Finite Group Databasebeta

← C7×#11021 #13188237

Subgroups — C7×#11021 #13188237

Order 1792.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×#137C211yesmaximal, characteristic
2C2×C7×#417C211yesmaximal, characteristic
3C22×C7×#103C211yesmaximal, characteristic, complemented
4C22×C7×#101C211yesmaximal, characteristic, complemented
5C2×C7×#408C211yesmaximal, characteristic
6C2×C7×#343C211yesmaximal, characteristic, complemented
7C2×C7×#341C211yesmaximal, characteristic, complemented
8C22×C7×#41C2211yescharacteristic
9C23×C7×Q8C2211yescharacteristic
10C2×C7×#137—22no—
11C2×C7×#137—22no—
12C2×C7×#137—22no—
13C2×C7×#137—22no—
14C2×C7×#137—22no—
15C2×C7×#137C414yescomplemented
16C22×C7×Q16—21no—
17C22×C7×SD16—21no—
18C22×C7×M16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C22×C7×M16C2211yescharacteristic
21C23×C7×C8C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C7×#417—22no—
24C7×#417—22no—
25C2×C7×#103—22no—
26C2×C7×#103—21no—
27C2×C7×#103—22no—
28C2×C7×#103—22no—
29C2×C7×#102—21no—
30C2×C7×#101—22no—
31C2×C7×#101—22no—
32C2×C7×#101—22no—
33C7×#408—22no—
34C7×#408—22no—
35C2×C7×C22⋊C8—22no—
36C7×#343—22no—
37C7×#341—22no—
38#11021C711yesmaximal, characteristic, direct product factor, Sylow
39C2×C7×#41—21no—
40C2×C7×#41—21no—
41C2×C7×#41—21no—
42C2×C7×#41—21no—
43C2×C7×#41—21no—
44C2×C7×#41—21no—
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41C2×C412yes—
50C2×C7×#41D412yes—
51C22×C7×Q8—21no—
52C22×C7×Q8—21no—
53C22×C7×Q8—21no—
54C22×C7×Q8—21no—
55C22×C7×Q8—21no—
56C22×C7×Q8—21no—
57C22×C7×Q8—21no—
58C22×C7×Q8—21no—
59C22×C7×Q8—21no—
60C22×C7×Q8—21no—
61C22×C7×Q8—21no—
62C22×C7×Q8C2×C412yes—
63C22×C7×Q8D412yes—
64C22×C7×Q8D412yes—
65C22×C7×Q8D411yescharacteristic
66C22×C7×D4—21no—
67C22×C7×D4D411yescharacteristic
68C23×C4×C7—21no—
69C23×C4×C7—21no—
70C23×C4×C7—21no—
71C23×C4×C7C2311yescharacteristic
72C7×#137—28no—
73C7×#137—28no—
74C7×#137—28no—
75C7×#137—28no—
76C2×C7×Q16—24no—
77C2×C7×Q16—24no—
78C2×C7×Q16—24no—
79C2×C7×SD16—24no—
80C2×C7×SD16—24no—
81C2×C7×SD16—24no—
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C2×C7×M16—21no—
85C2×C7×M16—21no—
86C2×C7×M16—21no—
87C2×C7×M16—21no—
88C2×C7×M16—21no—
89C2×C7×M16—21no—
90C2×C7×M16—21no—
91C2×C7×M16—21no—
92C2×C7×M16—21no—
93C2×C7×M16—21no—
94C2×C7×M16—21no—
95C2×C7×M16C2×C412yes—
96C2×C7×M16D412yes—
97C2×C7×M16D412yes—
98C2×C7×M16D412yes—
99C2×C7×M16D412yes—
100C22×C7×C8—21no—
101C22×C7×C8—21no—
102C22×C7×C8—21no—
103C22×C7×C8—21no—
104C22×C7×C8—21no—
105C22×C7×C8—21no—
106C22×C7×C8—21no—
107C22×C7×C8—21no—
108C22×C7×C8—21no—
109C22×C7×C8D412yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4—21no—
115C2×C7×C4⋊C4D412yes—
116C7×#103—28no—
117C7×#103—24no—
118C7×#102—24no—
119C7×#101—28no—
120C7×C22⋊C8—28no—
121C22×#137C2×C711yescharacteristic
122C2×#417C2×C711yescharacteristic
123C22×#103C2×C711yescharacteristic, complemented
124C22×#101C2×C711yescharacteristic, complemented
