Finite Group Databasebeta

← C73×#25963 #32935367

Subgroups — C73×#25963 #32935367

Order 18688.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#477×C73C211yesmaximal, characteristic, complemented
2C22×#103×C73C211yesmaximal, characteristic
3C73×#2440C211yesmaximal, characteristic
4Q8×C22⋊C4×C73C211yesmaximal, characteristic
5C73×#2095C211yesmaximal, characteristic, complemented
6C73×#2068C211yesmaximal, characteristic, complemented
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2024C211yesmaximal, characteristic, complemented
9C73×#1863C211yesmaximal, characteristic, complemented
10C73×#1863C211yesmaximal, characteristic, complemented
11C73×#1852C211yesmaximal, characteristic
12C73×#1850C211yesmaximal, characteristic
13C73×#1808C211yesmaximal, characteristic
14C73×#1803C211yesmaximal, characteristic, complemented
15C73×#1787C211yesmaximal, characteristic
16C23×Q8×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73—21no—
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×Q8×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#477×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29C2×C4⋊C8×C73C2211yescharacteristic
30C2×#103×C73—24no—
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
40#398×C73—21no—
41#395×C73—21no—
42#391×C73—21no—
43#391×C73—21no—
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#385×C73—21no—
49#384×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
61C22×Q8×C73—21no—
62C22×Q8×C73—21no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—41no—
67C22×Q8×C73—41no—
68C22×Q8×C73Q814yescomplemented
69C22×Q8×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C22×C8×C73—22no—
75C22×C8×C73—22no—
76C22×C8×C73—41no—
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C4⋊Q8×C73—22no—
82C4⋊Q8×C73—41no—
83C22⋊Q8×C73—44no—
84C4×Q8×C73—22no—
85C4×Q8×C73—22no—
86C4×Q8×C73—41no—
87C4×Q8×C73—41no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
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—41no—
98C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
107C2×C22⋊C4×C73D411yescharacteristic
108C2×C42×C73—21no—
109C2×C42×C73—21no—
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#107×C73—22no—
113#107×C73—22no—
114#107×C73—41no—
115#107×C73—41no—
116C4⋊C8×C73—22no—
117C4⋊C8×C73—41no—
118#103×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×C73D414yes—
126C22⋊C8×C73—22no—
127#95×C73—21no—
128#95×C73—21no—
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×C73D411yescharacteristic
136#95×C73D411yescharacteristic
137C24×C73C2×D411yescharacteristic
138C2×Q8×C73—24no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—28no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—42no—
149C2×Q8×C73—42no—
150C2×Q8×C73—42no—
151C2×Q8×C73—44no—
152C2×Q8×C73—44no—
153C2×Q8×C73—44no—
154C2×Q8×C73—42no—
155C2×Q8×C73—81no—
156C2×Q8×C73C2×D412yes—
157C2×Q8×C73C2×Q812yes—
158C2×Q8×C73C2×Q812yes—
159C2×Q8×C73#4112yes—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—24no—
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—42no—
174C22×C4×C73—42no—
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×C73C2×D411yescharacteristic
183C22×C4×C73C2×Q812yes—
184C22×C4×C73#4112yes—
185C22×C4×C73C2411yescharacteristic
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×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—44no—
198C2×C8×C73C2×D412yes—
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—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—42no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73C2×D412yes—
219C22⋊C4×C73—22no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73Q1614yes—
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×C73C22⋊Q812yes—
234C23×C73C2×Q1612yes—
235C23×C73AGL(1,ℤ/8)12yes—
236C23×C73C22×D411yescharacteristic
237Q8×C73—22no—
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—22no—
241Q8×C73—22no—
242Q8×C73—48no—
243Q8×C73—41no—
244Q8×C73—41no—
245Q8×C73—84no—
246Q8×C73C22⋊Q814yescomplemented
247C2×C4×C73—22no—
248C2×C4×C73—21no—
