Finite Group Databasebeta

← C73×#24908 #32934312

Subgroups — C73×#24908 #32934312

Order 18688.

958 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C73C211yesmaximal, characteristic
2C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
3C73×#2421C211yesmaximal, characteristic, complemented
4C73×#2341C211yesmaximal, characteristic
5C73×#2092C211yesmaximal, characteristic, complemented
6C73×#2076C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2035C211yesmaximal, characteristic, complemented
9C73×#1934C211yesmaximal, characteristic, complemented
10C73×#1923C211yesmaximal, characteristic, complemented
11C73×#1880C211yesmaximal, characteristic, complemented
12C73×#1878C211yesmaximal, characteristic, complemented
13C73×#1865C211yesmaximal, characteristic, complemented
14C73×#1805C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic
16C22×#41×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×Q8×C73C2211yescharacteristic
22C2×C4×Q8×C73C2211yescharacteristic
23#452×C73—24no—
24C4×Q16×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39#400×C73—21no—
40#397×C73—21no—
41#391×C73C2211yescharacteristic
42#390×C73—21no—
43#390×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#388×C73—21no—
48#387×C73—21no—
49#382×C73C2211yescharacteristic
50#380×C73—21no—
51#380×C73C2211yescharacteristic
52#380×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
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—41no—
66C2×#41×C73—41no—
67C22×Q8×C73C2311yescharacteristic
68C22×Q8×C73C2311yescharacteristic
69C22×D4×C73—21no—
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73C2311yescharacteristic
73C2×Q16×C73—22no—
74C2×Q16×C73—22no—
75C2×Q16×C73D414yes—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—41no—
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22⋊Q8×C73—22no—
84C22⋊Q8×C73—41no—
85C4×Q8×C73—22no—
86C4×Q8×C73—22no—
87C4×Q8×C73—22no—
88C4×Q8×C73—41no—
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×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
114C2×C42×C73C2311yescharacteristic
115#107×C73—22no—
116#106×C73—41no—
117C4⋊C8×C73—41no—
118#103×C73—22no—
119#103×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—41no—
126C22⋊C8×C73—22no—
127C22⋊C8×C73—41no—
128C4×C8×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
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
140#41×C73—44no—
141#41×C73—44no—
142#41×C73—44no—
143#41×C73—44no—
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×Q8×C73C2×D412yes—
153C2×Q8×C73C2×D412yes—
154C2×Q8×C73#4112yes—
155C2×Q8×C73#4112yes—
156C2×D4×C73—24no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73#4112yes—
165C22×C4×C73—21no—
166C22×C4×C73—24no—
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—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2411yescharacteristic
187Q16×C73—28no—
188SD16×C73—44no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73C2×D412yes—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C22⋊C4×C73—22no—
217C22⋊C4×C73—41no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—81no—
223C22⋊C4×C73—81no—
224C22⋊C4×C73—81no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—42no—
230C42×C73—42no—
231C42×C73—42no—
232C23×C73—21no—
233C23×C73—22no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73C22×D411yescharacteristic
247Q8×C73—22no—
248Q8×C73—22no—
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—22no—
252Q8×C73—41no—
253Q8×C73—41no—
254Q8×C73#12314yes—
255D4×C73—22no—
256D4×C73—22no—
257D4×C73—48no—
258D4×C73—41no—
259D4×C73—41no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
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—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—48no—
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×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73#13512yes—
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73H(5,𝔽2)11yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C8×C73—22no—
308C8×C73—41no—
309C8×C73—41no—
310C8×C73—41no—
311C22×C73—41no—
312C22×C73—42no—
313C22×C73—41no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73#52511yescharacteristic
326C22×C73D4211yescharacteristic
327C22×C73#54611yescharacteristic
328C22×C73C2×#13511yescharacteristic
329C22×C73#57511yescharacteristic
330C22×C73#57711yescharacteristic
331C22×C73#57811yescharacteristic
332C4×C73—24no—
333C4×C73—22no—
334C4×C73—41no—
335C4×C73—42no—
336C4×C73—41no—
337C4×C73—41no—
338C4×C73—41no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73—81no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73C2×#12311yescharacteristic
345C4×C73#53811yescharacteristic
346C4×C73#54611yescharacteristic
347C4×C73#55111yescharacteristic
348#24908C7311yesmaximal, characteristic, direct product factor, Sylow
349C2×C73—81no—
350C2×C73—82no—
351C2×C73#241811yescharacteristic
352C2×C73#310211yescharacteristic
353C2×C73#312011yescharacteristic
354C2×C73#327111yescharacteristic
355C2×C73#328511yescharacteristic
356C2×C73#330411yescharacteristic
357C2×C73#332711yescharacteristic
358C2×#452C2×C7311yescharacteristic
359C2×C4×Q16C2×C7311yescharacteristic, complemented
360#2421C2×C7311yescharacteristic, complemented
361#2341C2×C7311yescharacteristic
362#2092C2×C7311yescharacteristic, complemented
363#2076C2×C7311yescharacteristic, complemented
364#2055C2×C7311yescharacteristic, complemented
365#2035C2×C7311yescharacteristic, complemented
366#1934C2×C7311yescharacteristic, complemented
367#1923C2×C7311yescharacteristic, complemented
368#1880C2×C7311yescharacteristic, complemented
369#1878C2×C7311yescharacteristic, complemented
370#1865C2×C7311yescharacteristic, complemented