125C2×#408C2×C711yescharacteristic
126C2×#343C2×C711yescharacteristic, complemented
127C2×#341C2×C711yescharacteristic, complemented
128C24×C7—21no—
129C24×C7#4111yescharacteristic
130C7×#41—22no—
131C7×#41—22no—
132C7×#41—22no—
133C7×#41—22no—
134C7×#41—22no—
135C7×#41—22no—
136C7×#41—22no—
137C7×#41—22no—
138C7×#41—41no—
139C7×#41—41no—
140C7×#41—41no—
141C7×#41—41no—
142C7×#41—41no—
143C7×#41—41no—
144C7×#41—41no—
145C7×#41—41no—
146C2×C7×Q8—22no—
147C2×C7×Q8—22no—
148C2×C7×Q8—22no—
149C2×C7×Q8—21no—
150C2×C7×Q8—22no—
151C2×C7×Q8—22no—
152C2×C7×Q8—22no—
153C2×C7×Q8—22no—
154C2×C7×Q8—22no—
155C2×C7×Q8—21no—
156C2×C7×Q8—22no—
157C2×C7×Q8—22no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—22no—
161C2×C7×Q8—22no—
162C2×C7×Q8—22no—
163C2×C7×Q8—22no—
164C2×C7×Q8—22no—
165C2×C7×Q8—21no—
166C2×C7×Q8—41no—
167C2×C7×Q8—41no—
168C2×C7×Q8—41no—
169C2×C7×Q8—41no—
170C2×C7×Q8—41no—
171C2×C7×Q8—41no—
172C2×C7×Q8—41no—
173C2×C7×Q8—41no—
174C2×C7×Q8—41no—
175C2×C7×Q8—41no—
176C2×C7×Q8—41no—
177C2×C7×Q8—41no—
178C2×C7×Q8C22⋊C412yes—
179C2×C7×Q8C22⋊C414yes—
180C2×C7×D4—22no—
181C2×C7×D4—22no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
187C2×C7×D4—41no—
188C2×C7×D4—41no—
189C2×C7×D4—41no—
190C2×C7×D4—41no—
191C2×C7×D4C22⋊C412yes—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—21no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—41no—
200C22×C4×C7—41no—
201C22×C4×C7—41no—
202C22×C4×C7—41no—
203C22×C4×C7—41no—
204C22×C4×C7—41no—
205C22×C4×C7—41no—
206C22×C4×C7—41no—
207C22×C4×C7—41no—
208C22×C4×C7—41no—
209C22×C4×C7—82no—
210C22×C4×C7C22×C411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7#4111yescharacteristic
222C22×C4×C7#4111yescharacteristic
223C22×C4×C7#4111yescharacteristic
224C7×Q16—216no—
225C7×SD16—216no—
226C7×M16—22no—
227C7×M16—22no—
228C7×M16—22no—
229C7×M16—22no—
230C7×M16—22no—
231C7×M16—22no—
232C7×M16—22no—
233C7×M16—41no—
234C7×M16—41no—
235C7×M16—41no—
236C7×M16—41no—
237C7×M16C22⋊C414yes—
238C2×C7×C8—22no—
239C2×C7×C8—22no—
240C2×C7×C8—22no—
241C2×C7×C8—22no—
242C2×C7×C8—22no—
243C2×C7×C8—22no—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8—41no—
247C2×C7×C8—41no—
248C2×C7×C8—41no—
249C2×C7×C8—41no—
250C2×C7×C8—41no—
251C2×C7×C8—41no—
252C2×C7×C8—41no—
253C2×C7×C8—41no—
254C7×C4⋊C4—22no—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—41no—
257C7×C4⋊C4—41no—
258C22×#41C22×C711yescharacteristic
259C23×Q8C22×C711yescharacteristic
260C2×#137—22no—
261C2×#137—22no—
262C2×#137—22no—
263C2×#137—22no—
264C2×#137—22no—
265C2×#137C4×C714yescomplemented
266C22×Q16—21no—
267C22×SD16—21no—
268C22×M16C22×C711yescharacteristic
269C22×M16C22×C711yescharacteristic
270C22×M16C22×C711yescharacteristic
271C23×C8C22×C711yescharacteristic
272C22×C4⋊C4C22×C711yescharacteristic
273#417—22no—
274#417—22no—
275C2×#103—22no—
276C2×#103—21no—
277C2×#103—22no—
278C2×#103—22no—
279C2×#102—21no—
280C2×#101—22no—
