Finite Group Databasebeta

← C73×#26815 #32936219

Subgroups — C73×#26815 #32936219

Order 18688.

874 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×#478×C73C211yesmaximal, characteristic, complemented
3C73×#2490C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1924C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1854C211yesmaximal, characteristic, complemented
15C73×#1776C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22#482×C73—24no—
23#478×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×C4⋊C8×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39#397×C73—21no—
40#394×C73—21no—
41#390×C73—21no—
42#390×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#380×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×D8×C73—22no—
68C2×D8×C73—22no—
69C2×D8×C73—41no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74#125×C73—22no—
75#125×C73—41no—
76#121×C73—22no—
77#121×C73—22no—
78#121×C73—22no—
79#121×C73—41no—
80C4×D4×C73—22no—
81C4×D4×C73—41no—
82#117×C73—22no—
83#117×C73—41no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C22⋊C4×C73—21no—
94C2×C22⋊C4×C73—21no—
95C2×C22⋊C4×C73—21no—
96C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111#107×C73—22no—
112#107×C73—22no—
113#107×C73—22no—
114#106×C73—41no—
115#106×C73D414yescomplemented
116C4⋊C8×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123C22⋊C8×C73—22no—
124C22⋊C8×C73—22no—
125#97×C73—22no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C24×C73—21no—
133C24×C73—21no—
134C24×C73C2×D411yescharacteristic
135C2×D4×C73—24no—
136C2×D4×C73—21no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
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—42no—
148C2×D4×C73—42no—
149C2×D4×C73—81no—
150C2×D4×C73—81no—
151C2×D4×C73—81no—
152C2×D4×C73#4112yes—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
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—42no—
166C22×C4×C73—42no—
167C22×C4×C73—81no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2411yescharacteristic
174D8×C73—44no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73C2×D412yes—
186C2×C8×C73#4112yes—
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×C73C2×D412yes—
200C4⋊C4×C73C2×D412yes—
201C4⋊C4×C73#4112yes—
202C22⋊C4×C73—24no—
203C22⋊C4×C73—41no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—81no—
211C22⋊C4×C73—81no—
212C22⋊C4×C73—81no—
213C22⋊C4×C73—81no—
214C22⋊C4×C73—81no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—42no—
220C42×C73—81no—
221C42×C73—81no—
222C23×C73—22no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
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×C73C22×D411yescharacteristic
244D4×C73—22no—
245D4×C73—22no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73—41no—
250D4×C73—41no—
251D4×C73—41no—
252D4×C73—84no—
253D4×C73—84no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
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—84no—
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C732−1+411yescharacteristic
298C8×C73—22no—
299C8×C73—22no—
300C8×C73—41no—
301C8×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—42no—
306C22×C73—41no—
307C22×C73—42no—
308C22×C73—41no—
309C22×C73—42no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73#52511yescharacteristic
324C22×C73D4211yescharacteristic
325C22×C73#54711yescharacteristic
326C22×C73#57511yescharacteristic
327C22×C73#57511yescharacteristic
328C22×C73#57611yescharacteristic
329C22×C73#57611yescharacteristic
330C4×C73—41no—
331C4×C73—41no—
332C4×C73—42no—
333C4×C73—41no—
334C4×C73—41no—
335C4×C73—41no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73#53211yescharacteristic
342C4×C73#54211yescharacteristic
343C4×C73#54811yescharacteristic
344C4×C73#55111yescharacteristic
345#26815C7311yesmaximal, characteristic, direct product factor, Sylow
346C2×C73—81no—
347C2×C73—82no—
348C2×C73—161no—
349C2×C73#246111yescharacteristic
350C2×C73#311111yescharacteristic
351C2×C73#312211yescharacteristic
352C2×C73#326811yescharacteristic
353C2×C73#326811yescharacteristic
354C2×C73#334711yescharacteristic
355C2×C73#335511yescharacteristic
356C2×#482C2×C7311yescharacteristic, complemented
357C2×#478C2×C7311yescharacteristic, complemented
358#2490C2×C7311yescharacteristic, complemented
359#2363C2×C7311yescharacteristic, complemented
360#2067C2×C7311yescharacteristic, complemented
361#2059C2×C7311yescharacteristic, complemented
362#2033C2×C7311yescharacteristic, complemented
363#1999C2×C7311yescharacteristic
364#1972C2×C7311yescharacteristic, complemented
365#1925C2×C7311yescharacteristic, complemented
366#1925C2×C7311yescharacteristic, complemented
367#1924C2×C7311yescharacteristic, complemented
368#1879C2×C7311yescharacteristic, complemented
369#1854C2×C7311yescharacteristic, complemented
370#1776C2×C7311yescharacteristic, complemented
371C73#2681511yescharacteristic, direct product factor, Sylow
