Finite Group Databasebeta

← C73×#22579 #32931983

Subgroups — C73×#22579 #32931983

Order 18688.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#417×C73C211yesmaximal, characteristic
2C73×#2345C211yesmaximal, characteristic, complemented
3C73×#2341C211yesmaximal, characteristic
4C73×#1936C211yesmaximal, characteristic, complemented
5C73×#1934C211yesmaximal, characteristic, complemented
6C73×#1926C211yesmaximal, characteristic, complemented
7C73×#1925C211yesmaximal, characteristic, complemented
8C73×#1865C211yesmaximal, characteristic, complemented
9C73×#1863C211yesmaximal, characteristic, complemented
10C73×#1823C211yesmaximal, characteristic, complemented
11C73×#1809C211yesmaximal, characteristic, complemented
12C73×#1788C211yesmaximal, characteristic
13C73×#1763C211yesmaximal, characteristic, complemented
14C4×#103×C73C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C4×Q8×C73C2211yescharacteristic
19C2×C4×Q8×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23#417×C73C418yescomplemented
24C2×#103×C73C2211yescharacteristic
25C2×#103×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×C22⋊C8×C73C2211yescharacteristic
33C2×#97×C73C2211yescharacteristic
34C2×C4×C8×C73C2211yescharacteristic
35#390×C73—21no—
36#390×C73—21no—
37#390×C73C2211yescharacteristic
38#390×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#387×C73—21no—
42#387×C73—21no—
43#380×C73—21no—
44#380×C73—21no—
45#380×C73C2211yescharacteristic
46#380×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C4⋊C4×C73C2211yescharacteristic
49C4×C22⋊C4×C73—21no—
50C4×C22⋊C4×C73—21no—
51C4×C22⋊C4×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C2×#41×C73—22no—
61C2×#41×C73—22no—
62C2×#41×C73—22no—
63C2×#41×C73—41no—
64C2×#41×C73—41no—
65C2×#41×C73C2×C414yes—
66C22×Q8×C73C2311yescharacteristic
67C22×D4×C73—21no—
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C2×M16×C73—41no—
73C2×M16×C73—41no—
74C2×M16×C73C2×C414yes—
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C4×Q8×C73—22no—
80C4×Q8×C73—22no—
81C4×Q8×C73—41no—
82C4×Q8×C73—41no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73C2×C414yes—
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×C73D411yescharacteristic
103C2×C22⋊C4×C73D411yescharacteristic
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73—21no—
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110#107×C73—41no—
111#106×C73—41no—
112#103×C73—22no—
113#103×C73—22no—
114#103×C73C2×C414yes—
115#103×C73C2×C414yes—
116#102×C73—41no—
117#102×C73—41no—
118#102×C73C2×C414yes—
119#102×C73C2×C414yes—
120C22⋊C8×C73—22no—
121#97×C73—41no—
122C4×C8×C73—41no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73D411yescharacteristic
130#95×C73D411yescharacteristic
131C24×C73—21no—
132C24×C73C2×D411yescharacteristic
133#41×C73—28no—
134#41×C73—44no—
135#41×C73—44no—
136#41×C73—44no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73C22×C412yes—
141C2×Q8×C73#4112yes—
142C2×Q8×C73#4112yes—
143C2×D4×C73—24no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—42no—
150C2×D4×C73—42no—
151C2×D4×C73C22×C412yes—
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—24no—
160C22×C4×C73—24no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—81no—
168C22×C4×C73—81no—
169C22×C4×C73C22×C412yes—
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73#4112yes—
176C22×C4×C73C2411yescharacteristic
177M16×C73—44no—
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—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73C22×C412yes—
189C2×C8×C73C22×C412yes—
190C4⋊C4×C73—24no—
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—21no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—81no—
204C4⋊C4×C73—81no—
205C4⋊C4×C73C22×C412yes—
206C4⋊C4×C73C22×C412yes—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—81no—
213C22⋊C4×C73—81no—
214C22⋊C4×C73—81no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—42no—
220C42×C73—42no—
221C42×C73—81no—
222C42×C73—81no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—22no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73C4×D412yes—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—22no—