281C2×#101—22no—
282C2×#101—22no—
283#408—22no—
284#408—22no—
285C2×C22⋊C8—22no—
286#343—22no—
287#341—22no—
288C23×C7—22no—
289C23×C7—22no—
290C23×C7—22no—
291C23×C7—41no—
292C23×C7—41no—
293C23×C7—42no—
294C23×C7—42no—
295C23×C7C4×D411yescharacteristic
296C23×C7#12111yescharacteristic
297C23×C7#12111yescharacteristic
298C23×C7#12111yescharacteristic
299C23×C7#12311yescharacteristic
300C23×C7#12311yescharacteristic
301C23×C7#12411yescharacteristic
302C7×Q8—24no—
303C7×Q8—22no—
304C7×Q8—24no—
305C7×Q8—22no—
306C7×Q8—42no—
307C7×Q8—42no—
308C7×Q8—42no—
309C7×Q8—42no—
310C7×Q8—42no—
311C7×Q8—41no—
312C7×Q8—42no—
313C7×Q8—41no—
314C7×D4—22no—
315C7×D4—22no—
316C7×D4—42no—
317C7×D4—42no—
318C7×D4—42no—
319C7×D4—42no—
320C7×D4—41no—
321C7×D4—41no—
322C2×C4×C7—22no—
323C2×C4×C7—24no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—41no—
327C2×C4×C7—42no—
328C2×C4×C7—41no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—82no—
338C2×C4×C7—82no—
339C2×C4×C7—82no—
340C2×C4×C7C2×C22⋊C411yescharacteristic
341C2×C4×C7C2×C22⋊C411yescharacteristic
342C2×C4×C7C2×C22⋊C411yescharacteristic
343C2×C4×C7C4×D411yescharacteristic
344C2×C4×C7C4×D411yescharacteristic
345C2×C4×C7C4×D411yescharacteristic
346C2×C4×C7#12011yescharacteristic
347C2×C4×C7#12011yescharacteristic
348C2×C4×C7#12011yescharacteristic
349C2×C4×C7#12011yescharacteristic
350C2×C4×C7#12011yescharacteristic
351C2×C4×C7#12011yescharacteristic
352C2×C4×C7#12011yescharacteristic
353C2×C4×C7#12011yescharacteristic
354C2×C4×C7#12111yescharacteristic
355C2×C4×C7#12111yescharacteristic
356C2×C4×C7#12111yescharacteristic
357C2×C4×C7#12111yescharacteristic
358C2×C4×C7#12111yescharacteristic
359C2×C4×C7#12111yescharacteristic
360C2×C4×C7#12111yescharacteristic
361C2×C4×C7#12111yescharacteristic
362C2×C4×C7#12111yescharacteristic
363C2×C4×C7#12311yescharacteristic
364C2×C4×C7#12311yescharacteristic
365C2×C4×C7#12411yescharacteristic
366C2×C4×C7#12711yescharacteristic
367C2×C4×C7#12711yescharacteristic
368C7×C8—24no—
369C7×C8—42no—
370C7×C8—42no—
371C7×C8—42no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41C2×C4×C712yes—
383C2×#41C7×D412yes—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—21no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8C2×C4×C712yes—
396C22×Q8C7×D411yescharacteristic
397C22×Q8C7×D412yes—
398C22×Q8C7×D412yes—
399C22×D4—21no—
400C22×D4C7×D411yescharacteristic
401C23×C4—21no—
402C23×C4—21no—
403C23×C4—21no—
404C23×C4C23×C711yescharacteristic
405#137—28no—
406#137—28no—
407#137—28no—
408#137—28no—
409C2×Q16—24no—
410C2×Q16—24no—
411C2×Q16—24no—
412C2×SD16—24no—
413C2×SD16—24no—
414C2×SD16—24no—
415C2×M16—21no—
416C2×M16—21no—
417C2×M16—21no—
418C2×M16—21no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16—21no—
422C2×M16—21no—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16C2×C4×C712yes—
429C2×M16C7×D412yes—
430C2×M16C7×D412yes—
431C2×M16C7×D412yes—
