Finite Group Databasebeta

← C73×#26247 #32935651

Subgroups — C73×#26247 #32935651

Order 18688.

870 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C73C211yesmaximal, characteristic, complemented
2C2×#483×C73C211yesmaximal, characteristic, complemented
3C73×#2542C211yesmaximal, characteristic
4C73×#2352C211yesmaximal, characteristic
5C73×#2036C211yesmaximal, characteristic, complemented
6C73×#2036C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2035C211yesmaximal, characteristic, complemented
9C73×#1981C211yesmaximal, characteristic, complemented
10C73×#1960C211yesmaximal, characteristic, complemented
11C73×#1955C211yesmaximal, characteristic
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1872C211yesmaximal, characteristic, complemented
15C73×#1776C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C73C2211yescharacteristic
17C2×C22⋊Q8×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24#485×C73—24no—
25#483×C73—24no—
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic
41C2×C22⋊C8×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×#97×C73C2211yescharacteristic
44#399×C73—21no—
45#399×C73—21no—
46#390×C73—21no—
47#388×C73—21no—
48#387×C73—21no—
49#386×C73—21no—
50#384×C73—21no—
51#382×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53#380×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56C4×C22⋊C4×C73—21no—
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73D411yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69C22×C8×C73C2311yescharacteristic
70C22×C8×C73C2311yescharacteristic
71C4⋊Q8×C73—22no—
72C4⋊Q8×C73—22no—
73C22⋊Q8×C73—22no—
74C22⋊Q8×C73—22no—
75C22⋊Q8×C73—22no—
76C22⋊Q8×C73—22no—
77C22⋊Q8×C73—41no—
78C22⋊Q8×C73—41no—
79C22⋊Q8×C73—41no—
80C22⋊Q8×C73—41no—
81C4×D4×C73—22no—
82C4×D4×C73—22no—
83#117×C73—22no—
84#117×C73—41no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—41no—
94C2×C4⋊C4×C73D411yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C22⋊C4×C73D411yescharacteristic
110C2×C42×C73—21no—
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73C2311yescharacteristic
114#107×C73—22no—
115#107×C73—22no—
116#106×C73—22no—
117#106×C73D414yescomplemented
118C4⋊C8×C73—22no—
119#103×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—41no—
124#103×C73—41no—
125#103×C73—41no—
126#103×C73—41no—
127C22⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—41no—
130C22⋊C8×C73—41no—
131#97×C73—22no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138C24×C73C2×D411yescharacteristic
139C24×C73C2×D411yescharacteristic
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×D4×C73—22no—
153C2×D4×C73—22no—
154C2×D4×C73—41no—
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—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—42no—
176C22×C4×C73—42no—
177C22×C4×C73—81no—
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2411yescharacteristic
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×C73—21no—
194C2×C8×C73C2×D412yes—
195C4⋊C4×C73—22no—
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—21no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—42no—
210C4⋊C4×C73—42no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73C2×D412yes—
213C4⋊C4×C73C2×D412yes—
214C4⋊C4×C73#4112yes—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—22no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—81no—
224C42×C73—42no—
225C42×C73—42no—
226C42×C73—81no—
227C42×C73#4112yes—
228C42×C73#4112yes—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73#13712yes—
243C23×C73C22×D411yescharacteristic
244Q8×C73—41no—
245Q8×C73—41no—
246Q8×C73—41no—
247Q8×C73—41no—
248Q8×C73—41no—
249Q8×C73—41no—
250Q8×C73—41no—
251Q8×C73—41no—
252D4×C73—44no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
