Finite Group Databasebeta

← C73×#26812 #32936216

Subgroups — C73×#26812 #32936216

Order 18688.

910 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C2×#474×C73C211yesmaximal, characteristic, complemented
3C73×#2491C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic, complemented
6C73×#2058C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, 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×C4⋊Q8×C73C2211yescharacteristic
18C2×#124×C73—21no—
19C2×#121×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23#482×C73—24no—
24#474×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40#394×C73—21no—
41#393×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×Q8×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C2×D8×C73—22no—
69C2×D8×C73—22no—
70C2×D8×C73—41no—
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C4⋊Q8×C73—22no—
76C4⋊Q8×C73—41no—
77#124×C73—44no—
78#121×C73—22no—
79#121×C73—22no—
80#121×C73—22no—
81#121×C73—41no—
82C4×D4×C73—22no—
83C4×D4×C73—41no—
84#117×C73—22no—
85#117×C73—41no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#107×C73—22no—
113#107×C73D414yescomplemented
114#106×C73—22no—
115#106×C73—22no—
116#106×C73—41no—
117C4⋊C8×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—22no—
124C22⋊C8×C73—22no—
125C22⋊C8×C73—22no—
126#97×C73—22no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73D411yescharacteristic
132#95×C73D411yescharacteristic
133C24×C73—21no—
134C24×C73—21no—
135C24×C73C2×D411yescharacteristic
136C2×Q8×C73—42no—
137C2×Q8×C73—42no—
138C2×Q8×C73—81no—
139C2×D4×C73—24no—
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—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—42no—
152C2×D4×C73—42no—
153C2×D4×C73—81no—
154C2×D4×C73—81no—
155C2×D4×C73—81no—
156C2×D4×C73#4112yes—
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—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—81no—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2411yescharacteristic
178D8×C73—44no—
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×C73—21no—
189C2×C8×C73C2×D412yes—
190C2×C8×C73#4112yes—
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—42no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73C2×D412yes—
203C4⋊C4×C73C2×D412yes—
204C4⋊C4×C73#4112yes—
205C22⋊C4×C73—24no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—41no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—81no—
217C22⋊C4×C73—81no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—42no—
223C42×C73—42no—
224C42×C73—81no—
225C23×C73—22no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
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×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73C22×D411yescharacteristic
247Q8×C73—84no—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—41no—
251D4×C73—41no—
252D4×C73—41no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—84no—
257D4×C73—84no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
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—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
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—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—84no—
295C2×C4×C73AGL(1,ℤ/8)12yes—
296C2×C4×C73C22×D411yescharacteristic
297C2×C4×C73C2×#4111yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C732−1+411yescharacteristic
302C8×C73—22no—
303C8×C73—22no—
304C8×C73—41no—
305C8×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—42no—
310C22×C73—41no—
311C22×C73—42no—
312C22×C73—41no—
313C22×C73—42no—
314C22×C73—41no—
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—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73#52511yescharacteristic
328C22×C73D4211yescharacteristic
329C22×C73#54711yescharacteristic
330C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C73#57511yescharacteristic
332C22×C73#57611yescharacteristic
333C22×C73#57711yescharacteristic
334C4×C73—22no—
335C4×C73—41no—
336C4×C73—41no—
337C4×C73—42no—
338C4×C73—41no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—41no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73#53211yescharacteristic
346C4×C73#54211yescharacteristic
347C4×C73#54811yescharacteristic
348C4×C73#55111yescharacteristic
349#26812C7311yesmaximal, characteristic, direct product factor, Sylow
350C2×C73—81no—
351C2×C73—82no—
352C2×C73—161no—
353C2×C73#246111yescharacteristic
354C2×C73#311511yescharacteristic
355C2×C73#311811yescharacteristic
356C2×C73#326411yescharacteristic
357C2×C73#327111yescharacteristic
358C2×C73#334711yescharacteristic
359C2×C73#335411yescharacteristic
360C2×#482C2×C7311yescharacteristic, complemented
361C2×#474C2×C7311yescharacteristic, complemented
362#2491C2×C7311yescharacteristic, complemented
363#2363C2×C7311yescharacteristic, complemented
364#2065C2×C7311yescharacteristic, complemented
365#2058C2×C7311yescharacteristic, complemented
366#2034C2×C7311yescharacteristic, complemented
367#1999C2×C7311yescharacteristic
368#1972C2×C7311yescharacteristic, complemented
369#1926C2×C7311yescharacteristic, complemented
370#1925C2×C7311yescharacteristic, complemented
371#1924C2×C7311yescharacteristic, complemented
372#1879C2×C7311yescharacteristic, complemented
373#1854C2×C7311yescharacteristic, complemented
374#1776C2×C7311yescharacteristic, complemented
375C73#2681211yescharacteristic, direct product factor, Sylow
376C22×D8C22×C7311yescharacteristic
377C2×C4⋊Q8C22×C7311yescharacteristic
378C2×#124—21no—
379C2×#121C22×C7311yescharacteristic