372C22×D8C22×C7311yescharacteristic
373C2×#125C22×C7311yescharacteristic
374C2×#121C22×C7311yescharacteristic
375C2×#121C22×C7311yescharacteristic
376C2×C4×D4C22×C7311yescharacteristic
377C2×#117C22×C7311yescharacteristic
378#482—24no—
379#478—24no—
380C2×#107C22×C7311yescharacteristic
381C2×#107C22×C7311yescharacteristic
382C2×#107C22×C7311yescharacteristic
383C2×#106C22×C7311yescharacteristic
384C2×#106C22×C7311yescharacteristic
385C2×C4⋊C8C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×C22⋊C8C22×C7311yescharacteristic
393C2×C22⋊C8C22×C7311yescharacteristic
394C2×#97C22×C7311yescharacteristic
395#397—21no—
396#394—21no—
397#390—21no—
398#390—21no—
399#390C22×C7311yescharacteristic
400#390C22×C7311yescharacteristic
401#390C22×C7311yescharacteristic
402#389C22×C7311yescharacteristic
403#388—21no—
404#388—21no—
405#386—21no—
406#380C22×C7311yescharacteristic
407C4×C4⋊C4C22×C7311yescharacteristic
408C4×C4⋊C4C22×C7311yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#336C22×C7311yescharacteristic
416#336C22×C7311yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C7311yescharacteristic
420C22×D4C23×C7311yescharacteristic
421C23×C4—21no—
422C23×C4C23×C7311yescharacteristic
423C2×D8—22no—
424C2×D8—22no—
425C2×D8—41no—
426C22×C8C23×C7311yescharacteristic
427C22×C8C23×C7311yescharacteristic
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430#125—22no—
431#125—41no—
432#121—22no—
433#121—22no—
434#121—22no—
435#121—41no—
436C4×D4—22no—
437C4×D4—41no—
438#117—22no—
439#117—41no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4D4×C7311yescharacteristic
461C2×C22⋊C4D4×C7311yescharacteristic
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C7311yescharacteristic
466C2×C42C23×C7311yescharacteristic
467#107—22no—
468#107—22no—
469#107—22no—
470#106—41no—
471#106D4×C7314yescomplemented
472C4⋊C8—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481#97—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C7311yescharacteristic
487#95D4×C7311yescharacteristic
488C24—21no—
489C24—21no—
490C24C2×D4×C7311yescharacteristic
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4#41×C7312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4C2×D4×C7311yescharacteristic
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4C24×C7311yescharacteristic
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8C2×D4×C7312yes—
542C2×C8#41×C7312yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4C2×D4×C7312yes—
556C4⋊C4C2×D4×C7312yes—
557C4⋊C4#41×C7312yes—
558C22⋊C4—24no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—81no—
577C42—81no—
578C23—22no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C22×D4×C7311yescharacteristic
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4C22×D4×C7311yescharacteristic
649C2×C4C2×#41×C7311yescharacteristic
650C2×C4C2×#41×C7311yescharacteristic
651C2×C4C2×#41×C7311yescharacteristic
652C2×C4H(5,𝔽2)×C7311yescharacteristic
653C2×C42−1+4×C7311yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—41no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22#525×C7311yescharacteristic
680C22D42×C7311yescharacteristic
681C22#547×C7311yescharacteristic
682C22#575×C7311yescharacteristic
683C22#575×C7311yescharacteristic
684C22#576×C7311yescharacteristic
685C22#576×C7311yescharacteristic
686C4—41no—
687C4—41no—
688C4—41no—
689C4—42no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4#532×C7311yescharacteristic
698C4#542×C7311yescharacteristic
699C4#548×C7311yescharacteristic
700C4#551×C7311yescharacteristic
701C2—81no—
702C2—82no—
703C2—161no—
704C2C73×#246111yescharacteristic
705C2C73×#311111yescharacteristic
706C2C73×#312211yescharacteristic
707C2C73×#326811yescharacteristic
708C2C73×#326811yescharacteristic
709C2C73×#334711yescharacteristic
710C2C73×#335511yescharacteristic
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×#482×C73C2semidirect
2. C2×#478×C73C2semidirect
3. C73×#2490C2semidirect
4. C73×#2363C2semidirect
5. C73×#2067C2semidirect
6. C73×#2059C2semidirect
7. C73×#2033C2semidirect
9. C73×#1972C2semidirect
10. C73×#1925C2semidirect
11. C73×#1925C2semidirect
12. C73×#1924C2semidirect
13. C73×#1879C2semidirect
14. C73×#1854C2semidirect
15. C73×#1776C2semidirect
115. #106×C73D4semidirect
345. #26815C73direct (N × H)
356. C2×#482C2×C73semidirect
357. C2×#478C2×C73semidirect
358. #2490C2×C73semidirect
359. #2363C2×C73semidirect
360. #2067C2×C73semidirect
361. #2059C2×C73semidirect
362. #2033C2×C73semidirect
364. #1972C2×C73semidirect
365. #1925C2×C73semidirect
366. #1925C2×C73semidirect
367. #1924C2×C73semidirect
368. #1879C2×C73semidirect
369. #1854C2×C73semidirect
370. #1776C2×C73semidirect
371. C73#26815direct (N × H)
471. #106D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C2×#478×C732
C73×#24902
C73×#23632
C73×#20672
C73×#20592
C73×#20332
C73×#19992
C73×#19722
C73×#19252
C73×#19242
C73×#18792
C73×#18542
C73×#17762
#2681573