371#1805C2×C7311yescharacteristic, complemented
372#1788C2×C7311yescharacteristic
373C73#2490811yescharacteristic, direct product factor, Sylow
374C22×#41C22×C7311yescharacteristic
375C22×Q16C22×C7311yescharacteristic
376C22×SD16C22×C7311yescharacteristic
377C2×C22⋊Q8C22×C7311yescharacteristic
378C2×C4×Q8C22×C7311yescharacteristic
379C2×C4×Q8C22×C7311yescharacteristic
380C2×C4×Q8C22×C7311yescharacteristic
381#452—24no—
382C4×Q16—24no—
383C2×#107C22×C7311yescharacteristic
384C2×#106C22×C7311yescharacteristic
385C2×C4⋊C8C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#103C22×C7311yescharacteristic
388C2×#103C22×C7311yescharacteristic
389C2×#103C22×C7311yescharacteristic
390C2×#103C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×C22⋊C8C22×C7311yescharacteristic
395C2×C22⋊C8C22×C7311yescharacteristic
396C2×C4×C8C22×C7311yescharacteristic
397#400—21no—
398#397—21no—
399#391C22×C7311yescharacteristic
400#390—21no—
401#390—21no—
402#390C22×C7311yescharacteristic
403#390C22×C7311yescharacteristic
404#389C22×C7311yescharacteristic
405#388—21no—
406#387—21no—
407#382C22×C7311yescharacteristic
408#380—21no—
409#380C22×C7311yescharacteristic
410#380C22×C7311yescharacteristic
411C4×C22⋊C4—21no—
412C4×C22⋊C4C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#336C22×C7311yescharacteristic
418#336C22×C7311yescharacteristic
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—41no—
424C2×#41—41no—
425C22×Q8C23×C7311yescharacteristic
426C22×Q8C23×C7311yescharacteristic
427C22×D4—21no—
428C22×D4C23×C7311yescharacteristic
429C23×C4—21no—
430C23×C4C23×C7311yescharacteristic
431C2×Q16—22no—
432C2×Q16—22no—
433C2×Q16D4×C7314yes—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—41no—
437C22×C8C23×C7311yescharacteristic
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440C22×C8C23×C7311yescharacteristic
441C22⋊Q8—22no—
442C22⋊Q8—41no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—41no—
447C4×Q8—41no—
448C4×Q8—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C4⋊C4C23×C7311yescharacteristic
458C2×C4⋊C4C23×C7311yescharacteristic
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×C42—21no—
471C2×C42C23×C7311yescharacteristic
472C2×C42C23×C7311yescharacteristic
473#107—22no—
474#106—41no—
475C4⋊C8—41no—
476#103—22no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—41no—
484C22⋊C8—22no—
485C22⋊C8—41no—
486C4×C8—22no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95D4×C7311yescharacteristic
495#95D4×C7311yescharacteristic
496C24—21no—
497C24C2×D4×C7311yescharacteristic
498#41—44no—
499#41—44no—
500#41—44no—
501#41—44no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8C2×D4×C7312yes—
511C2×Q8C2×D4×C7312yes—
512C2×Q8#41×C7312yes—
513C2×Q8#41×C7312yes—
514C2×D4—24no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4#41×C7312yes—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7311yescharacteristic
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C24×C7311yescharacteristic
545Q16—28no—
546SD16—44no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8C2×D4×C7312yes—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C22⋊C4—22no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—42no—
588C42—42no—
589C42—42no—
590C23—21no—
591C23—22no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C7311yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8#123×C7314yes—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
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—21no—
636C2×C4—48no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4#135×C7312yes—
659C2×C4C22×D4×C7311yescharacteristic
660C2×C4C2×#41×C7311yescharacteristic
661C2×C4C2×#41×C7311yescharacteristic
662C2×C4C2×#41×C7311yescharacteristic
663C2×C4H(5,𝔽2)×C7311yescharacteristic
664C2×C4H(5,𝔽2)×C7311yescharacteristic
665C8—22no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#525×C7311yescharacteristic
684C22D42×C7311yescharacteristic
685C22#546×C7311yescharacteristic
686C22C2×#135×C7311yescharacteristic
687C22#575×C7311yescharacteristic
688C22#577×C7311yescharacteristic
689C22#578×C7311yescharacteristic
690C4—22no—
691C4—24no—
692C4—41no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—42no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C2×#123×C7311yescharacteristic
703C4#538×C7311yescharacteristic
704C4#546×C7311yescharacteristic
705C4#551×C7311yescharacteristic
706C2—81no—
707C2—82no—
708C2C73×#241811yescharacteristic
709C2C73×#310211yescharacteristic
710C2C73×#312011yescharacteristic
711C2C73×#327111yescharacteristic
712C2C73×#328511yescharacteristic
713C2C73×#330411yescharacteristic
714C2C73×#332711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×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×C4×Q16×C73C2semidirect
3. C73×#2421C2semidirect
5. C73×#2092C2semidirect
6. C73×#2076C2semidirect
7. C73×#2055C2semidirect
8. C73×#2035C2semidirect
9. C73×#1934C2semidirect
10. C73×#1923C2semidirect
11. C73×#1880C2semidirect
12. C73×#1878C2semidirect
13. C73×#1865C2semidirect
14. C73×#1805C2semidirect
348. #24908C73direct (N × H)
359. C2×C4×Q16C2×C73semidirect
360. #2421C2×C73semidirect
362. #2092C2×C73semidirect
363. #2076C2×C73semidirect
364. #2055C2×C73semidirect
365. #2035C2×C73semidirect
366. #1934C2×C73semidirect
367. #1923C2×C73semidirect
368. #1880C2×C73semidirect
369. #1878C2×C73semidirect
370. #1865C2×C73semidirect
371. #1805C2×C73semidirect
373. C73#24908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#452×C732
C2×C4×Q16×C732
C73×#24212
C73×#23412
C73×#20922
C73×#20762
C73×#20552
C73×#20352
C73×#19342
C73×#19232
C73×#18802
C73×#18782
C73×#18652
C73×#18052
C73×#17882
#2490873