241Q8×C73#11714yes—
242D4×C73—22no—
243D4×C73—22no—
244D4×C73—48no—
245D4×C73—41no—
246D4×C73—41no—
247C2×C4×C73—22no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—22no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—48no—
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—84no—
287C2×C4×C73C4×D412yes—
288C2×C4×C73#13712yes—
289C2×C4×C73C23×C411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73H(5,𝔽2)11yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C8×C73—22no—
296C8×C73—22no—
297C8×C73—41no—
298C8×C73—41no—
299C22×C73—22no—
300C22×C73—22no—
301C22×C73—22no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—42no—
307C22×C73—42no—
308C22×C73—42no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73C2×C4×D411yescharacteristic
314C22×C73#54611yescharacteristic
315C22×C73#54611yescharacteristic
316C22×C73C2×#13711yescharacteristic
317C22×C73#57511yescharacteristic
318C22×C73#57611yescharacteristic
319C22×C73#57711yescharacteristic
320C4×C73—22no—
321C4×C73—24no—
322C4×C73—22no—
323C4×C73—41no—
324C4×C73—42no—
325C4×C73—42no—
326C4×C73—41no—
327C4×C73—41no—
328C4×C73—81no—
329C4×C73—81no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73C2×#11711yescharacteristic
333C4×C73#51811yescharacteristic
334C4×C73#55111yescharacteristic
335C4×C73#55111yescharacteristic
336#22579C7311yesmaximal, characteristic, direct product factor, Sylow
337C2×C73—42no—
338C2×C73—82no—
339C2×C73#234211yescharacteristic
340C2×C73C4×#13711yescharacteristic
341C2×C73#294611yescharacteristic
342C2×C73#330911yescharacteristic
343C2×C73#331611yescharacteristic
344C2×C73#332611yescharacteristic
345C2×C73#333311yescharacteristic
346C2×#417C2×C7311yescharacteristic
347#2345C2×C7311yescharacteristic, complemented
348#2341C2×C7311yescharacteristic
349#1936C2×C7311yescharacteristic, complemented
350#1934C2×C7311yescharacteristic, complemented
351#1926C2×C7311yescharacteristic, complemented
352#1925C2×C7311yescharacteristic, complemented
353#1865C2×C7311yescharacteristic, complemented
354#1863C2×C7311yescharacteristic, complemented
355#1823C2×C7311yescharacteristic, complemented
356#1809C2×C7311yescharacteristic, complemented
357#1788C2×C7311yescharacteristic
358#1763C2×C7311yescharacteristic, complemented
359C4×#103C2×C7311yescharacteristic, complemented
360#1753C2×C7311yescharacteristic, complemented
361C73#2257911yescharacteristic, direct product factor, Sylow
362C22×#41C22×C7311yescharacteristic
363C22×M16C22×C7311yescharacteristic
364C2×C4×Q8C22×C7311yescharacteristic
365C2×C4×Q8C22×C7311yescharacteristic
366C22×C4⋊C4C22×C7311yescharacteristic
367C2×#107C22×C7311yescharacteristic
368C2×#106C22×C7311yescharacteristic
369#417C4×C7318yescomplemented
370C2×#103C22×C7311yescharacteristic
371C2×#103C22×C7311yescharacteristic
372C2×#103C22×C7311yescharacteristic
373C2×#103C22×C7311yescharacteristic
374C2×#102C22×C7311yescharacteristic
375C2×#102C22×C7311yescharacteristic
376C2×#102C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×C22⋊C8C22×C7311yescharacteristic
379C2×#97C22×C7311yescharacteristic
380C2×C4×C8C22×C7311yescharacteristic
381#390—21no—
382#390—21no—
383#390C22×C7311yescharacteristic
384#390C22×C7311yescharacteristic
385#389C22×C7311yescharacteristic
386#389C22×C7311yescharacteristic
387#387—21no—
388#387—21no—
389#380—21no—
390#380—21no—
391#380C22×C7311yescharacteristic
392#380C22×C7311yescharacteristic
393C4×C4⋊C4C22×C7311yescharacteristic
394C4×C4⋊C4C22×C7311yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4—21no—
397C4×C22⋊C4C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#336C22×C7311yescharacteristic
405#336C22×C7311yescharacteristic
406C2×#41—22no—
407C2×#41—22no—
408C2×#41—22no—
409C2×#41—41no—
410C2×#41—41no—
411C2×#41C2×C4×C7314yes—
412C22×Q8C23×C7311yescharacteristic
413C22×D4—21no—
414C22×D4C23×C7311yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4C23×C7311yescharacteristic
418C2×M16—41no—
419C2×M16—41no—
420C2×M16C2×C4×C7314yes—
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—41no—