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—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—84no—
296C2×C4×C73#12312yes—
297C2×C4×C73#12312yes—
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C8×C73—22no—
305C8×C73—41no—
306C8×C73—41no—
307C8×C73—41no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73C2×#12311yescharacteristic
323C22×C73D4211yescharacteristic
324C22×C73#54611yescharacteristic
325C22×C73C2×#13711yescharacteristic
326C22×C73#57511yescharacteristic
327C22×C73#57711yescharacteristic
328C22×C73#57811yescharacteristic
329C4×C73—22no—
330C4×C73—22no—
331C4×C73—41no—
332C4×C73—41no—
333C4×C73—42no—
334C4×C73—42no—
335C4×C73—42no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73#53211yescharacteristic
342C4×C73#54011yescharacteristic
343C4×C73#55011yescharacteristic
344C4×C73#55911yescharacteristic
345#26247C7311yesmaximal, characteristic, direct product factor, Sylow
346C2×C73—42no—
347C2×C73—81no—
348C2×C73#244511yescharacteristic
349C2×C73#309511yescharacteristic
350C2×C73#309711yescharacteristic
351C2×C73#326611yescharacteristic
352C2×C73#326911yescharacteristic
353C2×C73#330711yescharacteristic
354C2×C73#331211yescharacteristic
355C2×#485C2×C7311yescharacteristic, complemented
356C2×#483C2×C7311yescharacteristic, complemented
357#2542C2×C7311yescharacteristic
358#2352C2×C7311yescharacteristic
359#2036C2×C7311yescharacteristic, complemented
360#2036C2×C7311yescharacteristic, complemented
361#2036C2×C7311yescharacteristic, complemented
362#2035C2×C7311yescharacteristic, complemented
363#1981C2×C7311yescharacteristic, complemented
364#1960C2×C7311yescharacteristic, complemented
365#1955C2×C7311yescharacteristic
366#1949C2×C7311yescharacteristic, complemented
367#1873C2×C7311yescharacteristic, complemented
368#1872C2×C7311yescharacteristic, complemented
369#1776C2×C7311yescharacteristic, complemented
370C73#2624711yescharacteristic, direct product factor, Sylow
371C2×C4⋊Q8C22×C7311yescharacteristic
372C2×C22⋊Q8C22×C7311yescharacteristic
373C2×C22⋊Q8C22×C7311yescharacteristic
374C2×C22⋊Q8C22×C7311yescharacteristic
375C2×C22⋊Q8C22×C7311yescharacteristic
376C2×C4×D4C22×C7311yescharacteristic
377C2×#117C22×C7311yescharacteristic
378C22×C4⋊C4C22×C7311yescharacteristic
379#485—24no—
380#483—24no—
381C2×#107C22×C7311yescharacteristic
382C2×#107C22×C7311yescharacteristic
383C2×#106C22×C7311yescharacteristic
384C2×#106C22×C7311yescharacteristic
385C2×C4⋊C8C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#103C22×C7311yescharacteristic
388C2×#103C22×C7311yescharacteristic
389C2×#103C22×C7311yescharacteristic
390C2×#103C22×C7311yescharacteristic
391C2×#103C22×C7311yescharacteristic
392C2×#103C22×C7311yescharacteristic
393C2×#103C22×C7311yescharacteristic
394C2×C22⋊C8C22×C7311yescharacteristic
395C2×C22⋊C8C22×C7311yescharacteristic
396C2×C22⋊C8C22×C7311yescharacteristic
397C2×C22⋊C8C22×C7311yescharacteristic
398C2×#97C22×C7311yescharacteristic
399#399—21no—
400#399—21no—
401#390—21no—
402#388—21no—
403#387—21no—
404#386—21no—
405#384—21no—
406#382C22×C7311yescharacteristic
407#380C22×C7311yescharacteristic
408#380C22×C7311yescharacteristic
409C4×C4⋊C4C22×C7311yescharacteristic
410C4×C4⋊C4C22×C7311yescharacteristic
411C4×C22⋊C4—21no—
412#340C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416C22×Q8C23×C7311yescharacteristic
417C22×Q8C23×C7311yescharacteristic
418C22×D4D4×C7311yescharacteristic
419C23×C4—21no—
420C23×C4C23×C7311yescharacteristic
421C23×C4C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425C22×C8C23×C7311yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—41no—
433C22⋊Q8—41no—
434C22⋊Q8—41no—
435C22⋊Q8—41no—
436C4×D4—22no—
437C4×D4—22no—
