Finite Group Databasebeta

← C73×#28975 #32938379

Subgroups — C73×#28975 #32938379

Order 18688.

888 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2491C211yesmaximal, characteristic, complemented
2C73×#2422C211yesmaximal, characteristic, complemented
3C73×#2075C211yesmaximal, characteristic, complemented
4C73×#2071C211yesmaximal, characteristic, complemented
5C73×#2023C211yesmaximal, characteristic, complemented
6C73×#1999C211yesmaximal, characteristic
7C73×#1990C211yesmaximal, characteristic, complemented
8C73×#1970C211yesmaximal, characteristic, complemented
9C73×#1934C211yesmaximal, characteristic, complemented
10C73×#1918C211yesmaximal, characteristic, complemented
11C73×#1893C211yesmaximal, characteristic, complemented
12C73×#1893C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C4×#102×C73C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×#124×C73—21no—
20C2×#123×C73—21no—
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24C2×#107×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×C22⋊C8×C73C2211yescharacteristic
32C2×C4×C8×C73C2211yescharacteristic
33C2×C4×C8×C73C2211yescharacteristic
34#397×C73—21no—
35#394×C73—21no—
36#394×C73—21no—
37#393×C73—21no—
38#390×C73C2211yescharacteristic
39#390×C73C2211yescharacteristic
40#390×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#388×C73—21no—
43#385×C73—21no—
44#384×C73C2211yescharacteristic
45#380×C73C2211yescharacteristic
46#380×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C22⋊C4×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73—21no—
60C22×D4×C73—21no—
61C22×D4×C73—21no—
62C22×D4×C73C2311yescharacteristic
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C2×D8×C73—22no—
67C2×D8×C73—22no—
68C2×D8×C73—41no—
69C22×C8×C73—22no—
70C22×C8×C73—41no—
71C22×C8×C73—41no—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C4⋊Q8×C73—22no—
77C4⋊Q8×C73—41no—
78#124×C73—44no—
79#123×C73—44no—
80#121×C73—22no—
81#121×C73—22no—
82#121×C73—41no—
83#121×C73—41no—
84C4×D4×C73—22no—
85C4×D4×C73—41no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C22⋊C4×C73D411yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#107×C73—22no—
113#102×C73—22no—
114#102×C73—22no—
115#102×C73—22no—
116#102×C73—41no—
117#102×C73—41no—
118#102×C73—41no—
119C22⋊C8×C73—22no—
120C4×C8×C73—41no—
121C4×C8×C73—41no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73D411yescharacteristic
127#95×C73D411yescharacteristic
128C24×C73—21no—
129C24×C73—21no—
130C24×C73C2×D411yescharacteristic
131C2×Q8×C73—42no—
132C2×Q8×C73—42no—
133C2×Q8×C73—81no—
134C2×D4×C73—21no—
135C2×D4×C73—21no—
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—42no—
146C2×D4×C73—42no—
147C2×D4×C73—42no—
148C2×D4×C73—42no—
149C2×D4×C73—81no—
150C2×D4×C73—81no—
151C2×D4×C73#4112yes—
152C22×C4×C73—21no—
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—42no—
165C22×C4×C73—42no—
166C22×C4×C73—81no—
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2411yescharacteristic
173D8×C73—44no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
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—44no—
185C2×C8×C73#4112yes—
186C2×C8×C73#4112yes—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
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—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73#4112yes—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
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—81no—
215C22⋊C4×C73D814yescomplemented
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—42no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—22no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
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×C73C2×D812yes—
242C23×C73C22×D411yescharacteristic
243Q8×C73—84no—
244D4×C73—22no—
245D4×C73—22no—
246D4×C73—41no—
247D4×C73—41no—
