106—22no—
457#106—41no—
458#106D4×C7314yescomplemented
459C4⋊C8C2×C4×C7314yescomplemented
460C22⋊C8C2×C4×C7314yes—
461C22⋊C8C2×C4×C7314yescomplemented
462#97C2×C4×C7314yescomplemented
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471C24C2×D4×C7311yescharacteristic
472C24C2×D4×C7311yescharacteristic
473C2×D4—41no—
474C2×D4—41no—
475C2×D4C4⋊C4×C7314yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4C22×C4×C7312yes—
496C22×C4C22×C4×C7312yes—
497C22×C4C2×D4×C7311yescharacteristic
498C22×C4C2×D4×C7311yescharacteristic
499C22×C4C2×D4×C7311yescharacteristic
500C22×C4C2×D4×C7311yescharacteristic
501C22×C4C2×Q8×C7312yes—
502C22×C4C2×Q8×C7312yes—
503C22×C4C24×C7311yescharacteristic
504M16—28no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—28no—
512C2×C8C22×C4×C7312yes—
513C2×C8C22×C4×C7312yes—
514C2×C8C22×C4×C7312yes—
515C2×C8C22×C4×C7312yes—
516C2×C8C2×D4×C7312yes—
517C2×C8#41×C7312yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4C4⋊C4×C7314yes—
536C4⋊C4C2×D4×C7312yes—
537C4⋊C4C2×D4×C7312yes—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4C4⋊C4×C7314yes—
546C22⋊C4C4⋊C4×C7314yes—
547C42—42no—
548C42—42no—
549C42—42no—
550C42—42no—
551C42—81no—
552C42C22×C4×C7312yes—
553C42C2×Q8×C7312yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23C2×C4⋊C4×C7312yes—
567C23C2×C4⋊C4×C7312yes—
568C23C22×D4×C7311yescharacteristic
569D4—44no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—84no—
611C2×C4C2×C4⋊C4×C7312yes—
612C2×C4C2×C4⋊C4×C7312yes—
613C2×C4C2×C4⋊C4×C7312yes—
614C2×C4C2×C4⋊C4×C7312yes—
615C2×C4C23×C4×C7311yescharacteristic
616C2×C4C22×D4×C7311yescharacteristic
617C2×C4C22×Q8×C7311yescharacteristic
618C2×C4C2×#41×C7311yescharacteristic
619C2×C4H(5,𝔽2)×C7311yescharacteristic
620C2×C42−1+4×C7311yescharacteristic
621C8—22no—
622C8—22no—
623C8—22no—
624C8C4×D4×C7314yes—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C22×C4⋊C4×C7311yescharacteristic
640C22D42×C7311yescharacteristic
641C22#547×C7311yescharacteristic
642C22#575×C7311yescharacteristic
643C22#575×C7311yescharacteristic
644C22#576×C7311yescharacteristic
645C22#578×C7311yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—42no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C2×C4×D4×C7311yescharacteristic
659C4#520×C7311yescharacteristic
660C4D4×Q8×C7311yescharacteristic
661C4#554×C7311yescharacteristic
662C2—42no—
663C2—42no—
664C2D4×C4⋊C4×C7311yescharacteristic
665C2C73×#291111yescharacteristic
666C2C73×#291311yescharacteristic
667C2C73×#326811yescharacteristic
668C2C73×#326911yescharacteristic
669C2C73×#334711yescharacteristic
670C2C73×#334911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73D4
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
2. C2×#428×C73C2semidirect
3. C2×#427×C73C2semidirect
6. C73×#1949C2semidirect
7. C73×#1947C2semidirect
8. C73×#1854C2semidirect
9. C73×#1854C2semidirect
10. C73×#1854C2semidirect
11. C73×#1852C2semidirect
12. C73×#1847C2semidirect
13. C73×#1809C2semidirect
14. C73×#1808C2semidirect
15. C73×#1776C2semidirect
23. #435×C73C4semidirect
71. C22×C8×C73C2×C4semidirect
122. #106×C73D4semidirect
123. C4⋊C8×C73C2×C4semidirect
125. C22⋊C8×C73C2×C4semidirect
126. #97×C73C2×C4semidirect
326. #22660C73direct (N × H)
337. C2×#428C2×C73semidirect
338. C2×#427C2×C73semidirect
341. #1949C2×C73semidirect
342. #1947C2×C73semidirect
343. #1854C2×C73semidirect
344. #1854C2×C73semidirect
345. #1854C2×C73semidirect
346. #1852C2×C73semidirect
347. #1847C2×C73semidirect
348. #1809C2×C73semidirect
349. #1808C2×C73semidirect
350. #1776C2×C73semidirect
351. C73#22660direct (N × H)
359. #435C4×C73semidirect
407. C22×C8C2×C4×C73semidirect
458. #106D4×C73semidirect
459. C4⋊C8C2×C4×C73semidirect
461. C22⋊C8C2×C4×C73semidirect
462. #97C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C732
C2×#428×C732
C2×#427×C732
C73×#23542
C73×#23522
C73×#19492
C73×#19472
C73×#18542
C73×#18522
C73×#18472
C73×#18092
C73×#18082
C73×#17762
#2266073