432C2×M16C7×D412yes—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—21no—
437C22×C8—21no—
438C22×C8—21no—
439C22×C8—21no—
440C22×C8—21no—
441C22×C8—21no—
442C22×C8C7×D412yes—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4C7×D412yes—
449#103—28no—
450#103—24no—
451#102—24no—
452#101—28no—
453C22⋊C8—28no—
454C22×C7—22no—
455C22×C7—22no—
456C22×C7—22no—
457C22×C7—22no—
458C22×C7—21no—
459C22×C7—21no—
460C22×C7—21no—
461C22×C7—21no—
462C22×C7—44no—
463C22×C7—42no—
464C22×C7—82no—
465C22×C7—81no—
466C22×C7—81no—
467C22×C7#38611yescharacteristic
468C22×C7#38611yescharacteristic
469C22×C7#39011yescharacteristic
470C22×C7#39211yescharacteristic
471C22×C7#39411yescharacteristic
472C22×C7#39411yescharacteristic
473C22×C7#39411yescharacteristic
474C22×C7#47112yes—
475C22×C7#47312yes—
476C4×C7—42no—
477C4×C7—44no—
478C4×C7—82no—
479C4×C7#37911yescharacteristic
480C4×C7#38611yescharacteristic
481C4×C7#38611yescharacteristic
482C4×C7#39011yescharacteristic
483C4×C7#39211yescharacteristic
484C4×C7#39211yescharacteristic
485C4×C7#39211yescharacteristic
486C4×C7#39411yescharacteristic
487C24—21no—
488C24C7×#4111yescharacteristic
489#41—22no—
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—41no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—21no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—21no—
525C2×Q8—41no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8C7×C22⋊C412yes—
538C2×Q8C7×C22⋊C414yes—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4C7×C22⋊C412yes—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—82no—
569C22×C4C22×C4×C711yescharacteristic
570C22×C4C2×C7×D411yescharacteristic
571C22×C4C2×C7×D411yescharacteristic
572C22×C4C2×C7×D411yescharacteristic
573C22×C4C2×C7×D411yescharacteristic
574C22×C4C2×C7×D411yescharacteristic
575C22×C4C2×C7×D411yescharacteristic
576C22×C4C2×C7×D411yescharacteristic
577C22×C4C2×C7×D411yescharacteristic
578C22×C4C2×C7×D411yescharacteristic
579C22×C4C2×C7×D411yescharacteristic
580C22×C4C7×#4111yescharacteristic
581C22×C4C7×#4111yescharacteristic
582C22×C4C7×#4111yescharacteristic
583Q16—216no—
584SD16—216no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—22no—
590M16—22no—
591M16—22no—
592M16—41no—
593M16—41no—
594M16—41no—
595M16—41no—
596M16C7×C22⋊C414yes—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—41no—
606C2×C8—41no—
607C2×C8—41no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—41no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—41no—
616C4⋊C4—41no—
617C2×C7—21no—
618C2×C7—21no—
619C2×C7—21no—
620C2×C7—21no—
621C2×C7—82no—
622C2×C7#143811yescharacteristic
623C2×C7#190812yes—
624C2×C7#201911yescharacteristic
625C2×C7#202011yescharacteristic
626C2×C7#205212yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23C4×C7×D411yescharacteristic
635C23C7×#12111yescharacteristic
636C23C7×#12111yescharacteristic
637C23C7×#12111yescharacteristic
638C23C7×#12311yescharacteristic
