Finite Group Databasebeta

← C73×#26784 #32936188

Subgroups — C73×#26784 #32936188

Order 18688.

966 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C73C211yesmaximal, characteristic, complemented
2C2×#474×C73C211yesmaximal, characteristic, complemented
3C73×#2491C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic, complemented
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2057C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1970C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1852C211yesmaximal, characteristic, complemented
15C4×#107×C73C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2211yescharacteristic
18C2×#124×C73—21no—
19C2×#121×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×C4×D4×C73—21no—
22C2×C4×D4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#480×C73—24no—
25#474×C73—24no—
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#107×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#394×C73—21no—
42#393×C73—21no—
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#388×C73—21no—
48#388×C73—21no—
49#386×C73—21no—
50#385×C73—21no—
51#380×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C2×D8×C73—41no—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C4⋊Q8×C73—22no—
77C4⋊Q8×C73—41no—
78#124×C73—44no—
79#121×C73—22no—
80#121×C73—22no—
81#121×C73—22no—
82#121×C73—41no—
83C4×D4×C73—22no—
84C4×D4×C73—41no—
85C4×D4×C73—44no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—41no—
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×C22⋊C4×C73—21no—
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×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73—21no—
111C2×C42×C73C2311yescharacteristic
112C2×C42×C73C2311yescharacteristic
113#107×C73—22no—
114#107×C73—22no—
115#107×C73—22no—
116#107×C73—41no—
117#107×C73D414yescomplemented
118C4⋊C8×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—22no—
124#102×C73—22no—
125C22⋊C8×C73—22no—
126C22⋊C8×C73—22no—
127C4×C8×C73—22no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73D411yescharacteristic
133#95×C73D411yescharacteristic
134C24×C73—21no—
135C24×C73—21no—
136C24×C73C2×D411yescharacteristic
137C2×Q8×C73—42no—
138C2×Q8×C73—42no—
139C2×Q8×C73—81no—
140C2×D4×C73—24no—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—42no—
153C2×D4×C73—42no—
154C2×D4×C73—42no—
155C2×D4×C73—42no—
156C2×D4×C73—81no—
157C2×D4×C73#4112yes—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—42no—
173C22×C4×C73—42no—
174C22×C4×C73—81no—
175C22×C4×C73—81no—
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182D8×C73—44no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73C2×D412yes—
194C2×C8×C73#4112yes—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73C2×D412yes—
208C4⋊C4×C73C2×D412yes—
209C4⋊C4×C73#4112yes—
210C22⋊C4×C73—24no—
211C22⋊C4×C73—41no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—81no—
220C22⋊C4×C73—81no—
221C22⋊C4×C73D814yescomplemented
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—42no—
227C42×C73—42no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—22no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73C2×D812yes—
249C23×C73C22×D411yescharacteristic
250Q8×C73—84no—
251D4×C73—22no—
252D4×C73—22no—
253D4×C73—48no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—84no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—22no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—84no—
297C2×C4×C73—84no—
298C2×C4×C73C2×D812yes—
299C2×C4×C73C2×D812yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×C4×C732−1+411yescharacteristic
306C8×C73—22no—
307C8×C73—22no—
308C8×C73—41no—
309C8×C73—41no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73—81no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73#52511yescharacteristic
332C22×C73D4211yescharacteristic
333C22×C73#54711yescharacteristic
334C22×C73C22×D811yescharacteristic
335C22×C73#57511yescharacteristic
336C22×C73#57611yescharacteristic
337C22×C73#57811yescharacteristic
338C4×C73—22no—
339C4×C73—22no—
340C4×C73—41no—
341C4×C73—42no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—42no—
345C4×C73—42no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73—81no—
349C4×C73#53211yescharacteristic
350C4×C73#54211yescharacteristic
351C4×C73#54811yescharacteristic
352C4×C73#55111yescharacteristic
353#26784C7311yesmaximal, characteristic, direct product factor, Sylow
354C2×C73—42no—
355C2×C73—82no—
356C2×C73—161no—
357C2×C73#246111yescharacteristic
358C2×C73#310011yescharacteristic
359C2×C73#312411yescharacteristic
360C2×C73#327711yescharacteristic
361C2×C73D4×D811yescharacteristic
362C2×C73#333411yescharacteristic
363C2×C73#334711yescharacteristic
364C2×#480C2×C7311yescharacteristic, complemented
365C2×#474C2×C7311yescharacteristic, complemented
366#2491C2×C7311yescharacteristic, complemented
367#2361C2×C7311yescharacteristic, complemented
368#2067C2×C7311yescharacteristic, complemented
369#2057C2×C7311yescharacteristic, complemented
370#2033C2×C7311yescharacteristic, complemented
371#1999C2×C7311yescharacteristic
372#1970C2×C7311yescharacteristic, complemented
373#1925C2×C7311yescharacteristic, complemented
374#1925C2×C7311yescharacteristic, complemented
375#1923C2×C7311yescharacteristic, complemented
376#1879C2×C7311yescharacteristic, complemented
377#1852C2×C7311yescharacteristic, complemented
378C4×#107C2×C7311yescharacteristic, complemented
379C73#2678411yescharacteristic, direct product factor, Sylow
380C22×D8C22×C7311yescharacteristic
381C2×C4⋊Q8C22×C7311yescharacteristic