380C2×#121C22×C7311yescharacteristic
381C2×C4×D4C22×C7311yescharacteristic
382C2×#117C22×C7311yescharacteristic
383#482—24no—
384#474—24no—
385C2×#107C22×C7311yescharacteristic
386C2×#107C22×C7311yescharacteristic
387C2×#106C22×C7311yescharacteristic
388C2×#106C22×C7311yescharacteristic
389C2×#106C22×C7311yescharacteristic
390C2×C4⋊C8C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×#102C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×C22⋊C8C22×C7311yescharacteristic
398C2×C22⋊C8C22×C7311yescharacteristic
399C2×#97C22×C7311yescharacteristic
400#394—21no—
401#393—21no—
402#390—21no—
403#390C22×C7311yescharacteristic
404#390C22×C7311yescharacteristic
405#390C22×C7311yescharacteristic
406#389C22×C7311yescharacteristic
407#388—21no—
408#388—21no—
409#386—21no—
410#380C22×C7311yescharacteristic
411C4×C4⋊C4C22×C7311yescharacteristic
412C4×C4⋊C4C22×C7311yescharacteristic
413C4×C22⋊C4—21no—
414C4×C22⋊C4C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#336C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421C22×Q8—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C7311yescharacteristic
425C22×D4C23×C7311yescharacteristic
426C23×C4—21no—
427C23×C4C23×C7311yescharacteristic
428C2×D8—22no—
429C2×D8—22no—
430C2×D8—41no—
431C22×C8C23×C7311yescharacteristic
432C22×C8C23×C7311yescharacteristic
433C22×C8C23×C7311yescharacteristic
434C22×C8C23×C7311yescharacteristic
435C4⋊Q8—22no—
436C4⋊Q8—41no—
437#124—44no—
438#121—22no—
439#121—22no—
440#121—22no—
441#121—41no—
442C4×D4—22no—
443C4×D4—41no—
444#117—22no—
445#117—41no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C7311yescharacteristic
466C2×C22⋊C4D4×C7311yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C7311yescharacteristic
471C2×C42C23×C7311yescharacteristic
472#107—22no—
473#107D4×C7314yescomplemented
474#106—22no—
475#106—22no—
476#106—41no—
477C4⋊C8—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484C22⋊C8—22no—
485C22⋊C8—22no—
486#97—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95D4×C7311yescharacteristic
492#95D4×C7311yescharacteristic
493C24—21no—
494C24—21no—
495C24C2×D4×C7311yescharacteristic
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—81no—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4—81no—
516C2×D4#41×C7312yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4C2×D4×C7311yescharacteristic
533C22×C4C2×D4×C7311yescharacteristic
534C22×C4C2×D4×C7311yescharacteristic
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C24×C7311yescharacteristic
538D8—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C2×D4×C7312yes—
550C2×C8#41×C7312yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—81no—
562C4⋊C4C2×D4×C7312yes—
563C4⋊C4C2×D4×C7312yes—
564C4⋊C4#41×C7312yes—
565C22⋊C4—24no—
566C22⋊C4—22no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—42no—
584C42—81no—
585C23—22no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23C22×D4×C7311yescharacteristic
607Q8—84no—
608D4—22no—
609D4—22no—
610D4—41no—
611D4—41no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—84no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
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—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4AGL(1,ℤ/8)×C7312yes—
656C2×C4C22×D4×C7311yescharacteristic
657C2×C4C2×#41×C7311yescharacteristic
658C2×C4C2×#41×C7311yescharacteristic
659C2×C4C2×#41×C7311yescharacteristic
660C2×C4H(5,𝔽2)×C7311yescharacteristic
661C2×C42−1+4×C7311yescharacteristic
662C8—22no—
663C8—22no—
664C8—41no—
665C8—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—42no—
674C22—41no—
675C22—42no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22#525×C7311yescharacteristic
688C22D42×C7311yescharacteristic
689C22#547×C7311yescharacteristic
690C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
691C22#575×C7311yescharacteristic
692C22#576×C7311yescharacteristic
693C22#577×C7311yescharacteristic
694C4—22no—
695C4—41no—
696C4—42no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—81no—
705C4#532×C7311yescharacteristic
706C4#542×C7311yescharacteristic
707C4#548×C7311yescharacteristic
708C4#551×C7311yescharacteristic
709C2—81no—
710C2—82no—
711C2—161no—
712C2C73×#246111yescharacteristic
713C2C73×#311511yescharacteristic
714C2C73×#311811yescharacteristic
715C2C73×#326411yescharacteristic
716C2C73×#327111yescharacteristic
717C2C73×#334711yescharacteristic
718C2C73×#335411yescharacteristic
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×#474×C73C2semidirect
3. C73×#2491C2semidirect
4. C73×#2363C2semidirect
5. C73×#2065C2semidirect
6. C73×#2058C2semidirect
7. C73×#2034C2semidirect
9. C73×#1972C2semidirect
10. C73×#1926C2semidirect
11. C73×#1925C2semidirect
12. C73×#1924C2semidirect
13. C73×#1879C2semidirect
14. C73×#1854C2semidirect
15. C73×#1776C2semidirect
113. #107×C73D4semidirect
349. #26812C73direct (N × H)
360. C2×#482C2×C73semidirect
361. C2×#474C2×C73semidirect
362. #2491C2×C73semidirect
363. #2363C2×C73semidirect
364. #2065C2×C73semidirect
365. #2058C2×C73semidirect
366. #2034C2×C73semidirect
368. #1972C2×C73semidirect
369. #1926C2×C73semidirect
370. #1925C2×C73semidirect
371. #1924C2×C73semidirect
372. #1879C2×C73semidirect
373. #1854C2×C73semidirect
374. #1776C2×C73semidirect
375. C73#26812direct (N × H)
473. #107D4×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×#474×C732
C73×#24912
C73×#23632
C73×#20652
C73×#20582
C73×#20342
C73×#19992
C73×#19722
C73×#19262
C73×#19252
C73×#19242
C73×#18792
C73×#18542
C73×#17762
#2681273