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—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—22no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
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—84no—
289C2×C4×C73C2×D812yes—
290C2×C4×C73C2×D812yes—
291C2×C4×C73#13512yes—
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C8×C73—22no—
299C8×C73—22no—
300C8×C73—41no—
301C8×C73—41no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—42no—
310C22×C73—42no—
311C22×C73—42no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
318C22×C73—81no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73#53211yescharacteristic
324C22×C73#54611yescharacteristic
325C22×C73#54611yescharacteristic
326C22×C73C22×D811yescharacteristic
327C22×C73C2×#13511yescharacteristic
328C22×C73#57711yescharacteristic
329C22×C73#57711yescharacteristic
330C4×C73—22no—
331C4×C73—22no—
332C4×C73—22no—
333C4×C73—42no—
334C4×C73—41no—
335C4×C73—41no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73#52911yescharacteristic
342C4×C73#53811yescharacteristic
343C4×C73#55111yescharacteristic
344C4×C73#55911yescharacteristic
345#28975C7311yesmaximal, characteristic, direct product factor, Sylow
346C2×C73—42no—
347C2×C73—82no—
348C2×C73—161no—
349C2×C73#255711yescharacteristic
350C2×C73#316911yescharacteristic
351C2×C73#317311yescharacteristic
352C2×C73#329411yescharacteristic
353C2×C73#329411yescharacteristic
354C2×C73#330111yescharacteristic
355C2×C73#330311yescharacteristic
356#2491C2×C7311yescharacteristic, complemented
357#2422C2×C7311yescharacteristic, complemented
358#2075C2×C7311yescharacteristic, complemented
359#2071C2×C7311yescharacteristic, complemented
360#2023C2×C7311yescharacteristic, complemented
361#1999C2×C7311yescharacteristic
362#1990C2×C7311yescharacteristic, complemented
363#1970C2×C7311yescharacteristic, complemented
364#1934C2×C7311yescharacteristic, complemented
365#1918C2×C7311yescharacteristic, complemented
366#1893C2×C7311yescharacteristic, complemented
367#1893C2×C7311yescharacteristic, complemented
368#1879C2×C7311yescharacteristic, complemented
369C4×#102C2×C7311yescharacteristic, complemented
370C8×C22⋊C4C2×C7311yescharacteristic, complemented
371C73#2897511yescharacteristic, direct product factor, Sylow
372C22×D8C22×C7311yescharacteristic
373C23×C8C22×C7311yescharacteristic
374C2×C4⋊Q8C22×C7311yescharacteristic
375C2×#124—21no—
376C2×#123—21no—
377C2×#121C22×C7311yescharacteristic
378C2×#121C22×C7311yescharacteristic
379C2×C4×D4C22×C7311yescharacteristic
380C2×#107C22×C7311yescharacteristic
381C2×#102C22×C7311yescharacteristic
382C2×#102C22×C7311yescharacteristic
383C2×#102C22×C7311yescharacteristic
384C2×#102C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×#102C22×C7311yescharacteristic
387C2×C22⋊C8C22×C7311yescharacteristic
388C2×C4×C8C22×C7311yescharacteristic
389C2×C4×C8C22×C7311yescharacteristic
390#397—21no—
391#394—21no—
392#394—21no—
393#393—21no—
394#390C22×C7311yescharacteristic
395#390C22×C7311yescharacteristic
396#390C22×C7311yescharacteristic
397#389C22×C7311yescharacteristic
398#388—21no—
399#385—21no—
400#384C22×C7311yescharacteristic
401#380C22×C7311yescharacteristic
402#380C22×C7311yescharacteristic
403C4×C4⋊C4C22×C7311yescharacteristic
404C4×C22⋊C4C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#340C22×C7311yescharacteristic
412#340C22×C7311yescharacteristic
413#336C22×C7311yescharacteristic
414#336C22×C7311yescharacteristic
415C22×Q8—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4C23×C7311yescharacteristic
419C22×D4C23×C7311yescharacteristic
420C23×C4—21no—
421C23×C4C23×C7311yescharacteristic
422C2×D8—22no—
423C2×D8—22no—
424C2×D8—41no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—41no—
428C22×C8C23×C7311yescharacteristic
429C22×C8C23×C7311yescharacteristic
430C22×C8C23×C7311yescharacteristic
431C22×C8C23×C7311yescharacteristic
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434#124—44no—