428C4×Q8—41no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4C2×C4×C7314yes—
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7311yescharacteristic
438C2×C4⋊C4C23×C7311yescharacteristic
439C2×C4⋊C4C23×C7311yescharacteristic
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C7311yescharacteristic
449C2×C22⋊C4D4×C7311yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42—21no—
454C2×C42C23×C7311yescharacteristic
455C2×C42C23×C7311yescharacteristic
456#107—41no—
457#106—41no—
458#103—22no—
459#103—22no—
460#103C2×C4×C7314yes—
461#103C2×C4×C7314yes—
462#102—41no—
463#102—41no—
464#102C2×C4×C7314yes—
465#102C2×C4×C7314yes—
466C22⋊C8—22no—
467#97—41no—
468C4×C8—41no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95D4×C7311yescharacteristic
476#95D4×C7311yescharacteristic
477C24—21no—
478C24C2×D4×C7311yescharacteristic
479#41—28no—
480#41—44no—
481#41—44no—
482#41—44no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C22×C4×C7312yes—
487C2×Q8#41×C7312yes—
488C2×Q8#41×C7312yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C22×C4×C7312yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C22×C4×C7312yes—
516C22×C4C2×D4×C7311yescharacteristic
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4#41×C7312yes—
522C22×C4C24×C7311yescharacteristic
523M16—44no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8C22×C4×C7312yes—
535C2×C8C22×C4×C7312yes—
536C4⋊C4—24no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—81no—
551C4⋊C4C22×C4×C7312yes—
552C4⋊C4C22×C4×C7312yes—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—81no—
568C42—81no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C4×D4×C7312yes—
583C23C22×D4×C7311yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8#117×C7314yes—
588D4—22no—
589D4—22no—
590D4—48no—
591D4—41no—
592D4—41no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
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—84no—
633C2×C4C4×D4×C7312yes—
634C2×C4#137×C7312yes—
635C2×C4C23×C4×C7311yescharacteristic
636C2×C4C2×#41×C7311yescharacteristic
637C2×C4C2×#41×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4H(5,𝔽2)×C7311yescharacteristic
640C2×C4H(5,𝔽2)×C7311yescharacteristic
641C8—22no—
642C8—22no—
643C8—41no—
644C8—41no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22C2×C4×D4×C7311yescharacteristic
660C22#546×C7311yescharacteristic
661C22#546×C7311yescharacteristic
662C22C2×#137×C7311yescharacteristic
663C22#575×C7311yescharacteristic
664C22#576×C7311yescharacteristic
665C22#577×C7311yescharacteristic
666C4—22no—
667C4—22no—
668C4—24no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—42no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4C2×#117×C7311yescharacteristic
679C4#518×C7311yescharacteristic
680C4#551×C7311yescharacteristic
681C4#551×C7311yescharacteristic
682C2—42no—
683C2—82no—
684C2C73×#234211yescharacteristic
685C2C4×#137×C7311yescharacteristic
686C2C73×#294611yescharacteristic
687C2C73×#330911yescharacteristic
688C2C73×#331611yescharacteristic
689C2C73×#332611yescharacteristic
690C2C73×#333311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC22×#41×C73C22
LCSG ▷ C2×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. C73×#2345C2semidirect
4. C73×#1936C2semidirect
5. C73×#1934C2semidirect
6. C73×#1926C2semidirect
7. C73×#1925C2semidirect
8. C73×#1865C2semidirect
9. C73×#1863C2semidirect
10. C73×#1823C2semidirect
11. C73×#1809C2semidirect
13. C73×#1763C2semidirect
14. C4×#103×C73C2semidirect
15. C73×#1753C2semidirect
23. #417×C73C4semidirect
336. #22579C73direct (N × H)
347. #2345C2×C73semidirect
349. #1936C2×C73semidirect
350. #1934C2×C73semidirect
351. #1926C2×C73semidirect
352. #1925C2×C73semidirect
353. #1865C2×C73semidirect
354. #1863C2×C73semidirect
355. #1823C2×C73semidirect
356. #1809C2×C73semidirect
358. #1763C2×C73semidirect
359. C4×#103C2×C73semidirect
360. #1753C2×C73semidirect
361. C73#22579direct (N × H)
369. #417C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#417×C732
C73×#23452
C73×#23412
C73×#19362
C73×#19342
C73×#19262
C73×#19252
C73×#18652
C73×#18632
C73×#18232
C73×#18092
C73×#17882
C73×#17632
C4×#103×C732
C73×#17532
#2257973