639C23C7×#12311yescharacteristic
640C23C7×#12411yescharacteristic
641Q8—24no—
642Q8—22no—
643Q8—24no—
644Q8—22no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—41no—
651Q8—42no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—41no—
660D4—41no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4C2×C7×C22⋊C411yescharacteristic
680C2×C4C2×C7×C22⋊C411yescharacteristic
681C2×C4C2×C7×C22⋊C411yescharacteristic
682C2×C4C4×C7×D411yescharacteristic
683C2×C4C4×C7×D411yescharacteristic
684C2×C4C4×C7×D411yescharacteristic
685C2×C4C7×#12011yescharacteristic
686C2×C4C7×#12011yescharacteristic
687C2×C4C7×#12011yescharacteristic
688C2×C4C7×#12011yescharacteristic
689C2×C4C7×#12011yescharacteristic
690C2×C4C7×#12011yescharacteristic
691C2×C4C7×#12011yescharacteristic
692C2×C4C7×#12011yescharacteristic
693C2×C4C7×#12111yescharacteristic
694C2×C4C7×#12111yescharacteristic
695C2×C4C7×#12111yescharacteristic
696C2×C4C7×#12111yescharacteristic
697C2×C4C7×#12111yescharacteristic
698C2×C4C7×#12111yescharacteristic
699C2×C4C7×#12111yescharacteristic
700C2×C4C7×#12111yescharacteristic
701C2×C4C7×#12111yescharacteristic
702C2×C4C7×#12311yescharacteristic
703C2×C4C7×#12311yescharacteristic
704C2×C4C7×#12411yescharacteristic
705C2×C4C7×#12711yescharacteristic
706C2×C4C7×#12711yescharacteristic
707C8—24no—
708C8—42no—
709C8—42no—
710C8—42no—
711C7#1102111yescharacteristic, direct product factor, Sylow
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—44no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—82no—
725C22C7×#38611yescharacteristic
726C22C7×#38611yescharacteristic
727C22C7×#39011yescharacteristic
728C22C7×#39211yescharacteristic
729C22C7×#39411yescharacteristic
730C22C7×#39411yescharacteristic
731C22C7×#39411yescharacteristic
732C22C7×#47112yes—
733C22C7×#47312yes—
734C4—42no—
735C4—44no—
736C4—82no—
737C4C7×#37911yescharacteristic
738C4C7×#38611yescharacteristic
739C4C7×#38611yescharacteristic
740C4C7×#39011yescharacteristic
741C4C7×#39211yescharacteristic
742C4C7×#39211yescharacteristic
743C4C7×#39211yescharacteristic
744C4C7×#39411yescharacteristic
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—82no—
750C2C7×#143811yescharacteristic
751C2C7×#190812yes—
752C2C7×#201911yescharacteristic
753C2C7×#202011yescharacteristic
754C2C7×#205212yes—
subgroupG/H
center, socleC23×C7#121
commutatorC22×C4C22×C4×C7
Frattini, cosocleC23×C4C23×C7
prime radicalC22×C7×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C22×C7×#103C2semidirect
4. C22×C7×#101C2semidirect
6. C2×C7×#343C2semidirect
7. C2×C7×#341C2semidirect
15. C2×C7×#137C4semidirect
38. #11021C7direct (N × H)
123. C22×#103C2×C7semidirect
124. C22×#101C2×C7semidirect
126. C2×#343C2×C7semidirect
127. C2×#341C2×C7semidirect
265. C2×#137C4×C7semidirect
711. C7#11021direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1372
C2×C7×#4172
C22×C7×#1032
C22×C7×#1012
C2×C7×#4082
C2×C7×#3432
C2×C7×#3412
#110217