Finite Group Databasebeta

← C73×#25173 #32934577

Subgroups — C73×#25173 #32934577

Order 18688.

1046 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×#462×C73C211yesmaximal, characteristic, complemented
2C2×#451×C73C211yesmaximal, characteristic
3C2×#451×C73C211yesmaximal, characteristic
4C2×#441×C73C211yesmaximal, characteristic, complemented
5C73×#2429C211yesmaximal, characteristic
6Q8×C22⋊C4×C73C211yesmaximal, characteristic
7C73×#2066C211yesmaximal, characteristic, complemented
8C73×#2035C211yesmaximal, characteristic
9C73×#2035C211yesmaximal, characteristic
10C73×#2016C211yesmaximal, characteristic, complemented
11C73×#1971C211yesmaximal, characteristic, complemented
12C73×#1924C211yesmaximal, characteristic
13C73×#1878C211yesmaximal, characteristic, complemented
14C73×#1878C211yesmaximal, characteristic, complemented
15C73×#1865C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic
19C22×Q16×C73C2211yescharacteristic
20C22×Q16×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25C2×C4×Q8×C73C2211yescharacteristic
26C2×C4×Q8×C73C2211yescharacteristic
27#462×C73—24no—
28#451×C73—24no—
29#451×C73—24no—
30#441×C73—24no—
31C2×#106×C73C2211yescharacteristic
32C2×#106×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×#97×C73C2211yescharacteristic
45#398×C73—21no—
46#396×C73—21no—
47#391×C73—21no—
48#391×C73—21no—
49#391×C73C2211yescharacteristic
50#391×C73C2211yescharacteristic
51#391×C73C2211yescharacteristic
52#389×C73—21no—
53#389×C73C2211yescharacteristic
54#388×C73—21no—
55#380×C73—21no—
56#380×C73C2211yescharacteristic
57C4×C22⋊C4×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—21no—
66C22×Q8×C73—22no—
67C22×Q8×C73—22no—
68C22×Q8×C73—41no—
69C22×Q8×C73—41no—
70C22×Q8×C73C2311yescharacteristic
71C22×Q8×C73C2311yescharacteristic
72C22×Q8×C73C2311yescharacteristic
73C22×Q8×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73C2311yescharacteristic
76C2×Q16×C73—22no—
77C2×Q16×C73—22no—
78C2×Q16×C73—22no—
79C2×Q16×C73—22no—
80C2×Q16×C73—22no—
81C2×Q16×C73—22no—
82C2×Q16×C73—22no—
83C2×Q16×C73—22no—
84C2×Q16×C73—22no—
85C2×Q16×C73—41no—
86C2×Q16×C73—41no—
87C2×Q16×C73D414yes—
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C4⋊Q8×C73—22no—
93C4⋊Q8×C73—41no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—41no—
97C22⋊Q8×C73—41no—
98C4×Q8×C73—22no—
99C4×Q8×C73—22no—
100C4×Q8×C73—22no—
101C4×Q8×C73—41no—
102C4×Q8×C73—41no—
103C4×Q8×C73—41no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C22⋊C4×C73D411yescharacteristic
121C2×C42×C73—21no—
122C2×C42×C73—21no—
123C2×C42×C73—21no—
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126#106×C73—22no—
127#106×C73—41no—
128C4⋊C8×C73—22no—
129#103×C73—22no—
130#103×C73—22no—
131#103×C73—22no—
132#103×C73—22no—
133#103×C73—22no—
134#103×C73—22no—
135#103×C73—41no—
136#103×C73D414yes—
137C22⋊C8×C73—22no—
138C22⋊C8×C73—22no—
139#97×C73—22no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144#95×C73—21no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73D411yescharacteristic
149#95×C73D411yescharacteristic
150C24×C73C2×D411yescharacteristic
151C2×Q8×C73—24no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—42no—
172C2×Q8×C73—42no—
173C2×Q8×C73—44no—
174C2×Q8×C73—44no—
175C2×Q8×C73—44no—
176C2×Q8×C73—44no—
177C2×Q8×C73C2×D412yes—
178C2×Q8×C73C2×D412yes—
179C2×Q8×C73C2×D412yes—
180C2×Q8×C73#4112yes—
181C2×Q8×C73#4112yes—
182C22×C4×C73—21no—
183C22×C4×C73—24no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—42no—
198C22×C4×C73—42no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205Q16×C73—28no—
206Q16×C73—44no—
207Q16×C73—44no—
208Q16×C73—44no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73C2×D412yes—
220C2×C8×C73C2×D412yes—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—42no—
229C4⋊C4×C73—42no—
230C4⋊C4×C73—42no—
231C4⋊C4×C73—42no—
232C4⋊C4×C73—42no—
233C4⋊C4×C73—42no—
234C4⋊C4×C73—42no—
235C4⋊C4×C73—42no—
236C4⋊C4×C73C2×D412yes—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C42×C73—21no—
243C42×C73—21no—
244C42×C73—21no—
245C42×C73—21no—
