Finite Group Databasebeta

← C73×#26548 #32935952

Subgroups — C73×#26548 #32935952

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×C4×D8×C73C211yesmaximal, characteristic, complemented
3C73×#2420C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5C73×#2092C211yesmaximal, characteristic, complemented
6C73×#2054C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1949C211yesmaximal, characteristic, complemented
10C73×#1942C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1864C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C2×#121×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22#482×C73—24no—
23C4×D8×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×C4×C8×C73C2211yescharacteristic
39#397×C73—21no—
40#394×C73—21no—
41#390×C73—21no—
42#390×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#386×C73—21no—
48#386×C73—21no—
49#382×C73C2211yescharacteristic
50#381×C73—21no—
51#380×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×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C2×D8×C73—22no—
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75#121×C73—22no—
76#121×C73—22no—
77#121×C73—22no—
78#121×C73—41no—
79C4×D4×C73—22no—
80C4×D4×C73—22no—
81C4×D4×C73—41no—
82C4×D4×C73—41no—
83#117×C73—22no—
84#117×C73—41no—
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×C73D411yescharacteristic
104C2×C22⋊C4×C73D411yescharacteristic
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109#107×C73—22no—
110#107×C73—22no—
111#107×C73—22no—
112#106×C73—22no—
113#106×C73—41no—
114C4⋊C8×C73—22no—
115#102×C73—22no—
116#102×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—41no—
120#102×C73D414yescomplemented
121C22⋊C8×C73—22no—
122C22⋊C8×C73—22no—
123C4×C8×C73—22no—
124#95×C73—21no—
125#95×C73—21no—
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—42no—
147C2×D4×C73—42no—
148C2×D4×C73—81no—
149C2×D4×C73—81no—
150C2×D4×C73—81no—
151C2×D4×C73C2×D412yes—
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—42no—
168C22×C4×C73—42no—
169C22×C4×C73—81no—
170C22×C4×C73—81no—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2411yescharacteristic
177D8×C73—28no—
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×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73C2×D412yes—
189C2×C8×C73#4112yes—
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—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—81no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73C2×D412yes—
203C4⋊C4×C73#4112yes—
204C22⋊C4×C73—24no—
205C22⋊C4×C73—22no—
206C22⋊C4×C73—41no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—81no—
213C22⋊C4×C73—81no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73—81no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—42no—
221C42×C73—81no—
222C23×C73—22no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—22no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
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—22no—
247D4×C73—22no—
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—21no—
256C2×C4×C73—21no—
257C2×C4×C73—22no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
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—41no—
271C2×C4×C73—41no—
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—84no—
291C2×C4×C73—84no—
292C2×C4×C73#13512yes—
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C732−1+411yescharacteristic
299C8×C73—22no—
300C8×C73—22no—
301C8×C73—41no—
302C8×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—42no—
307C22×C73—41no—
308C22×C73—42no—
309C22×C73—41no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—41no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—41no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73#52511yescharacteristic
325C22×C73D4211yescharacteristic
326C22×C73#54711yescharacteristic
327C22×C73C2×#13511yescharacteristic
328C22×C73#57511yescharacteristic
329C22×C73#57611yescharacteristic
330C22×C73#57611yescharacteristic
331C4×C73—22no—
332C4×C73—41no—
333C4×C73—41no—
334C4×C73—42no—
335C4×C73—41no—
336C4×C73—41no—
337C4×C73—42no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73—81no—
342C4×C73#52511yescharacteristic
343C4×C73#53911yescharacteristic
344C4×C73#54711yescharacteristic
345C4×C73#55911yescharacteristic
346#26548C7311yesmaximal, characteristic, direct product factor, Sylow
347C2×C73—81no—
348C2×C73—82no—
349C2×C73—82no—
350C2×C73#245511yescharacteristic
351C2×C73#310211yescharacteristic
352C2×C73#312211yescharacteristic
353C2×C73#326811yescharacteristic
354C2×C73#328011yescharacteristic
355C2×C73#334111yescharacteristic
356C2×C73#335511yescharacteristic
357C2×#482C2×C7311yescharacteristic, complemented
358C2×C4×D8C2×C7311yescharacteristic, complemented
359#2420C2×C7311yescharacteristic, complemented
360#2363C2×C7311yescharacteristic, complemented
361#2092C2×C7311yescharacteristic, complemented
362#2054C2×C7311yescharacteristic, complemented
363#2033C2×C7311yescharacteristic, complemented
364#1999C2×C7311yescharacteristic
365#1949C2×C7311yescharacteristic, complemented
366#1942C2×C7311yescharacteristic, complemented
367#1925C2×C7311yescharacteristic, complemented
368#1923C2×C7311yescharacteristic, complemented
369#1864C2×C7311yescharacteristic, complemented
370#1864C2×C7311yescharacteristic, complemented
371#1854C2×C7311yescharacteristic, complemented
372C73#2654811yescharacteristic, direct product factor, Sylow