249C2×C4×C73—22no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—22no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—48no—
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×C73C22⋊Q812yes—
290C2×C4×C73C2×Q1612yes—
291C2×C4×C73C2×Q1612yes—
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C22×Q811yescharacteristic
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—41no—
300C8×C73—41no—
301C8×C73—41no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73#47714yescomplemented
309C22×C73C2×C22⋊Q811yescharacteristic
310C22×C73D4211yescharacteristic
311C22×C73#54611yescharacteristic
312C22×C73C22×Q1611yescharacteristic
313C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C73#57711yescharacteristic
315C22×C73#57811yescharacteristic
316C4×C73—22no—
317C4×C73—24no—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—42no—
321C4×C73—41no—
322C4×C73—42no—
323C4×C73—41no—
324C4×C73—81no—
325C4×C73—81no—
326C4×C73—81no—
327C4×C73—81no—
328C4×C73—81no—
329C4×C73C2×C22⋊Q811yescharacteristic
330C4×C73#54311yescharacteristic
331C4×C73#54611yescharacteristic
332C4×C73#55111yescharacteristic
333#25963C7311yesmaximal, characteristic, direct product factor, Sylow
334C2×C73—24no—
335C2×C73#243711yescharacteristic
336C2×C73C2×#47711yescharacteristic
337C2×C73#308211yescharacteristic
338C2×C73#326511yescharacteristic
339C2×C73D4×Q1611yescharacteristic
340C2×C73#329911yescharacteristic
341C2×C73#330811yescharacteristic
342C2×#477C2×C7311yescharacteristic, complemented
343C22×#103C2×C7311yescharacteristic
344#2440C2×C7311yescharacteristic
345Q8×C22⋊C4C2×C7311yescharacteristic
346#2095C2×C7311yescharacteristic, complemented
347#2068C2×C7311yescharacteristic, complemented
348#2068C2×C7311yescharacteristic, complemented
349#2024C2×C7311yescharacteristic, complemented
350#1863C2×C7311yescharacteristic, complemented
351#1863C2×C7311yescharacteristic, complemented
352#1852C2×C7311yescharacteristic
353#1850C2×C7311yescharacteristic
354#1808C2×C7311yescharacteristic
355#1803C2×C7311yescharacteristic, complemented
356#1787C2×C7311yescharacteristic
357C73#2596311yescharacteristic, direct product factor, Sylow
358C23×Q8C22×C7311yescharacteristic
359C23×C8C22×C7311yescharacteristic
360C2×C4⋊Q8C22×C7311yescharacteristic
361C2×C22⋊Q8—21no—
362C2×C4×Q8C22×C7311yescharacteristic
363C2×C4×Q8C22×C7311yescharacteristic
364C22×C4⋊C4C22×C7311yescharacteristic
365#477—24no—
366C2×#107C22×C7311yescharacteristic
367C2×#107C22×C7311yescharacteristic
368C2×#107C22×C7311yescharacteristic
369C2×#107C22×C7311yescharacteristic
370C2×C4⋊C8C22×C7311yescharacteristic
371C2×C4⋊C8C22×C7311yescharacteristic
372C2×#103—24no—
373C2×#103C22×C7311yescharacteristic
374C2×#103C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#103C22×C7311yescharacteristic
377C2×#103C22×C7311yescharacteristic
378C2×#103C22×C7311yescharacteristic
379C2×#103C22×C7311yescharacteristic
380C2×#103C22×C7311yescharacteristic
381C2×C22⋊C8C22×C7311yescharacteristic
382#398—21no—
383#395—21no—
384#391—21no—
385#391—21no—
386#391C22×C7311yescharacteristic
387#391C22×C7311yescharacteristic
388#389C22×C7311yescharacteristic
389#389C22×C7311yescharacteristic
390#385—21no—
391#384C22×C7311yescharacteristic
392#380—21no—
393#380C22×C7311yescharacteristic
394#380C22×C7311yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399#340C22×C7311yescharacteristic
400#340C22×C7311yescharacteristic
401#336C22×C7311yescharacteristic
402#336C22×C7311yescharacteristic
403C22×Q8—21no—
404C22×Q8—21no—
405C22×Q8—22no—
406C22×Q8—22no—
407C22×Q8—22no—
408C22×Q8—41no—
409C22×Q8—41no—
410C22×Q8Q8×C7314yescomplemented
411C22×Q8C23×C7311yescharacteristic
412C22×Q8C23×C7311yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C23×C7311yescharacteristic
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—41no—
419C22×C8C23×C7311yescharacteristic
420C22×C8C23×C7311yescharacteristic
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C4⋊Q8—22no—
424C4⋊Q8—41no—
425C22⋊Q8—44no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—41no—
429C4×Q8—41no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C7311yescharacteristic