246C42×C73—42no—
247C42×C73—42no—
248C42×C73—42no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73#13712yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73—22no—
261Q8×C73—22no—
262Q8×C73—22no—
263Q8×C73—22no—
264Q8×C73—48no—
265Q8×C73—41no—
266Q8×C73—41no—
267Q8×C73—41no—
268Q8×C73—41no—
269Q8×C73—41no—
270Q8×C73—41no—
271Q8×C73—41no—
272Q8×C73—41no—
273Q8×C73#12114yes—
274C2×C4×C73—22no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—21no—
279C2×C4×C73—22no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—48no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73#13712yes—
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73C2×#4111yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C73H(5,𝔽2)11yescharacteristic
324C8×C73—22no—
325C8×C73—22no—
326C8×C73—41no—
327C8×C73—41no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73#52511yescharacteristic
336C22×C73D4211yescharacteristic
337C22×C73D4211yescharacteristic
338C22×C73C2×#13711yescharacteristic
339C22×C73C2×#13711yescharacteristic
340C22×C73#57811yescharacteristic
341C22×C73#57811yescharacteristic
342C4×C73—24no—
343C4×C73—22no—
344C4×C73—41no—
345C4×C73—42no—
346C4×C73—42no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—42no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73—81no—
355C4×C73C2×#12111yescharacteristic
356C4×C73#53811yescharacteristic
357C4×C73#54611yescharacteristic
358C4×C73#54611yescharacteristic
359#25173C7311yesmaximal, characteristic, direct product factor, Sylow
360C2×C73—42no—
361C2×C73#242411yescharacteristic
362C2×C73#311311yescharacteristic
363C2×C73#312711yescharacteristic
364C2×C73#327011yescharacteristic
365C2×C73#327011yescharacteristic
366C2×C73#327011yescharacteristic
367C2×C73#327611yescharacteristic
368C2×#462C2×C7311yescharacteristic, complemented
369C2×#451C2×C7311yescharacteristic
370C2×#451C2×C7311yescharacteristic
371C2×#441C2×C7311yescharacteristic, complemented
372#2429C2×C7311yescharacteristic
373Q8×C22⋊C4C2×C7311yescharacteristic
374#2066C2×C7311yescharacteristic, complemented
375#2035C2×C7311yescharacteristic
376#2035C2×C7311yescharacteristic
377#2016C2×C7311yescharacteristic, complemented
378#1971C2×C7311yescharacteristic, complemented
379#1924C2×C7311yescharacteristic
380#1878C2×C7311yescharacteristic, complemented
381#1878C2×C7311yescharacteristic, complemented
382#1865C2×C7311yescharacteristic, complemented
383C73#2517311yescharacteristic, direct product factor, Sylow
384C23×Q8C22×C7311yescharacteristic
385C22×Q16C22×C7311yescharacteristic
386C22×Q16C22×C7311yescharacteristic
387C22×Q16C22×C7311yescharacteristic
388C22×Q16C22×C7311yescharacteristic
389C2×C4⋊Q8C22×C7311yescharacteristic
390C2×C22⋊Q8C22×C7311yescharacteristic
391C2×C22⋊Q8C22×C7311yescharacteristic
392C2×C4×Q8C22×C7311yescharacteristic
393C2×C4×Q8C22×C7311yescharacteristic
394C2×C4×Q8C22×C7311yescharacteristic
395#462—24no—
396#451—24no—
397#451—24no—
398#441—24no—
399C2×#106C22×C7311yescharacteristic
400C2×#106C22×C7311yescharacteristic
401C2×C4⋊C8C22×C7311yescharacteristic
402C2×#103C22×C7311yescharacteristic
403C2×#103C22×C7311yescharacteristic
404C2×#103C22×C7311yescharacteristic
405C2×#103C22×C7311yescharacteristic
406C2×#103C22×C7311yescharacteristic
407C2×#103C22×C7311yescharacteristic
408C2×#103C22×C7311yescharacteristic
409C2×#103C22×C7311yescharacteristic
410C2×C22⋊C8C22×C7311yescharacteristic
411C2×C22⋊C8C22×C7311yescharacteristic
412C2×#97C22×C7311yescharacteristic
413#398—21no—
414#396—21no—
415#391—21no—
416#391—21no—
417#391C22×C7311yescharacteristic
418#391C22×C7311yescharacteristic
419#391C22×C7311yescharacteristic
420#389—21no—
421#389C22×C7311yescharacteristic
422#388—21no—
423#380—21no—
424#380C22×C7311yescharacteristic
425C4×C22⋊C4—21no—
426C4×C22⋊C4C22×C7311yescharacteristic
427#340C22×C7311yescharacteristic
428#340C22×C7311yescharacteristic
429#336C22×C7311yescharacteristic
430#336C22×C7311yescharacteristic
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C23×C7311yescharacteristic
439C22×Q8C23×C7311yescharacteristic
