Finite Group Databasebeta

← C73×#26980 #32936384

Subgroups — C73×#26980 #32936384

Order 18688.

880 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C73C211yesmaximal, characteristic
2C2×#441×C73C211yesmaximal, characteristic, complemented
3C73×#2426C211yesmaximal, characteristic
4C73×#2423C211yesmaximal, characteristic, complemented
5C73×#2084C211yesmaximal, characteristic, complemented
6C73×#2034C211yesmaximal, characteristic
7C73×#2015C211yesmaximal, characteristic, complemented
8C73×#2001C211yesmaximal, characteristic, complemented
9C73×#1959C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1935C211yesmaximal, characteristic, complemented
12C73×#1892C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1865C211yesmaximal, characteristic, complemented
15C73×#1752C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×#124×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×C4×Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25#465×C73—24no—
26#441×C73—24no—
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40#399×C73—21no—
41#398×C73—21no—
42#396×C73—21no—
43#394×C73—21no—
44#391×C73C2211yescharacteristic
45#390×C73—21no—
46#390×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#388×C73—21no—
50#388×C73—21no—
51#387×C73—21no—
52#384×C73C2211yescharacteristic
53#380×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×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66C2×Q16×C73—22no—
67C2×Q16×C73—22no—
68C2×Q16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—41no—
72C22×C8×C73—22no—
73C22×C8×C73—22no—
74C22×C8×C73—41no—
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79#124×C73—22no—
80#124×C73—41no—
81C22⋊Q8×C73—22no—
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—41no—
84C22⋊Q8×C73—41no—
85#121×C73—22no—
86#121×C73—41no—
87C4×Q8×C73—22no—
88C4×Q8×C73—22no—
89C4×Q8×C73—41no—
90C4×Q8×C73—41no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73D411yescharacteristic
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#106×C73—22no—
119#106×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—41no—
123#103×C73—41no—
124#103×C73D414yes—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—41no—
128C22⋊C8×C73—22no—
129#97×C73—22no—
130#97×C73—41no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73D411yescharacteristic
137#95×C73D411yescharacteristic
138C24×C73—21no—
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×C73C2×D412yes—
151C2×Q8×C73#4112yes—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—81no—
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×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180Q16×C73—28no—
181SD16×C73—44no—
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×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—44no—
192C2×C8×C73C2×D412yes—
193C2×C8×C73#4112yes—
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×C73—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—81no—
210C4⋊C4×C73—81no—
211C4⋊C4×C73—81no—
212C4⋊C4×C73C2×D412yes—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—41no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—81no—
222C22⋊C4×C73—81no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—42no—
228C42×C73—42no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73#13712yes—
243C23×C73C22×D411yescharacteristic
244Q8×C73—22no—
245Q8×C73—22no—
246Q8×C73—22no—
247Q8×C73—22no—
248Q8×C73—41no—
249Q8×C73—41no—
250Q8×C73—41no—
251Q8×C73—41no—
252D4×C73—41no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—84no—
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—21no—
264C2×C4×C73—21no—
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—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C8×C73—22no—
304C8×C73—22no—
305C8×C73—22no—
306C8×C73—41no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73#53211yescharacteristic
322C22×C73D4211yescharacteristic
323C22×C73#54611yescharacteristic
324C22×C73C2×#13711yescharacteristic
325C22×C73#57511yescharacteristic
326C22×C73#57711yescharacteristic
327C22×C73#57711yescharacteristic
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—42no—
331C4×C73—41no—
332C4×C73—42no—
333C4×C73—41no—
334C4×C73—41no—
335C4×C73—41no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73#52511yescharacteristic
341C4×C73#54011yescharacteristic
342C4×C73#54611yescharacteristic
343C4×C73#55311yescharacteristic
344#26980C7311yesmaximal, characteristic, direct product factor, Sylow
345C2×C73—42no—
346C2×C73—161no—
347C2×C73#246411yescharacteristic
348C2×C73#317311yescharacteristic
349C2×C73#318111yescharacteristic
350C2×C73#326611yescharacteristic
351C2×C73#327111yescharacteristic
352C2×C73#331611yescharacteristic
353C2×C73#331711yescharacteristic
354C2×#465C2×C7311yescharacteristic
355C2×#441C2×C7311yescharacteristic, complemented
356#2426C2×C7311yescharacteristic
357#2423C2×C7311yescharacteristic, complemented
358#2084C2×C7311yescharacteristic, complemented
359#2034C2×C7311yescharacteristic
360#2015C2×C7311yescharacteristic, complemented
361#2001C2×C7311yescharacteristic, complemented
362#1959C2×C7311yescharacteristic, complemented
363#1936C2×C7311yescharacteristic, complemented
364#1935C2×C7311yescharacteristic, complemented
365#1892C2×C7311yescharacteristic, complemented
366#1880C2×C7311yescharacteristic, complemented
367#1865C2×C7311yescharacteristic, complemented
368#1752C2×C7311yescharacteristic, complemented
369C73#2698011yescharacteristic, direct product factor, Sylow
370C22×Q16C22×C7311yescharacteristic
371C22×SD16C22×C7311yescharacteristic
372C23×C8C22×C7311yescharacteristic