449C2×C22⋊C4D4×C7311yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42C23×C7311yescharacteristic
453C2×C42C23×C7311yescharacteristic
454#107—22no—
455#107—22no—
456#107—41no—
457#107—41no—
458C4⋊C8—22no—
459C4⋊C8—41no—
460#103—22no—
461#103—22no—
462#103—22no—
463#103—22no—
464#103—22no—
465#103—41no—
466#103—41no—
467#103D4×C7314yes—
468C22⋊C8—22no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95D4×C7311yescharacteristic
478#95D4×C7311yescharacteristic
479C24C2×D4×C7311yescharacteristic
480C2×Q8—24no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—28no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—42no—
497C2×Q8—81no—
498C2×Q8C2×D4×C7312yes—
499C2×Q8C2×Q8×C7312yes—
500C2×Q8C2×Q8×C7312yes—
501C2×Q8#41×C7312yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—81no—
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4C2×D4×C7311yescharacteristic
523C22×C4C2×D4×C7311yescharacteristic
524C22×C4C2×D4×C7311yescharacteristic
525C22×C4C2×Q8×C7312yes—
526C22×C4#41×C7312yes—
527C22×C4C24×C7311yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
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—44no—
540C2×C8C2×D4×C7312yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
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—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C7312yes—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4Q16×C7314yes—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—42no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C22⋊Q8×C7312yes—
576C23C2×Q16×C7312yes—
577C23AGL(1,ℤ/8)×C7312yes—
578C23C22×D4×C7311yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—48no—
585Q8—41no—
586Q8—41no—
587Q8—84no—
588Q8C22⋊Q8×C7314yescomplemented
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—48no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
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—84no—
631C2×C4C22⋊Q8×C7312yes—
632C2×C4C2×Q16×C7312yes—
633C2×C4C2×Q16×C7312yes—
634C2×C4C22×D4×C7311yescharacteristic
635C2×C4C22×Q8×C7311yescharacteristic
636C2×C4C2×#41×C7311yescharacteristic
637C2×C4C2×#41×C7311yescharacteristic
638C2×C4H(5,𝔽2)×C7311yescharacteristic
639C2×C4H(5,𝔽2)×C7311yescharacteristic
640C8—22no—
641C8—41no—
642C8—41no—
643C8—41no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#477×C7314yescomplemented
651C22C2×C22⋊Q8×C7311yescharacteristic
652C22D42×C7311yescharacteristic
653C22#546×C7311yescharacteristic
654C22C22×Q16×C7311yescharacteristic
655C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
656C22#577×C7311yescharacteristic
657C22#578×C7311yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—24no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C2×C22⋊Q8×C7311yescharacteristic
672C4#543×C7311yescharacteristic
673C4#546×C7311yescharacteristic
674C4#551×C7311yescharacteristic
675C2—24no—
676C2C73×#243711yescharacteristic
677C2C2×#477×C7311yescharacteristic
678C2C73×#308211yescharacteristic
679C2C73×#326511yescharacteristic
680C2D4×Q16×C7311yescharacteristic
681C2C73×#329911yescharacteristic
682C2C73×#330811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
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. C2×#477×C73C2semidirect
5. C73×#2095C2semidirect
6. C73×#2068C2semidirect
7. C73×#2068C2semidirect
8. C73×#2024C2semidirect
9. C73×#1863C2semidirect
10. C73×#1863C2semidirect
14. C73×#1803C2semidirect
68. C22×Q8×C73Q8semidirect
246. Q8×C73C22⋊Q8semidirect
308. C22×C73#477semidirect
333. #25963C73direct (N × H)
342. C2×#477C2×C73semidirect
346. #2095C2×C73semidirect
347. #2068C2×C73semidirect
348. #2068C2×C73semidirect
349. #2024C2×C73semidirect
350. #1863C2×C73semidirect
351. #1863C2×C73semidirect
355. #1803C2×C73semidirect
357. C73#25963direct (N × H)
410. C22×Q8Q8×C73semidirect
588. Q8C22⋊Q8×C73semidirect
650. C22#477×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#477×C732
C22×#103×C732
C73×#24402
Q8×C22⋊C4×C732
C73×#20952
C73×#20682
C73×#20242
C73×#18632
C73×#18522
C73×#18502
C73×#18082
C73×#18032
C73×#17872
#2596373