435#123—44no—
436#121—22no—
437#121—22no—
438#121—41no—
439#121—41no—
440C4×D4—22no—
441C4×D4—41no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C7311yescharacteristic
464C2×C22⋊C4D4×C7311yescharacteristic
465C2×C42—21no—
466C2×C42C23×C7311yescharacteristic
467C2×C42C23×C7311yescharacteristic
468#107—22no—
469#102—22no—
470#102—22no—
471#102—22no—
472#102—41no—
473#102—41no—
474#102—41no—
475C22⋊C8—22no—
476C4×C8—41no—
477C4×C8—41no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95D4×C7311yescharacteristic
483#95D4×C7311yescharacteristic
484C24—21no—
485C24—21no—
486C24C2×D4×C7311yescharacteristic
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—81no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
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—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4#41×C7312yes—
508C22×C4—21no—
509C22×C4—21no—
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—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4C2×D4×C7311yescharacteristic
524C22×C4C2×D4×C7311yescharacteristic
525C22×C4C2×D4×C7311yescharacteristic
526C22×C4C2×D4×C7311yescharacteristic
527C22×C4C2×D4×C7311yescharacteristic
528C22×C4C24×C7311yescharacteristic
529D8—44no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—44no—
541C2×C8#41×C7312yes—
542C2×C8#41×C7312yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—81no—
558C4⋊C4#41×C7312yes—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4D8×C7314yescomplemented
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C2×D8×C7312yes—
598C23C22×D4×C7311yescharacteristic
599Q8—84no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
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—84no—
645C2×C4C2×D8×C7312yes—
646C2×C4C2×D8×C7312yes—
647C2×C4#135×C7312yes—
648C2×C4C2×#41×C7311yescharacteristic
649C2×C4C2×#41×C7311yescharacteristic
650C2×C4C2×#41×C7311yescharacteristic
651C2×C4C2×#41×C7311yescharacteristic
652C2×C4H(5,𝔽2)×C7311yescharacteristic
653C2×C4H(5,𝔽2)×C7311yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22#532×C7311yescharacteristic
680C22#546×C7311yescharacteristic
681C22#546×C7311yescharacteristic
682C22C22×D8×C7311yescharacteristic
683C22C2×#135×C7311yescharacteristic
684C22#577×C7311yescharacteristic
685C22#577×C7311yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4#529×C7311yescharacteristic
698C4#538×C7311yescharacteristic
699C4#551×C7311yescharacteristic
700C4#559×C7311yescharacteristic
701C2—42no—
702C2—82no—
703C2—161no—
704C2C73×#255711yescharacteristic
705C2C73×#316911yescharacteristic
706C2C73×#317311yescharacteristic
707C2C73×#329411yescharacteristic
708C2C73×#329411yescharacteristic
709C2C73×#330111yescharacteristic
710C2C73×#330311yescharacteristic
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. C73×#2491C2semidirect
2. C73×#2422C2semidirect
3. C73×#2075C2semidirect
4. C73×#2071C2semidirect
5. C73×#2023C2semidirect
7. C73×#1990C2semidirect
8. C73×#1970C2semidirect
9. C73×#1934C2semidirect
10. C73×#1918C2semidirect
11. C73×#1893C2semidirect
12. C73×#1893C2semidirect
13. C73×#1879C2semidirect
14. C4×#102×C73C2semidirect
15. C8×C22⋊C4×C73C2semidirect
215. C22⋊C4×C73D8semidirect
345. #28975C73direct (N × H)
356. #2491C2×C73semidirect
357. #2422C2×C73semidirect
358. #2075C2×C73semidirect
359. #2071C2×C73semidirect
360. #2023C2×C73semidirect
362. #1990C2×C73semidirect
363. #1970C2×C73semidirect
364. #1934C2×C73semidirect
365. #1918C2×C73semidirect
366. #1893C2×C73semidirect
367. #1893C2×C73semidirect
368. #1879C2×C73semidirect
369. C4×#102C2×C73semidirect
370. C8×C22⋊C4C2×C73semidirect
371. C73#28975direct (N × H)
571. C22⋊C4D8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#24912
C73×#24222
C73×#20752
C73×#20712
C73×#20232
C73×#19992
C73×#19902
C73×#19702
C73×#19342
C73×#19182
C73×#18932
C73×#18792
C4×#102×C732
C8×C22⋊C4×C732
#2897573