373C2×#124C22×C7311yescharacteristic
374C2×C22⋊Q8C22×C7311yescharacteristic
375C2×C22⋊Q8C22×C7311yescharacteristic
376C2×#121C22×C7311yescharacteristic
377C2×C4×Q8C22×C7311yescharacteristic
378C2×C4×Q8C22×C7311yescharacteristic
379#465—24no—
380#441—24no—
381C2×#106C22×C7311yescharacteristic
382C2×#106C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#103C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#103C22×C7311yescharacteristic
388C2×#102C22×C7311yescharacteristic
389C2×#102C22×C7311yescharacteristic
390C2×#102C22×C7311yescharacteristic
391C2×C22⋊C8C22×C7311yescharacteristic
392C2×#97C22×C7311yescharacteristic
393C2×#97C22×C7311yescharacteristic
394#399—21no—
395#398—21no—
396#396—21no—
397#394—21no—
398#391C22×C7311yescharacteristic
399#390—21no—
400#390C22×C7311yescharacteristic
401#389C22×C7311yescharacteristic
402#389C22×C7311yescharacteristic
403#388—21no—
404#388—21no—
405#387—21no—
406#384C22×C7311yescharacteristic
407#380C22×C7311yescharacteristic
408C4×C22⋊C4C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#336C22×C7311yescharacteristic
414#336C22×C7311yescharacteristic
415C22×Q8C23×C7311yescharacteristic
416C22×Q8C23×C7311yescharacteristic
417C22×D4—21no—
418C22×D4C23×C7311yescharacteristic
419C23×C4C23×C7311yescharacteristic
420C2×Q16—22no—
421C2×Q16—22no—
422C2×Q16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—41no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—41no—
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432C22×C8C23×C7311yescharacteristic
433#124—22no—
434#124—41no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—41no—
439#121—22no—
440#121—41no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
466C2×C22⋊C4D4×C7311yescharacteristic
467C2×C22⋊C4D4×C7311yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C7311yescharacteristic
471C2×C42C23×C7311yescharacteristic
472#106—22no—
473#106—22no—
474#103—22no—
475#103—22no—
476#103—41no—
477#103—41no—
478#103D4×C7314yes—
479#102—22no—
480#102—22no—
481#102—41no—
482C22⋊C8—22no—
483#97—22no—
484#97—41no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95D4×C7311yescharacteristic
491#95D4×C7311yescharacteristic
492C24—21no—
493C24C2×D4×C7311yescharacteristic
494C2×Q8—21no—
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×Q8C2×D4×C7312yes—
505C2×Q8#41×C7312yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—81no—
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×C4C2×D4×C7311yescharacteristic
529C22×C4C2×D4×C7311yescharacteristic
530C22×C4C2×D4×C7311yescharacteristic
531C22×C4C2×D4×C7311yescharacteristic
532C22×C4C2×D4×C7311yescharacteristic
533C22×C4C24×C7311yescharacteristic
534Q16—28no—
535SD16—44no—
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×C8—44no—
546C2×C8C2×D4×C7312yes—
547C2×C8#41×C7312yes—
548C2×C8#41×C7312yes—
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—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—81no—
564C4⋊C4—81no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C7312yes—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C22⋊C4—81no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—42no—
582C42—42no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23#137×C7312yes—
597C23C22×D4×C7311yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—84no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
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—21no—
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—41no—
651C2×C4C22×D4×C7311yescharacteristic
652C2×C4C2×#41×C7311yescharacteristic
653C2×C4C2×#41×C7311yescharacteristic
654C2×C4C2×#41×C7311yescharacteristic
655C2×C4H(5,𝔽2)×C7311yescharacteristic
656C2×C4H(5,𝔽2)×C7311yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8—41no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22#532×C7311yescharacteristic
676C22D42×C7311yescharacteristic
677C22#546×C7311yescharacteristic
678C22C2×#137×C7311yescharacteristic
679C22#575×C7311yescharacteristic
680C22#577×C7311yescharacteristic
681C22#577×C7311yescharacteristic
682C4—41no—
683C4—42no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—41no—
688C4—41no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4#525×C7311yescharacteristic
695C4#540×C7311yescharacteristic
696C4#546×C7311yescharacteristic
697C4#553×C7311yescharacteristic
698C2—42no—
699C2—161no—
700C2C73×#246411yescharacteristic
701C2C73×#317311yescharacteristic
702C2C73×#318111yescharacteristic
703C2C73×#326611yescharacteristic
704C2C73×#327111yescharacteristic
705C2C73×#331611yescharacteristic
706C2C73×#331711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
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
2. C2×#441×C73C2semidirect
4. C73×#2423C2semidirect
5. C73×#2084C2semidirect
7. C73×#2015C2semidirect
8. C73×#2001C2semidirect
9. C73×#1959C2semidirect
10. C73×#1936C2semidirect
11. C73×#1935C2semidirect
12. C73×#1892C2semidirect
13. C73×#1880C2semidirect
14. C73×#1865C2semidirect
15. C73×#1752C2semidirect
344. #26980C73direct (N × H)
355. C2×#441C2×C73semidirect
357. #2423C2×C73semidirect
358. #2084C2×C73semidirect
360. #2015C2×C73semidirect
361. #2001C2×C73semidirect
362. #1959C2×C73semidirect
363. #1936C2×C73semidirect
364. #1935C2×C73semidirect
365. #1892C2×C73semidirect
366. #1880C2×C73semidirect
367. #1865C2×C73semidirect
368. #1752C2×C73semidirect
369. C73#26980direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#465×C732
C2×#441×C732
C73×#24262
C73×#24232
C73×#20842
C73×#20342
C73×#20152
C73×#20012
C73×#19592
C73×#19362
C73×#19352
C73×#18922
C73×#18802
C73×#18652
C73×#17522
#2698073