382C2×#124—21no—
383C2×#121C22×C7311yescharacteristic
384C2×#121C22×C7311yescharacteristic
385C2×C4×D4—21no—
386C2×C4×D4C22×C7311yescharacteristic
387C22×C4⋊C4C22×C7311yescharacteristic
388#480—24no—
389#474—24no—
390C2×#107C22×C7311yescharacteristic
391C2×#107C22×C7311yescharacteristic
392C2×#107C22×C7311yescharacteristic
393C2×#107C22×C7311yescharacteristic
394C2×#107C22×C7311yescharacteristic
395C2×C4⋊C8C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×#102C22×C7311yescharacteristic
401C2×#102C22×C7311yescharacteristic
402C2×C22⋊C8C22×C7311yescharacteristic
403C2×C22⋊C8C22×C7311yescharacteristic
404C2×C4×C8C22×C7311yescharacteristic
405#394—21no—
406#393—21no—
407#390C22×C7311yescharacteristic
408#390C22×C7311yescharacteristic
409#390C22×C7311yescharacteristic
410#389C22×C7311yescharacteristic
411#388—21no—
412#388—21no—
413#386—21no—
414#385—21no—
415#380C22×C7311yescharacteristic
416C4×C4⋊C4C22×C7311yescharacteristic
417C4×C4⋊C4C22×C7311yescharacteristic
418C4×C22⋊C4C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#340C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#336C22×C7311yescharacteristic
424#336C22×C7311yescharacteristic
425C22×Q8—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C23×C7311yescharacteristic
429C22×D4C23×C7311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C23×C7311yescharacteristic
433C2×D8—22no—
434C2×D8—22no—
435C2×D8—41no—
436C22×C8C23×C7311yescharacteristic
437C22×C8C23×C7311yescharacteristic
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440C4⋊Q8—22no—
441C4⋊Q8—41no—
442#124—44no—
443#121—22no—
444#121—22no—
445#121—22no—
446#121—41no—
447C4×D4—22no—
448C4×D4—41no—
449C4×D4—44no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C4⋊C4C23×C7311yescharacteristic
458C2×C4⋊C4C23×C7311yescharacteristic
459C2×C4⋊C4C23×C7311yescharacteristic
460C2×C4⋊C4C23×C7311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4D4×C7311yescharacteristic
472C2×C22⋊C4D4×C7311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C7311yescharacteristic
476C2×C42C23×C7311yescharacteristic
477#107—22no—
478#107—22no—
479#107—22no—
480#107—41no—
481#107D4×C7314yescomplemented
482C4⋊C8—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95D4×C7311yescharacteristic
497#95D4×C7311yescharacteristic
498C24—21no—
499C24—21no—
500C24C2×D4×C7311yescharacteristic
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—81no—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4#41×C7312yes—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7311yescharacteristic
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C24×C7311yescharacteristic
546D8—44no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8C2×D4×C7312yes—
558C2×C8#41×C7312yes—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4C2×D4×C7312yes—
572C4⋊C4C2×D4×C7312yes—
573C4⋊C4#41×C7312yes—
574C22⋊C4—24no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4D8×C7314yescomplemented
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—42no—
591C42—42no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23C2×D8×C7312yes—
613C23C22×D4×C7311yescharacteristic
614Q8—84no—
615D4—22no—
616D4—22no—
617D4—48no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4C2×D8×C7312yes—
663C2×C4C2×D8×C7312yes—
664C2×C4C22×D4×C7311yescharacteristic
665C2×C4C2×#41×C7311yescharacteristic
666C2×C4C2×#41×C7311yescharacteristic
667C2×C4C2×#41×C7311yescharacteristic
668C2×C4H(5,𝔽2)×C7311yescharacteristic
669C2×C42−1+4×C7311yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22#525×C7311yescharacteristic
696C22D42×C7311yescharacteristic
697C22#547×C7311yescharacteristic
698C22C22×D8×C7311yescharacteristic
699C22#575×C7311yescharacteristic
700C22#576×C7311yescharacteristic
701C22#578×C7311yescharacteristic
702C4—22no—
703C4—22no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—42no—
708C4—41no—
709C4—42no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4#532×C7311yescharacteristic
714C4#542×C7311yescharacteristic
715C4#548×C7311yescharacteristic
716C4#551×C7311yescharacteristic
717C2—42no—
718C2—82no—
719C2—161no—
720C2C73×#246111yescharacteristic
721C2C73×#310011yescharacteristic
722C2C73×#312411yescharacteristic
723C2C73×#327711yescharacteristic
724C2D4×D8×C7311yescharacteristic
725C2C73×#333411yescharacteristic
726C2C73×#334711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#1999C2
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×#480×C73C2semidirect
2. C2×#474×C73C2semidirect
3. C73×#2491C2semidirect
4. C73×#2361C2semidirect
5. C73×#2067C2semidirect
6. C73×#2057C2semidirect
7. C73×#2033C2semidirect
9. C73×#1970C2semidirect
10. C73×#1925C2semidirect
11. C73×#1925C2semidirect
12. C73×#1923C2semidirect
13. C73×#1879C2semidirect
14. C73×#1852C2semidirect
15. C4×#107×C73C2semidirect
117. #107×C73D4semidirect
221. C22⋊C4×C73D8semidirect
353. #26784C73direct (N × H)
364. C2×#480C2×C73semidirect
365. C2×#474C2×C73semidirect
366. #2491C2×C73semidirect
367. #2361C2×C73semidirect
368. #2067C2×C73semidirect
369. #2057C2×C73semidirect
370. #2033C2×C73semidirect
372. #1970C2×C73semidirect
373. #1925C2×C73semidirect
374. #1925C2×C73semidirect
375. #1923C2×C73semidirect
376. #1879C2×C73semidirect
377. #1852C2×C73semidirect
378. C4×#107C2×C73semidirect
379. C73#26784direct (N × H)
481. #107D4×C73semidirect
585. C22⋊C4D8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C732
C2×#474×C732
C73×#24912
C73×#23612
C73×#20672
C73×#20572
C73×#20332
C73×#19992
C73×#19702
C73×#19252
C73×#19232
C73×#18792
C73×#18522
C4×#107×C732
#2678473