438#117—22no—
439#117—41no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4D4×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4D4×C7311yescharacteristic
464C2×C22⋊C4D4×C7311yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C7311yescharacteristic
469#107—22no—
470#107—22no—
471#106—22no—
472#106D4×C7314yescomplemented
473C4⋊C8—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#103—22no—
478#103—41no—
479#103—41no—
480#103—41no—
481#103—41no—
482C22⋊C8—22no—
483C22⋊C8—22no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486#97—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493C24C2×D4×C7311yescharacteristic
494C24C2×D4×C7311yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—41no—
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—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4C2×D4×C7311yescharacteristic
534C22×C4C2×D4×C7311yescharacteristic
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C24×C7311yescharacteristic
538C2×C8—21no—
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—
550C4⋊C4—22no—
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—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4C2×D4×C7312yes—
568C4⋊C4C2×D4×C7312yes—
569C4⋊C4#41×C7312yes—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C42—42no—
580C42—42no—
581C42—81no—
582C42#41×C7312yes—
583C42#41×C7312yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23#137×C7312yes—
598C23C22×D4×C7311yescharacteristic
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607D4—44no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
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—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—84no—
651C2×C4#123×C7312yes—
652C2×C4#123×C7312yes—
653C2×C4C22×D4×C7311yescharacteristic
654C2×C4C2×#41×C7311yescharacteristic
655C2×C4C2×#41×C7311yescharacteristic
656C2×C4C2×#41×C7311yescharacteristic
657C2×C4H(5,𝔽2)×C7311yescharacteristic
658C2×C4H(5,𝔽2)×C7311yescharacteristic
659C8—22no—
660C8—41no—
661C8—41no—
662C8—41no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22C2×#123×C7311yescharacteristic
678C22D42×C7311yescharacteristic
679C22#546×C7311yescharacteristic
680C22C2×#137×C7311yescharacteristic
681C22#575×C7311yescharacteristic
682C22#577×C7311yescharacteristic
683C22#578×C7311yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4#532×C7311yescharacteristic
697C4#540×C7311yescharacteristic
698C4#550×C7311yescharacteristic
699C4#559×C7311yescharacteristic
700C2—42no—
701C2—81no—
702C2C73×#244511yescharacteristic
703C2C73×#309511yescharacteristic
704C2C73×#309711yescharacteristic
705C2C73×#326611yescharacteristic
706C2C73×#326911yescharacteristic
707C2C73×#330711yescharacteristic
708C2C73×#331211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C73C2semidirect
2. C2×#483×C73C2semidirect
5. C73×#2036C2semidirect
6. C73×#2036C2semidirect
7. C73×#2036C2semidirect
8. C73×#2035C2semidirect
9. C73×#1981C2semidirect
10. C73×#1960C2semidirect
12. C73×#1949C2semidirect
13. C73×#1873C2semidirect
14. C73×#1872C2semidirect
15. C73×#1776C2semidirect
117. #106×C73D4semidirect
345. #26247C73direct (N × H)
355. C2×#485C2×C73semidirect
356. C2×#483C2×C73semidirect
359. #2036C2×C73semidirect
360. #2036C2×C73semidirect
361. #2036C2×C73semidirect
362. #2035C2×C73semidirect
363. #1981C2×C73semidirect
364. #1960C2×C73semidirect
366. #1949C2×C73semidirect
367. #1873C2×C73semidirect
368. #1872C2×C73semidirect
369. #1776C2×C73semidirect
370. C73#26247direct (N × H)
472. #106D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C732
C2×#483×C732
C73×#25422
C73×#23522
C73×#20362
C73×#20352
C73×#19812
C73×#19602
C73×#19552
C73×#19492
C73×#18732
C73×#18722
C73×#17762
#2624773