373C22×D8C22×C7311yescharacteristic
374C2×#121C22×C7311yescharacteristic
375C2×#121C22×C7311yescharacteristic
376C2×C4×D4C22×C7311yescharacteristic
377C2×C4×D4C22×C7311yescharacteristic
378C2×#117C22×C7311yescharacteristic
379#482—24no—
380C4×D8—24no—
381C2×#107C22×C7311yescharacteristic
382C2×#107C22×C7311yescharacteristic
383C2×#107C22×C7311yescharacteristic
384C2×#106C22×C7311yescharacteristic
385C2×#106C22×C7311yescharacteristic
386C2×C4⋊C8C22×C7311yescharacteristic
387C2×#102C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×C22⋊C8C22×C7311yescharacteristic
394C2×C22⋊C8C22×C7311yescharacteristic
395C2×C4×C8C22×C7311yescharacteristic
396#397—21no—
397#394—21no—
398#390—21no—
399#390C22×C7311yescharacteristic
400#390C22×C7311yescharacteristic
401#389C22×C7311yescharacteristic
402#389C22×C7311yescharacteristic
403#388—21no—
404#386—21no—
405#386—21no—
406#382C22×C7311yescharacteristic
407#381—21no—
408#380C22×C7311yescharacteristic
409C4×C4⋊C4C22×C7311yescharacteristic
410C4×C22⋊C4—21no—
411C4×C22⋊C4C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416#336C22×C7311yescharacteristic
417#336C22×C7311yescharacteristic
418C22×D4—21no—
419C22×D4—21no—
420C22×D4C23×C7311yescharacteristic
421C22×D4C23×C7311yescharacteristic
422C23×C4—21no—
423C23×C4—21no—
424C23×C4C23×C7311yescharacteristic
425C2×D8—22no—
426C2×D8—22no—
427C2×D8—22no—
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432#121—22no—
433#121—22no—
434#121—22no—
435#121—41no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—41no—
439C4×D4—41no—
440#117—22no—
441#117—41no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
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×C42C23×C7311yescharacteristic
465C2×C42C23×C7311yescharacteristic
466#107—22no—
467#107—22no—
468#107—22no—
469#106—22no—
470#106—41no—
471C4⋊C8—22no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—41no—
477#102D4×C7314yescomplemented
478C22⋊C8—22no—
479C22⋊C8—22no—
480C4×C8—22no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C7311yescharacteristic
488#95D4×C7311yescharacteristic
489C24—21no—
490C24—21no—
491C24C2×D4×C7311yescharacteristic
492C2×D4—24no—
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×D4C2×D4×C7312yes—
509C2×D4#41×C7312yes—
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—21no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C2×D4×C7311yescharacteristic
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4C2×D4×C7311yescharacteristic
531C22×C4C2×D4×C7311yescharacteristic
532C22×C4C2×D4×C7311yescharacteristic
533C22×C4C24×C7311yescharacteristic
534D8—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C2×D4×C7312yes—
546C2×C8#41×C7312yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4C2×D4×C7312yes—
560C4⋊C4#41×C7312yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—81no—
579C23—22no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×D4×C7311yescharacteristic
601D4—22no—
602D4—22no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—84no—
610D4—84no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
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—41no—
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×C4—84no—
649C2×C4#135×C7312yes—
650C2×C4C22×D4×C7311yescharacteristic
651C2×C4C2×#41×C7311yescharacteristic
652C2×C4C2×#41×C7311yescharacteristic
653C2×C4C2×#41×C7311yescharacteristic
654C2×C4H(5,𝔽2)×C7311yescharacteristic
655C2×C42−1+4×C7311yescharacteristic
656C8—22no—
657C8—22no—
658C8—41no—
659C8—41no—
660C22—41no—
661C22—42no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22#525×C7311yescharacteristic
682C22D42×C7311yescharacteristic
683C22#547×C7311yescharacteristic
684C22C2×#135×C7311yescharacteristic
685C22#575×C7311yescharacteristic
686C22#576×C7311yescharacteristic
687C22#576×C7311yescharacteristic
688C4—22no—
689C4—41no—
690C4—41no—
691C4—42no—
692C4—41no—
693C4—41no—
694C4—42no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4#525×C7311yescharacteristic
700C4#539×C7311yescharacteristic
701C4#547×C7311yescharacteristic
702C4#559×C7311yescharacteristic
703C2—81no—
704C2—82no—
705C2—82no—
706C2C73×#245511yescharacteristic
707C2C73×#310211yescharacteristic
708C2C73×#312211yescharacteristic
709C2C73×#326811yescharacteristic
710C2C73×#328011yescharacteristic
711C2C73×#334111yescharacteristic
712C2C73×#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×C4×D8×C73C2semidirect
3. C73×#2420C2semidirect
4. C73×#2363C2semidirect
5. C73×#2092C2semidirect
6. C73×#2054C2semidirect
7. C73×#2033C2semidirect
9. C73×#1949C2semidirect
10. C73×#1942C2semidirect
11. C73×#1925C2semidirect
12. C73×#1923C2semidirect
13. C73×#1864C2semidirect
14. C73×#1864C2semidirect
15. C73×#1854C2semidirect
120. #102×C73D4semidirect
346. #26548C73direct (N × H)
357. C2×#482C2×C73semidirect
358. C2×C4×D8C2×C73semidirect
359. #2420C2×C73semidirect
360. #2363C2×C73semidirect
361. #2092C2×C73semidirect
362. #2054C2×C73semidirect
363. #2033C2×C73semidirect
365. #1949C2×C73semidirect
366. #1942C2×C73semidirect
367. #1925C2×C73semidirect
368. #1923C2×C73semidirect
369. #1864C2×C73semidirect
370. #1864C2×C73semidirect
371. #1854C2×C73semidirect
372. C73#26548direct (N × H)
477. #102D4×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×C4×D8×C732
C73×#24202
C73×#23632
C73×#20922
C73×#20542
C73×#20332
C73×#19992
C73×#19492
C73×#19422
C73×#19252
C73×#19232
C73×#18642
C73×#18542
#2654873