440C22×Q8C23×C7311yescharacteristic
441C22×Q8C23×C7311yescharacteristic
442C23×C4—21no—
443C23×C4C23×C7311yescharacteristic
444C2×Q16—22no—
445C2×Q16—22no—
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—22no—
451C2×Q16—22no—
452C2×Q16—22no—
453C2×Q16—41no—
454C2×Q16—41no—
455C2×Q16D4×C7314yes—
456C22×C8C23×C7311yescharacteristic
457C22×C8C23×C7311yescharacteristic
458C22×C8C23×C7311yescharacteristic
459C22×C8C23×C7311yescharacteristic
460C4⋊Q8—22no—
461C4⋊Q8—41no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465C22⋊Q8—41no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—41no—
470C4×Q8—41no—
471C4×Q8—41no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4C23×C7311yescharacteristic
481C2×C4⋊C4C23×C7311yescharacteristic
482C2×C4⋊C4C23×C7311yescharacteristic
483C2×C4⋊C4C23×C7311yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4D4×C7311yescharacteristic
488C2×C22⋊C4D4×C7311yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—21no—
492C2×C42C23×C7311yescharacteristic
493C2×C42C23×C7311yescharacteristic
494#106—22no—
495#106—41no—
496C4⋊C8—22no—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—22no—
502#103—22no—
503#103—41no—
504#103D4×C7314yes—
505C22⋊C8—22no—
506C22⋊C8—22no—
507#97—22no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95D4×C7311yescharacteristic
517#95D4×C7311yescharacteristic
518C24C2×D4×C7311yescharacteristic
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8—44no—
542C2×Q8—44no—
543C2×Q8—44no—
544C2×Q8—44no—
545C2×Q8C2×D4×C7312yes—
546C2×Q8C2×D4×C7312yes—
547C2×Q8C2×D4×C7312yes—
548C2×Q8#41×C7312yes—
549C2×Q8#41×C7312yes—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4C2×D4×C7311yescharacteristic
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C24×C7311yescharacteristic
573Q16—28no—
574Q16—44no—
575Q16—44no—
576Q16—44no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8C2×D4×C7312yes—
588C2×C8C2×D4×C7312yes—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4C2×D4×C7312yes—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—42no—
615C42—42no—
616C42—42no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#137×C7312yes—
624C23C22×D4×C7311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8#121×C7314yes—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4#137×C7312yes—
686C2×C4C22×D4×C7311yescharacteristic
687C2×C4C22×D4×C7311yescharacteristic
688C2×C4C2×#41×C7311yescharacteristic
689C2×C4C2×#41×C7311yescharacteristic
690C2×C4H(5,𝔽2)×C7311yescharacteristic
691C2×C4H(5,𝔽2)×C7311yescharacteristic
692C8—22no—
693C8—22no—
694C8—41no—
695C8—41no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22#525×C7311yescharacteristic
704C22D42×C7311yescharacteristic
705C22D42×C7311yescharacteristic
706C22C2×#137×C7311yescharacteristic
707C22C2×#137×C7311yescharacteristic
708C22#578×C7311yescharacteristic
709C22#578×C7311yescharacteristic
710C4—22no—
711C4—24no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C2×#121×C7311yescharacteristic
724C4#538×C7311yescharacteristic
725C4#546×C7311yescharacteristic
726C4#546×C7311yescharacteristic
727C2—42no—
728C2C73×#242411yescharacteristic
729C2C73×#311311yescharacteristic
730C2C73×#312711yescharacteristic
731C2C73×#327011yescharacteristic
732C2C73×#327011yescharacteristic
733C2C73×#327011yescharacteristic
734C2C73×#327611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#462×C73C2semidirect
4. C2×#441×C73C2semidirect
7. C73×#2066C2semidirect
10. C73×#2016C2semidirect
11. C73×#1971C2semidirect
13. C73×#1878C2semidirect
14. C73×#1878C2semidirect
15. C73×#1865C2semidirect
359. #25173C73direct (N × H)
368. C2×#462C2×C73semidirect
371. C2×#441C2×C73semidirect
374. #2066C2×C73semidirect
377. #2016C2×C73semidirect
378. #1971C2×C73semidirect
380. #1878C2×C73semidirect
381. #1878C2×C73semidirect
382. #1865C2×C73semidirect
383. C73#25173direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#462×C732
C2×#451×C732
C2×#441×C732
C73×#24292
Q8×C22⋊C4×C732
C73×#20662
C73×#20352
C73×#20162
C73×#19712
C73×#19242
C73×#18782
C73×#18652
#2517373